JP2009186244A - Tilt angle estimation system, relative angle estimation system, and angular velocity estimation system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a system capable of estimating the attitude or the velocity state of a rotary object, without including integration operation in data processing, or by including minimally an integration operation processing step. <P>SOLUTION: This tilt angle estimation system, which is a system having one rotation center point, for estimating a tilt angle of an object rotating and simultaneously tilting on one plane around the rotation center point, includes at least two acceleration sensors mounted on the object, and an operation processing unit for receiving each output from at least two acceleration sensors and calculating the tilt angle of the object based on the output, and has characteristics wherein at least two acceleration sensors are aligned on one straight line and a line connecting at least two acceleration sensors passes the rotation center point. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a system for estimating the posture or speed state of a rotating object. More specifically, the present invention relates to a tilt angle estimation system, a relative angle estimation system, and an angular velocity estimation system that can be constructed at low cost and can calculate an estimated value that does not include an integration error or minimizes an integration error.

With the arrival of an aging society, the demand for a system for evaluating human physical movement is increasing. For example, when an elderly hospitalized for a long time is discharged, it is very important to determine whether the muscle strength of the legs and hips has been restored to a level that does not interfere with daily life. There is also a problem of being discharged before the hospital, and then hurting other body parts and being hospitalized again.
Systems other than medical-related fields are used to evaluate human body movements. A typical example is the field of sports science. Many attempts have been made to improve performance in the sports field by evaluating and analyzing the physical movement characteristics of athletes and accumulating the data.
As an application example of the motion evaluation system to a person other than a human, an application to a robot, particularly a humanoid robot can be given. It is common to measure the robot's tilt angle while walking on stairs or hills, and feed back this tilt angle to the robot's control unit to control the robot's posture so that the robot does not fall over. Has already been done.

In recent years, in the field of development of such a motion evaluation system, conventionally, when analyzing the motion of a measurement object, a method of attaching a large number of colored markers and imaging with a plurality of cameras has been employed (for example, , See Patent Document 1).
As a major drawback of the technique for analyzing the motion of the measurement object based on the image data obtained by a plurality of cameras, it can be mentioned that it is subject to a place restriction and requires a large amount of money for system construction. For example, as described in Patent Document 1, such a system performs data analysis based on a color difference, but has a problem that it is easily affected by ambient light quantity that changes from moment to moment, and is often strong. A method of applying light to a measurement object is employed. Therefore, it is very difficult to acquire operation data in a wide space or outdoor space. Further, it requires a plurality of cameras and an image analysis system, and it is impossible to construct the system at a low cost.

In recent years, a technique that enables analysis of the motion of a measurement object, regardless of image analysis, has been developed. A system that does not use this image analysis is generally constructed by combining a gyro sensor, an acceleration sensor, and a geomagnetic sensor (see, for example, Patent Document 2). Most of these systems perform nonlinear integration on the three-axis angular velocities obtained from the gyro sensor to calculate the angle, and output from the accelerometer and geomagnetic sensor to the calculated angle. Is used for correction.
Since this method using a plurality of types of sensors does not use an expensive imaging device or image analysis system, the system can be constructed at a lower cost than the above-described technique. Moreover, it is excellent in that the problem of being affected by fluctuations in the amount of ambient light can be solved.

JP-A-6-50983 JP 2007-75967 A

Although the above-described technique using a plurality of types of sensors has many advantages over the conventional method using an image analysis apparatus, there are some problems.
First, errors are accumulated by applying nonlinear integration to angular velocity data obtained from the gyro sensor. In particular, if there is a drift in the angular velocity, the accumulated error increases. Due to the accumulation of this error, it is necessary to perform a correction process by an output from another sensor (acceleration sensor or geomagnetic sensor). As a result, it is inevitable to use a plurality of types of sensors, and accordingly, the complexity of data processing increases. In addition, the use of multiple types of sensors and complicated data processing steps cause deterioration in accuracy of the estimated value of the operation of the measurement object (the inclination angle of the posture of the measurement object). In order to obtain a highly accurate estimated value, it is necessary to take measures such as an increase in the number of divisions in the integration process, and as a result, the use of an expensive data processing system is inevitable.
Further, the gyro sensor is inexpensive when compared with an image processing system, but is expensive when compared with a general acceleration sensor. In addition, when the correction process is performed by the geomagnetic sensor, there is a place restriction on the use of the tilt angle estimation system because of the vulnerability of the geomagnetic sensor to the disturbance factor.

  The present invention has been made in view of the above circumstances, and does not include integration calculation in data processing, or performs integration calculation processing steps at a minimum, and determines the posture, speed, or acceleration state of a rotating object. An object is to provide a system for estimation.

The invention according to claim 1 is a system for estimating an inclination angle of an object that has one rotation center point and is inclined while rotating in one plane around the rotation center point, and is attached to the object. And at least two acceleration sensors, and an arithmetic processing unit that receives outputs from the at least two acceleration sensors and calculates an inclination angle of the object based on the outputs, and the at least two acceleration sensors are on a line. The tilt angle estimation system is characterized in that a line connecting the at least two acceleration sensors passes through the rotation center point while being aligned.
The invention according to claim 2 is the tilt angle estimation system according to claim 1, wherein the distances of at least two acceleration sensors from the rotation center point are different from each other.
The invention according to claim 3 is the tilt angle estimation system according to claim 2, characterized in that the position of one of the at least two acceleration sensors coincides with the rotation center point.

According to a fourth aspect of the present invention, a first reference axis that defines the one plane and passes through the rotation center point is defined in the arithmetic processing unit, and one acceleration of the at least two acceleration sensors is defined. A sensor and another acceleration sensor each output a first acceleration in a direction along a line connecting the at least two acceleration sensors, and the arithmetic processing unit calculates a distance from the rotation center point to the one acceleration sensor. The step of integrating the output values from the other acceleration sensors to calculate a first integrated value, and the distance from the rotation center point to the other acceleration sensor as the output value from the one acceleration sensor And calculating the second integrated value, and based on a difference value between the first integrated value and the second integrated value, the first reference axis and the at least two acceleration sensors. A tilt angle estimation system according to claim 1, wherein performing the step of calculating the sine function of the included angle between the line connecting.
According to a fifth aspect of the present invention, in the arithmetic processing unit, a first reference axis that defines the one plane and passes through the rotation center point is defined, and one acceleration of the at least two acceleration sensors is defined. Each of the sensor and the other acceleration sensor outputs a second acceleration in a direction orthogonal to a line connecting the at least two acceleration sensors and parallel to the moving plane of the object, and the arithmetic processing unit includes: A step of integrating a distance from the rotation center point to the one acceleration sensor with an output value from the other acceleration sensor to calculate a third integrated value; and a step from the rotation center point to the other acceleration sensor. Based on the step of calculating the fourth integrated value by integrating the distance with the output value from the one acceleration sensor, and the difference value between the third integrated value and the fourth integrated value, Wherein the reference axis is a tilt angle estimation system according to claim 1, wherein performing the step of calculating the cosine function values of included angle between at least two lines connecting the acceleration sensor.
According to a sixth aspect of the present invention, a first reference axis that defines the one plane and passes through the rotation center point is defined in the arithmetic processing unit, and one acceleration of the at least two acceleration sensors is defined. A sensor has a first acceleration in a direction along a line connecting the at least two acceleration sensors and a first acceleration in a direction parallel to the moving plane of the object and orthogonal to the line connecting the at least two acceleration sensors. 2, the other acceleration sensor is orthogonal to the first acceleration in the direction along the line connecting the at least two acceleration sensors and the line connecting the at least two acceleration sensors, and A third acceleration in a direction parallel to the moving plane is orthogonal to a line connecting the at least two acceleration sensors and is on the moving plane of the object. The at least two acceleration sensors output the fourth acceleration in a parallel direction, and the arithmetic processing unit outputs the distance from the rotation center point to the one acceleration sensor by the other acceleration sensor. And calculating the first integrated value and outputting the distance from the rotation center point to the other acceleration sensor by the one acceleration sensor. A step of integrating the acceleration output values in the direction along the line connecting the at least two acceleration sensors and calculating a second integrated value; and a distance from the rotation center point to the one acceleration sensor. Adding to an output value of acceleration in a direction orthogonal to a line connecting the at least two acceleration sensors output by the other acceleration sensor, and calculating a third integrated value; A distance from the rotation center point to the other acceleration sensor is added to an acceleration output value in a direction orthogonal to a line connecting the at least two acceleration sensors output by the one acceleration sensor; And a sine of an angle between the first reference axis and a line connecting the at least two acceleration sensors based on a difference value between the first integrated value and the second integrated value A cosine function of an angle between a step of calculating a function value and a line connecting the first reference axis and the at least two acceleration sensors based on a difference value between the third integrated value and the fourth integrated value 2. The tilt angle estimation system according to claim 1, wherein a step of calculating a value is executed.

The invention according to claim 7 is characterized in that the arithmetic processing unit has a first upper limit value incremented by a predetermined angle with respect to an odd multiple of π / 2 and a predetermined angle with respect to the odd multiple of π / 2. A first threshold value range defined between the first lower limit values decremented by the first threshold value is recognized, and the value of the included angle obtained from the sine function value and the cosine function value is a range of the first threshold value range. The tilt angle estimation system according to claim 6, wherein an integrated value or a divided value of the sine function and the cosine function is used for the calculation of the included angle.
The invention according to claim 8 is characterized in that the arithmetic processing unit has a first upper limit value incremented by a predetermined angle with respect to an odd multiple of π / 2 and a predetermined angle with respect to the odd multiple of π / 2. A first threshold value range defined between the first lower limit values decremented by the first threshold value is recognized, and the value of the included angle obtained from the sine function value and the cosine function value is a range of the first threshold value range. The tilt angle estimation system according to claim 6, wherein the arithmetic processing unit outputs a included angle calculated based on the cosine function value.
According to a ninth aspect of the present invention, the arithmetic processing unit has a second upper limit value that is incremented by a predetermined angle with respect to a multiple value of π, and a second value that is decremented by a predetermined angle with respect to the multiple value of π. Recognizing a second threshold region defined between the lower limit value and the sine function value and the cosine function value obtained from the cosine function value are within the range of the second threshold region, The tilt angle estimation system according to claim 6, wherein an integrated value or a divided value of the sine function and the cosine function is used for calculating the included angle.
According to a tenth aspect of the present invention, the arithmetic processing unit includes a second upper limit value that is incremented by a predetermined angle with respect to a multiple value of π, and a second value that is decremented by a predetermined angle with respect to the multiple value of π. Recognizing a second threshold region defined between the lower limit values of the sine function value and the squeezing function value obtained from the sine function value and the cosine function value is within the range of the second threshold region, The tilt angle estimation system according to claim 6, wherein the arithmetic processing unit outputs the included angle calculated based on the sine function value.

The invention according to claim 11 is the tilt angle estimation system according to claim 1, wherein the rotation center point moves linearly within the one plane.
A twelfth aspect of the present invention is the tilt angle estimation system according to the eleventh aspect, wherein the linear moving speed of the rotation center point changes with time.

According to a thirteenth aspect of the present invention, in the arithmetic processing unit, a first reference axis that defines the one plane, passes through the rotation center point, and is parallel to a gravitational acceleration vector, and the first reference axis A second reference axis that is orthogonal to each other, the rotation center point linearly moves within the one plane, and the linear movement speed of the rotation center point is determined by the component along the first reference axis and the Defined by the component along the second reference axis, and the linear movement speed of the rotation center point changes with time, and the amount of time change of the component along the first reference axis and the second reference axis 13. The tilt angle estimation system according to claim 12, wherein a component along the line is known.
The invention according to claim 14 is characterized in that, among the at least two acceleration sensors, one acceleration sensor and another acceleration sensor each output a first acceleration in a direction along a line connecting the at least two acceleration sensors, The arithmetic processing unit integrating a distance from the rotation center point to the one acceleration sensor with an output value from the other acceleration sensor to calculate a first integrated value; and the rotation center point The distance from the other acceleration sensor to the output value from the one acceleration sensor to calculate a second integrated value, and the first integrated value and the second integrated value 14. The tilt angle estimation system according to claim 13, wherein a step of calculating an included angle between the first reference axis and a line connecting the at least two acceleration sensors is performed based on the difference value.
According to a fifteenth aspect of the present invention, of the at least two acceleration sensors, one acceleration sensor and another acceleration sensor are orthogonal to a line connecting the at least two acceleration sensors, and are on the moving plane of the object. A second acceleration in a direction parallel to the first acceleration sensor, and the arithmetic processing unit integrates a distance from the rotation center point to the first acceleration sensor with respect to an output value from the other acceleration sensor; Calculating an integrated value of 3, integrating a distance from the rotation center point to the other acceleration sensor with respect to an output value from the one acceleration sensor, and calculating a fourth integrated value; Performing a step of calculating an included angle between the first reference axis and a line connecting the at least two acceleration sensors based on a difference value between the third integrated value and the fourth integrated value; The inclination angle estimation system according to claim 13, wherein that.

  According to a sixteenth aspect of the present invention, the rotation center point linearly moves in a direction orthogonal to the direction of the gravitational acceleration vector within the one plane, and the movement acceleration of the rotation center point is an unknown number. The arithmetic processing unit recognizes the movement locus of the rotation center point as a first reference axis, and one acceleration sensor of the at least two acceleration sensors connects the at least two acceleration sensors. And a second acceleration in a direction perpendicular to a line connecting the at least two acceleration sensors, and another acceleration sensor is connected to a line connecting the at least two acceleration sensors. A first acceleration in a direction along the line and a direction perpendicular to the line connecting the at least two acceleration sensors and parallel to the plane of movement of the object 3 and a fourth acceleration in a direction orthogonal to the line connecting the at least two acceleration sensors and parallel to the moving plane of the object, and the arithmetic processing unit outputs the rotation center point The distance from the first acceleration sensor to the one acceleration sensor is integrated with the acceleration output value in the direction along the line connecting the at least two acceleration sensors output by the other acceleration sensor, and a first integrated value is calculated. And integrating the distance from the rotation center point to the other acceleration sensor with respect to the output value of the acceleration in the direction along the line connecting the at least two acceleration sensors output by the one acceleration sensor. Calculating a second integrated value; and a distance from the rotation center point to the one acceleration sensor, the at least one output from the other acceleration sensor Calculating a third integrated value by integrating the acceleration output values in a direction perpendicular to a line connecting the two acceleration sensors and parallel to the moving plane of the object, and from the rotation center point to the other The distance to the acceleration sensor is integrated with the acceleration output value in a direction orthogonal to the line connecting the at least two acceleration sensors output by the one acceleration sensor and parallel to the plane of movement of the object. Calculating a fourth integrated value; a first difference value obtained by calculating a difference between the first integrated value and the second integrated value; the third integrated value; and the fourth integrated value. The step of removing an acceleration component of linear movement of the rotation center point along the first reference axis is performed using a second difference value obtained by calculating a difference between the integrated values of The tilt angle estimation system according to item 1 It is.

According to a seventeenth aspect of the present invention, there is provided one acceleration sensor for the acceleration component in a direction parallel to a line connecting the at least two acceleration sensors among the acceleration components output by the at least two acceleration sensors. And the difference between the output value of the other acceleration sensor and the output value of the other acceleration sensor, and the distance between one of the at least two acceleration sensors and the rotation center point, the other acceleration sensor, and the rotation. 3. The tilt angle estimation system according to claim 2, wherein the angular velocity of the object is calculated by calculating a difference in distance from a center point and dividing the difference in output value by the difference in distance. It is.
According to an eighteenth aspect of the present invention, the arithmetic processing unit is orthogonal to a line connecting the at least two acceleration sensors out of the acceleration components output by the at least two acceleration sensors and is parallel to the moving plane of the object. For an acceleration component in a certain direction, the difference between the output value of one acceleration sensor and the output value of another acceleration sensor is calculated, and one of the at least two acceleration sensors and the rotation center point Calculating the angular acceleration of the object by calculating the difference in distance between the other acceleration sensor and the rotation center point, and dividing the difference in output value by the difference in distance. The tilt angle estimation system according to claim 2, wherein the tilt angle estimation system is a tilt angle estimation system.

According to a nineteenth aspect of the present invention, in a three-dimensional space defined by three orthogonal coordinate axes, a rotational motion is performed around two coordinate axes of the three orthogonal coordinate axes, with an intersection of the orthogonal coordinate axes as a rotation center point, and an inclined posture. An inclination angle of an object that takes the following equation: an at least two acceleration sensors attached to the object, outputs from the at least two acceleration sensors, and an inclination angle of the object based on the outputs An inclination angle estimation system comprising an arithmetic processing unit for calculating, wherein the at least two acceleration sensors are aligned on a line, and a line connecting the at least two acceleration sensors passes through the rotation center point. is there.
The invention according to claim 20 is characterized in that the at least two acceleration sensors have a first acceleration component parallel to a line connecting the two acceleration sensors, a line connecting the two acceleration sensors, and a moving plane of the object. 21. A second acceleration component in a direction orthogonal to the first acceleration component, and a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component are output. It is an inclination angle estimation system of description.

  According to a twenty-first aspect of the present invention, the arithmetic processing unit is configured such that, with respect to the three output values of acceleration output from one of the at least two acceleration sensors, another acceleration sensor and the rotation center point. A first integrating step for obtaining three integrated values, and for the three output values of acceleration output by the other acceleration sensors, the one acceleration sensor and the rotation center point For each of the second integrated step for obtaining three integrated values and the three integrated values obtained from the first integrating step, the corresponding values obtained from the second integrating step. Performing a difference step of calculating a difference using an integrated value of acceleration components in a direction, and calculating a tilt angle component with respect to an axis serving as a center of the rotational motion of the object based on the difference value obtained from the difference step. To do The inclination angle estimation system according to claim 20, wherein.

The invention according to claim 23 is the tilt angle estimation system according to claim 19, wherein the object further rotates about the line connecting the at least two acceleration sensors.
The invention according to claim 24 is characterized in that the three orthogonal coordinate axes are a first coordinate axis in a direction parallel to the gravity vector, a second coordinate axis in a direction orthogonal to the first coordinate axis, and the first coordinate axis. 1 coordinate axis and a third coordinate axis orthogonal to the second coordinate axis, and the arithmetic processing unit sets the three output values of acceleration output from one acceleration sensor among the at least two acceleration sensors. On the other hand, the distance between the other acceleration sensor and the rotation center point is integrated to obtain three integrated values, and the three output values of the acceleration output from the other acceleration sensor. A second integration step of integrating the distance between the one acceleration sensor and the rotation center point to obtain three integrated values, and an acceleration component in a direction parallel to a line connecting the at least two acceleration sensors Said The difference between the integration value from the integration step and the integration value from the second integration step, the distance between the one acceleration sensor and the rotation center point, and the other acceleration sensor and the rotation center point 24. The tilt angle estimation according to claim 23, wherein a sine function value of a tilt angle component due to rotation about the second coordinate axis or the third coordinate axis is calculated based on a difference between the distance and the distance. System.
According to a twenty-fifth aspect of the invention, the arithmetic processing unit is configured to calculate the second calculated value based on a sine function value of a tilt angle component generated by rotation about the calculated second coordinate axis or the third coordinate axis. The cosine function value of the tilt angle component due to rotation about the coordinate axis or the third coordinate axis is calculated, and the calculated cosine function value is parallel to the axis orthogonal to the rotational movement plane of the object. The difference between the integrated value from the first integrating step and the integrated value from the second integrating step, and the distance between the one acceleration sensor and the rotation center point, and the one A cosine function value of an inclination angle related to a rotation operation about a line connecting the at least two acceleration sensors is calculated based on a difference between a distance between the acceleration sensor and the rotation center point. The tilt according to claim 24. It is the angle estimation system.
According to a twenty-sixth aspect of the present invention, the arithmetic processing unit is configured to calculate the second calculated value based on a sine function value of a tilt angle component caused by rotation about the calculated second coordinate axis or the third coordinate axis. The cosine function value of the tilt angle component due to rotation about the coordinate axis or the third coordinate axis is calculated, the calculated cosine function value, the axis orthogonal to the rotational movement plane of the object, and the at least 2 An integrated value from the first integrating step and an integrated value from the second integrating step with respect to an acceleration component in a direction parallel to an axis perpendicular to an axis parallel to a line connecting two acceleration sensors A line connecting the at least two acceleration sensors based on a difference and a difference between the distance between the one acceleration sensor and the rotation center point and a distance between the other acceleration sensor and the rotation center point. Axis Calculating a sine function value of the inclination angle of the rotation is the tilt angle estimation system according to claim 24, wherein.
According to a twenty-seventh aspect of the present invention, the arithmetic processing unit further includes the output value of the one acceleration sensor and the other acceleration relating to an acceleration component in a direction parallel to an axis orthogonal to the rotational movement plane of the object. The difference between the sensor output value and the acceleration in the direction parallel to the axis orthogonal to the axis perpendicular to the rotational movement plane of the object and the axis parallel to the line connecting the at least two acceleration sensors. A difference between an output value of the one acceleration sensor and an output value of the other acceleration sensor regarding a component, a distance between the rotation center point and the one acceleration sensor, a distance between the rotation center point and the other acceleration sensor, Based on the difference between the angular acceleration about the direction parallel to the axis orthogonal to the rotational movement plane of the object, the axis orthogonal to the rotational movement plane of the object, and the at least 2 The inclination angle estimation system according to claim 25 or 26, wherein that of the line connecting the acceleration sensor between calculated direction parallel angular acceleration with respect to the axis perpendicular to the parallel axes.
The invention according to claim 28 is characterized in that the arithmetic processing unit further integrates and calculates an angular acceleration with a direction parallel to an axis orthogonal to the rotational movement plane of the object as the second coordinate axis. 28. The tilt angle estimation system according to claim 27, wherein a tilt angle within a plane defined by the third coordinate axis is calculated.

According to a twenty-ninth aspect of the present invention, there is provided an object having one rotation center point and rotating about the one rotation center point, and connected to the one object at the one rotation center point and the one object. And a first acceleration sensor group consisting of at least two acceleration sensors attached to the one object. A second acceleration sensor group including at least two acceleration sensors attached to the other object, and outputs from the acceleration sensors of the first and second acceleration sensor groups, and based on the outputs An arithmetic processing unit for calculating an inclination angle of the object, wherein the at least two acceleration sensors of the first acceleration sensor group are aligned on a line on the one object; The at least two acceleration sensors of the second acceleration sensor group are aligned on a line on the one object, and a line connecting the at least two acceleration sensors constituting the first acceleration sensor group and the second acceleration sensor group. The relative angle estimation system is characterized in that a line connecting the at least two acceleration sensors constituting the acceleration sensor group passes through the one rotation center point.
The invention according to claim 30 is characterized in that the at least two acceleration sensors of the first acceleration sensor group include a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors, and the object. Outputting an acceleration related to a second acceleration component in a direction orthogonal to the rotational movement plane, and a first acceleration component and a third acceleration component in a direction orthogonal to the second acceleration component. 30. The relative angle estimation system according to claim 29.
The invention according to claim 31 is characterized in that the at least two acceleration sensors of the second acceleration sensor group include a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors, and the object. Outputting an acceleration related to a second acceleration component in a direction orthogonal to the rotational movement plane, and a first acceleration component and a third acceleration component in a direction orthogonal to the second acceleration component. 30. The relative angle estimation system according to claim 29.
According to a thirty-second aspect of the present invention, the arithmetic processing unit calculates a first acceleration vector at a rotation center point of the one object based on an output from an acceleration sensor constituting the first acceleration sensor group. The relative angle estimation system according to claim 30, wherein:
According to a thirty-third aspect of the present invention, the arithmetic processing unit calculates a second acceleration vector at a rotation center point of the other object based on an output from an acceleration sensor constituting the second acceleration sensor group. 32. The relative angle estimation system according to claim 31, wherein:
The invention according to claim 34 is characterized in that the at least two acceleration sensors of the first acceleration sensor group include a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors, and the object. An output relating to an acceleration composed of a second acceleration component in a direction perpendicular to the rotational movement plane, a first acceleration component and a third acceleration component in a direction orthogonal to the second acceleration component; The at least two acceleration sensors of the second acceleration sensor group are orthogonal to a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors and a rotational movement plane of the object. A second acceleration component in the direction, and an output relating to the acceleration composed of the first acceleration component and the third acceleration component in the direction orthogonal to the second acceleration component, and The processing unit calculates a first acceleration vector at the rotation center point of the one object based on an output from an acceleration sensor that constitutes the first acceleration sensor group, and constitutes the second acceleration sensor group. Based on the output from the acceleration sensor, a second acceleration vector at the rotation center point of the other object is calculated, and the one object is calculated from the difference between the first acceleration vector and the second acceleration vector. 30. The relative angle estimation system according to claim 29, wherein a relative angle between the first object and the other object is estimated.

  The invention according to claim 35 is the following: one acceleration sensor arranged at the rotation center point of the rotating object, three acceleration sensors arranged apart from the one acceleration sensor, and the one acceleration sensor An arithmetic processing unit for receiving outputs from the three acceleration sensors, lines connecting the one acceleration sensor and the three acceleration sensors are orthogonal to each other, and the one acceleration sensor is connected to the one acceleration sensor. An acceleration component in a direction parallel to a line connecting the three acceleration sensors is output, and each of the three acceleration sensors outputs an acceleration component in a direction parallel to a straight line toward the one acceleration sensor. At least one of the three acceleration sensors outputs an acceleration component in a direction parallel to a line connecting the other acceleration sensor and the one acceleration sensor. Based on the relationship between the output of each of the one acceleration sensor the three acceleration sensors, angular velocity estimation system for estimating the angular velocity of rotation of the object.

  The invention according to claim 36 is a system for estimating an inclination angle of an object having one rotation center point and tilting while rotating in one plane around the rotation center point, and is attached to the object. And at least one acceleration sensor and an arithmetic processing unit that receives an output from the at least one acceleration sensor and calculates an inclination angle of the object based on the output. One acceleration of the at least one acceleration sensor The tilt angle estimation system is characterized in that a sensor is arranged on the rotation center point.

According to the first and second aspects of the invention, since the sensor to be used is only the acceleration sensor, it is possible to construct a tilt angle estimation system simply and inexpensively. Therefore, the estimation system can be easily set as compared with the prior art.
According to the third aspect of the present invention, one of the parameters used for data processing can be set to “0”, and the arithmetic processing load of the arithmetic processing unit can be reduced.

According to the fourth to sixth aspects of the present invention, it is possible to estimate the tilt angle without performing an integration operation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.
According to the eighth to tenth aspects of the present invention, it is possible to select a function used for calculating an estimated value to be output, in accordance with the calculated estimated value of the tilt angle.

According to the eleventh aspect of the present invention, it is possible to execute the estimation of the tilt angle for a linearly moving object.
According to the twelfth aspect of the present invention, it is possible to estimate the tilt angle for an object that moves linearly.
According to the thirteenth to fifteenth aspects of the present invention, when the moving speed of the object that moves linearly is known, the inclination angle can be estimated without performing the integral calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.
According to the sixteenth aspect of the present invention, when the moving speed of the object moving in the horizontal direction is unknown, the inclination angle can be estimated without performing the integration calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.

According to the seventeenth aspect of the present invention, it is possible to execute the angular velocity related to the inclined rotational motion of the object without performing the integral calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.
According to the eighteenth aspect of the present invention, the angular acceleration related to the tilting and rotating motion of the object can be executed without performing the integral calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.

According to the nineteenth aspect of the present invention, it is possible to estimate the tilt angle of an object that rotates and tilts in a three-dimensional space, and since only the acceleration sensor is used, it is possible to construct a tilt angle estimation system simply and inexpensively. Become. Therefore, the estimation system can be easily set as compared with the prior art.
According to the twentieth and twenty-first aspects of the present invention, it is possible to estimate the tilt angle without performing an integration operation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.
According to the twenty-second aspect of the present invention, it is possible to execute the angular velocity related to the inclined rotational motion of the object without performing the integral calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.

The invention according to claim 23 makes it possible to estimate a tilt angle with respect to a measurement object that rotates and tilts in a three-dimensional space and rotates around its axis.
According to the twenty-fourth to twenty-seventh aspects of the present invention, it is possible to execute the angular velocity related to the inclined rotational motion of the object without performing the integral calculation. Therefore, unlike the conventional technique, an estimated value including an integration error is not output, and high accuracy can be ensured.
According to the twenty-eighth aspect of the present invention, it is possible to estimate all three directional components of the tilting motion of the measurement object with a minimum integral calculation. Therefore, as in the prior art, the integration error can be minimized and high accuracy can be ensured. Moreover, since the estimated value in the rotational direction other than the direction requiring the integral calculation does not include an integration error, high accuracy can be maintained.

According to the invention described in claims 29 to 34, it is possible to estimate the relative angle between two objects connected at the rotation center point, and this calculation of the relative angle does not require an integral operation process. The estimated value does not include an integration error, and a highly accurate estimated value can be output.
According to the thirty-fifth aspect of the present invention, it is possible to estimate the angular velocity of the rotating object without requiring an integral calculation process. Therefore, the estimated value does not include an integration error, and a highly accurate estimated value can be output.
According to the thirty-sixth aspect of the present invention, since only one acceleration sensor is used, it is possible to construct a tilt angle estimation system simply and inexpensively. Therefore, the estimation system can be easily set as compared with the prior art.

Hereinafter, an inclination angle estimation system according to the present invention will be described with reference to the drawings.
FIG. 1 is a schematic diagram of a tilt angle estimation system according to the present invention.
The tilt angle estimation system (1) includes a plurality of acceleration sensors (2) attached to a measurement object (P) and a data arithmetic processing unit (computer) (3) capable of data communication with the acceleration sensor (2). .
In the example shown in FIG. 1, the measurement object (P) is rotatably supported at one end thereof. The measurement object (P) rotates in one direction with this support point as the rotation center point (R) and tilts its posture. Therefore, in the example shown in FIG. 1, the measurement object (P) rotates in one plane.
Although there is no particular limitation on the measurement object (P) to which the acceleration sensor (2) is attached, it is preferable that the measurement object (P) has a rigidity that does not cause deformation due to an inertial force generated during the rotation and tilting operation of the measurement object. This is because the deformation of the measurement object (P) at the time of data acquisition for tilt angle estimation is directly connected to the error of the estimated value. Therefore, the measurement object (P) targeted by the present invention includes not only a perfect rigid body but also those that can be deformed to such an extent that an error allowed by the purpose of tilt angle estimation is generated.

In FIG. 1, two acceleration sensors (2) are shown on the measurement object (P). However, the number of acceleration sensors is not limited to two, and may be three or more. Good.
As is clear from FIG. 1, the rotation center point (R) of the measurement object (P) is located on the extended line connecting the two acceleration sensors (2). In the present specification or claims, the term “the line connecting the acceleration sensors (2) passes through the rotation center point (R)” is used, but this term is not necessarily the same between the acceleration sensors (2). This does not mean that the line connecting the two accurately passes through the rotation center point (R), but also means that the line connecting the acceleration sensors (2) passes near the rotation center point (R). The distance between the line connecting the acceleration sensors (2) and the rotation center point (R) is directly linked to the error of the estimated value obtained from the tilt angle estimation system (1). If the distance between the line connecting the acceleration sensors (2) and the rotation center point (R) to the extent that produces an error within the allowable error range, it is understood that they belong to the technical scope of the present invention. Should.

The distance from the rotation center point (R) to each acceleration sensor (2) is input in advance to the data arithmetic processing unit (3).
The data arithmetic processing unit (3) receives the output value (acceleration data) from the acceleration sensor (2), and inputs the input value (rotation center point (R) to each acceleration sensor (2) to the data arithmetic processing unit (3). )) And the output value (acceleration data) from the acceleration sensor (2), the inclination angle of the measurement object (P) is calculated.

FIG. 2 is a conceptual diagram of the arithmetic processing of the data arithmetic processing unit (3).
In FIG. 2, two coordinate systems are shown. In this specification, one coordinate system is referred to as a global coordinate system, and the other coordinate system is referred to as an instantaneous stationary coordinate system.
In the global coordinate system, a direction parallel to the gravitational acceleration vector is defined as the Z axis. Further, in the plane in which the measurement object (P) shown in FIG. 1 rotates, the direction orthogonal to the Z axis is taken as the X axis. Here, the global coordinate system is defined so that the intersection of the X axis and the Z axis coincides with the rotation center point (R) of the measurement object (P).
In the instantaneous stationary coordinate system, a line connecting the two acceleration sensors (2) is defined as the x axis. In addition, in the plane in which the measurement object (P) shown in FIG. Here, the instantaneous stationary coordinate system is defined so that the intersection of the x axis and the z axis coincides with the rotation center point (R) of the measurement object (P).
In the example shown in FIG. 2, the included angle between the X axis of the global coordinate system and the x axis of the instantaneous stationary coordinate system is indicated by the symbol “α”.
As is apparent from the above description and the definition of the coordinate system, FIG. 2 shows the position where the measurement object (P) has its axis (the line connecting the acceleration sensors (2)) placed on the X axis of the overall coordinate system. Represents the state of the measurement object (P) at the moment of rotational movement by an angle α.
Hereinafter, an arithmetic processing step for calculating the inclination angle α of the measurement object (P) will be described.

Each of the two acceleration sensors (2) attached to the measurement object (P) has acceleration data (represented by a calculation symbol “a _x or b _x ”) in a direction parallel to the instantaneous stationary coordinate system x-axis, Acceleration data (expressed by an operation symbol “a _z or b _z ”) in a direction parallel to the instantaneous stationary coordinate system z-axis is output.
The acceleration component parallel to the x axis of the instantaneous stationary coordinate system generated by the rotation and tilting operation of the measurement object (P) can be obtained from Equation 1 below. Further, the acceleration component parallel to the z axis of the instantaneous stationary coordinate system generated by the rotation and tilting operation of the measurement object (P) can be obtained from Equation 2 below.
In Equation 1, “r” means the distance from the rotation center point (R) to the acceleration sensor (2). Further, in Equations 1 and 2, the angular velocity component and the angular acceleration component of the rotational motion of the measurement object (P) are expressed as differential values of the calculation symbol “θ”.

Here, the acceleration sensor (2) attached to the side away from the rotation center point (R) is denoted by reference numeral “2A”, and the acceleration sensor (2) attached to the side closer to the rotation center point (R) is indicated. , Represented by the symbol “2B”. Further, it is assumed that the value “r _A ” is input to the arithmetic processing unit (3) as the distance between the rotation center point (R) and the acceleration sensor (2A), and the rotation center point (R) and the acceleration sensor ( It is assumed that the value “r _B ” is input as the distance of 2B).
Since the output of the acceleration sensor (2) is affected by the inertial force, the relationship between the output of the acceleration sensor, the acceleration component resulting from the rotation operation of the measurement object (P), and the gravitational acceleration is expressed by the following Equations 3 to 3. It can be expressed by Equation 6. Equations 3 and 4 are for the acceleration sensor (2A), and output acceleration data in a direction parallel to the instantaneous stationary coordinate system x-axis is indicated by an operation symbol “a _x ”, and the instantaneous stationary coordinate system z-axis is represented by Output acceleration data in the parallel direction is indicated by an operation symbol “a _z ”. Equations 5 and 6 are for the acceleration sensor (2B), and output acceleration data in a direction parallel to the instantaneous stationary coordinate system x-axis is indicated by an operation symbol “b _x ”. Output acceleration data is indicated by a calculation symbol “b _z ”.

From the relationship between Equation 3 and Equation 5, the angle α of the measurement object can be obtained by the following procedure.
(1) The distance from the rotation center point (R) to the acceleration sensor (2B) is integrated with respect to the output value of the acceleration sensor (2A).
(2) The distance from the rotation center point (R) to the acceleration sensor (2A) is added to the output value of the acceleration sensor (2B).
(3) The difference between the integrated values obtained from the procedures (1) and (2) is taken, and the angular velocity component of the measurement object (P) is removed.
An arithmetic expression for the angle α obtained through the above procedure is shown in the following Expression 7.

From the relationship between Equation 4 and Equation 6, the angle α of the measurement object can be obtained by the following procedure.
(1) The distance from the rotation center point (R) to the acceleration sensor (2B) is integrated with respect to the output value of the acceleration sensor (2A).
(2) The distance from the rotation center point (R) to the acceleration sensor (2A) is added to the output value of the acceleration sensor (2B).
(3) The difference between the integrated values obtained from the procedures (1) and (2) is taken, and the angular acceleration component of the measurement object (P) is removed.
An arithmetic expression for the angle α obtained through the above procedure is shown in the following Expression 8.

The angle α can be calculated by using either of the above formulas 7 and 8. However, when Expression 7 is used, if the angle α is in the vicinity of a value that is an odd multiple of π / 2, the influence of the measurement error appears to be large. Further, when Expression 8 is used, when the angle α is in the vicinity of a value that is an integer multiple of π, the influence of the measurement error appears to be large.
Therefore, it is preferable that threshold data can be input as an input value for the arithmetic processing unit (3). For example, a value slightly below 90 ° (for example, 85 °) and a value slightly above 90 ° (for example, 95 °) are input to the arithmetic processing unit (3) as the first threshold range. Further, as the second threshold range, a value slightly below 0 ° (for example, −5 °) and a value slightly above 0 ° (for example, 5 °) are input.
If the calculation result of the angle α according to Equation 7 and / or Equation 8 is within the first threshold range input to the arithmetic processing unit (3), the value calculated based on Equation 8 is used as the arithmetic processing unit (3 ) Is output. On the other hand, if the calculation result of the angle α according to Formula 7 and / or Formula 8 is the second threshold range input to the calculation processing unit (3), the value calculated based on Formula 7 is used as the calculation processing unit. (3) is output.
As another method, a tangent function value may be calculated from the calculation results based on Formula 7 and Formula 8, and the angle α may be calculated based on the tangent function value, or obtained based on Formula 7 and Formula 8. The values α may be integrated, and the angle α may be calculated based on the half-angle formula of the sine function.

In addition, since the sine function value with respect to the angle α is determined by Equation 7, it is possible to calculate the angular velocity of the rotational tilt motion of the measurement object (P) by substituting this sine function value into Equations 3 and 5 above. is there. In addition, since the cosine function value with respect to the angle α is determined by Equation 8, it is possible to calculate the angular acceleration of the rotational tilt motion of the measurement object (P) by substituting this cosine function value into the above Equations 4 and 6. It is.
Equations 9 and 10 below show the calculation formulas of the angular velocity and angular acceleration of the rotational tilt motion of the measurement object (P) thus obtained.

  In this way, in the embodiment shown in FIGS. 1 and 2, the tilt angle estimation system (1) according to the present invention calculates the tilt angle, the tilt angular velocity, and the tilt angular acceleration without executing the integration calculation step. Is possible. Therefore, as compared with a method using a conventional gyro sensor, the tilt angle estimated value does not include an integration error. In this way, the tilt angle estimation system (1) according to the present invention can ensure high accuracy for the output estimated value.

  Note that, as is clear from Equation 3 and Equation 4 or Equation 5 and Equation 6, when the distance from the rotation center point (R) to the acceleration sensor (2) is “0”, the distance from the acceleration sensor (2) is as follows. The output value does not include an angular velocity component or an angular acceleration component related to the rotation operation of the measurement object (P). Therefore, by attaching the acceleration sensor (2) so as to coincide with the rotation center point (R), the output value of the acceleration sensor (2) is divided by the gravitational acceleration, so that the sine function value or cosine function of the inclination angle α is obtained. A value can be determined. In this case, in order to obtain an angular velocity component or an angular acceleration component related to the rotation operation of the measurement object (P), it is necessary to perform a time differentiation process on the calculated angle α.

In the example shown in FIGS. 1 and 2, the case where the global coordinate system (X, Z) is stationary is considered, but the present invention can also be applied to the case where the global coordinate system is accelerating. Here, for convenience, the origin (X _O , Z _O ) of the global coordinate system will be described as a reference point. However, this reference point may be replaced with one of the two acceleration sensors (2). When the global coordinate system (X, Z) is accelerating in one plane, the acceleration (D _X , D _Y ) in the global coordinate system is expressed by the following formulas 11 and 12, respectively.

This can be transformed into the instantaneous stationary coordinate system (x, _z ) to obtain the acceleration component (D _x , D _z ) of the reference point (X _O , Z _O ) in the instantaneous stationary coordinate system (x, z). . The calculation related to coordinate transformation is shown in the following Equation 13.

Similarly to the equations 3 to 6, the output (a _x , a _z , b _x , b _z ) from the acceleration sensor (2) is expressed when the entire coordinate system is moved. 14 can be obtained.

When the acceleration components in both directions of the reference point (X _O , Z _O ) are known values, the following equation 15 is obtained by executing the following procedure in the same manner as the procedure described with reference to FIGS. And the relationship shown in Formula 16 can be obtained.
(1) The distance from the rotation center point (R) to the acceleration sensor (2B) is integrated with respect to the output value of the acceleration sensor (2A).
(2) The distance from the rotation center point (R) to the acceleration sensor (2A) is added to the output value of the acceleration sensor (2B).
(3) The difference between the integrated values obtained from the procedures (1) and (2) is taken, and the angular velocity component or angular acceleration component of the measurement object (P) is removed.

Since Expressions 15 and 16 are functions of one variable, the inclination angle α can be calculated from either one of the expressions, and the sine function value or the cosine function value can be calculated by combining Expressions 15 and 16. It may be calculated.
Moreover, it is possible to calculate the angular velocity and the angular acceleration of the rotational motion of the measurement object (P) without using the integration calculation step by using the same method as that described with reference to FIGS.

Even when one of the acceleration components of the reference point (X _O , Z _O ) is unknown, the above formula 15 and formula 16 form two formulas related to the same unknown parameter, so that the inclination of the measurement object (P) The unknown acceleration component of the angle α and the reference point (X _O , Z _O ) can be calculated by combining Equations 15 and 16. In particular, this relationship is very advantageous when the target measurement object (P) moves linearly only in one direction. In particular, when a human walking motion is targeted, in many cases there is no vertical movement, and only horizontal movement is handled. Therefore, in this case, the acceleration component in the Z direction can be handled as a known value “0”, and the inclination angle of the measurement object (P) can be determined by the following equation 17 obtained by combining the above equations 15 and 16. Can be calculated.

FIG. 3 shows a mode in which the measurement object (P) rotates and tilts in a three-dimensional space.
In the embodiment described with reference to FIGS. 1 and 2, the measurement object (P) moves in the two-dimensional plane, but the tilt angle estimation system (1) of the present invention is in the three-dimensional space. The present invention can also be applied to a measurement object (P) that rotates and tilts.
In FIG. 3, the measurement object (P) at the initial position is indicated by a dotted line, and the measurement object (P) after starting the rotation and tilting operation is indicated by a solid line. The Z axis of the global coordinate system (X, Y, Z) in the three-dimensional space is set in a direction parallel to the gravitational acceleration. Further, the initial position of the measurement object (P) is determined by the acceleration sensor (P) attached to the axis of the measurement object (P), that is, the measurement object (P), in order to facilitate understanding of the present invention. 2) It is assumed that a line connecting each other is arranged to be orthogonal to the Z axis. Further, the X axis is determined so as to coincide with a line connecting the plurality of acceleration sensors (2) attached to the measurement object (P). The Y axis is defined as an axis that passes through the intersection of the X axis and the Z axis and is orthogonal to the X axis and the Z axis.
The rotation center point (R) of the measurement object (P) is assumed to coincide with the intersection of the X axis, the Y axis, and the Z axis.

  Next, the definition of the instantaneous stationary coordinate system will be described. In the instantaneous stationary coordinate system, the axis of the measurement object (P) after the start of the rotational tilt operation is defined as the x axis. Therefore, the instantaneous stationary coordinate system (x, y, z) is a coordinate obtained by rotating the entire coordinate system (X, Y, Z) by a predetermined angle around the Y axis and then rotating by a predetermined angle around the Z axis. it can.

4 and 5 are diagrams for explaining the coordinate conversion from the global coordinate system (X, Y, Z) to the instantaneous stationary coordinate system (x, y, z), and FIG. 4 illustrates the rotation around the Y axis. FIG. 5 shows a state when rotation around the Z-axis is made from the state shown in FIG.
As an example of coordinate transformation, a point G (0, 0, g) on the global coordinates (X, Y, Z) is considered. This point G is a point meaning gravitational acceleration when the overall coordinates are coordinates representing acceleration. FIG. 4 shows a state in which the point G is rotated around the Y axis by the angle α _Y toward the X axis. The coordinates (x _g1 , y _g1 , z _g1 ) of the point G _Y after this rotation operation are expressed by the following mathematical formula 18.

FIG. 5 shows a state in which the point G _Y shown in FIG. 4 is rotated around the z axis by an angle α _z toward the Y axis. The coordinates (x _g , y _g , z _g ) of the point G _YZ after this rotation operation are expressed by the following Equation 19.

The explanation related to FIG. 3 to FIG. 5 clarifies the relationship between the global coordinate system and the instantaneous stationary coordinate system in the three-dimensional space. Next, consider the acceleration component of a point on the measurement object (P) in the instantaneous stationary coordinate system. Similar to the explanation made in connection with FIGS. 1 and 2, the acceleration detected by the two acceleration sensors (2A, 2B) mounted on the measurement object (P) will be considered.
An acceleration component at an arbitrary position (x, y, z) on the measurement object (P) after the rotation operation is expressed by the following Equation 20. The acceleration component in the direction along the x-axis of the instantaneous stationary coordinate system is expressed as a function of the angular velocity around the y-axis of the instantaneous stationary coordinate system and the angular velocity around the z-axis, and the acceleration component in the direction along the y-axis of the instantaneous stationary coordinate system. The acceleration component is expressed as a function of angular acceleration around the y axis of the instantaneous stationary coordinate system, and the acceleration component in the direction along the z axis of the instantaneous stationary coordinate system is a function of angular acceleration around the z axis of the instantaneous stationary coordinate system. expressed.

As described with reference to FIGS. 1 and 2, the acceleration output from the acceleration sensor (2) includes an acceleration component caused by the rotation / tilt operation of the measurement object (P) and an acceleration component caused by gravity acceleration (inertial force). Therefore, the acceleration output from the acceleration sensor (2) is expressed by the following Expression 21 and Expression 22. Equation 21 is an acceleration sensor (2) that is arranged at a position away from the rotation center point (R) (a distance r _A from the rotation center point (R) to the acceleration sensor (2A)). 2A), the position coordinates in the instantaneous still coordinates of the acceleration sensor (2A) are represented by (x _A , y _A , z _A ), and the acceleration components corresponding to the position coordinates are represented by (a _x , a _y , a _z ). Further, the mathematical expression 22 is an acceleration sensor (2B) arranged at a position close to the rotation center point (R) (distance r _B from the rotation center point (R) to the acceleration sensor (2B)) in the acceleration sensor (2). ), The position coordinates in the instantaneous still coordinates of the acceleration sensor (2B) are represented by (x _B , y _B , z _B ), and the acceleration components corresponding to the position coordinates are represented by (b _x , b _y , b _z ).

The inclination angles α _y and α _z can be calculated by the following procedure similar to that related to FIGS. 1 and 2.
(1) The distance from the rotation center point (R) to the acceleration sensor (2B) is integrated with respect to the output value of the acceleration sensor (2A).
(2) The distance from the rotation center point (R) to the acceleration sensor (2A) is added to the output value of the acceleration sensor (2B).
(3) The difference between the integrated values obtained from the procedures (1) and (2) is taken, and the angular velocity component or angular acceleration component of the measurement object (P) is removed.
A set of relational expressions obtained according to this procedure is shown in Equation 23 below.

As is clear from Equation 23 above, there are many methods for calculating the inclination angles α _y and α _z from the relational expression shown in Equation 23. For example, a cosine function value related to the inclination angle α _y around the Y axis can be calculated from the acceleration component data in the z-axis direction of the instantaneous stationary coordinate system. Based on the cosine function value related to the inclination angle α _y around the Y axis, the sine function value related to the inclination angle α _y around the Y axis can be calculated. By substituting the calculated sine function value related to the tilt angle α _y about the Y axis into the above relational expression of the acceleration component in the x axis direction or the y axis direction of the instantaneous stationary coordinate system, the tilt angle α _z around the Z axis is calculated. A cosine function value or a sine function value can be calculated.
In this way, it is possible to calculate the tilt angle without performing the integration calculation step even for the measurement object (P) rotating in the three-dimensional space.

The angular acceleration of the rotational and tilting motion of the measurement object (P) in the three-dimensional space can also be calculated without performing the integration calculation step.
Reference is made to Equation 21 and Equation 22 above. Here, by taking the difference between the acceleration component in the y-axis direction of the instantaneous stationary coordinate system output from the acceleration sensor (2A) and the acceleration component in the y-axis direction of the instantaneous stationary coordinate system output from the acceleration sensor (2B), The angular acceleration around the global coordinate system Z-axis can be calculated. Equation 24 below shows the relationship between the angular acceleration around the global coordinate system Z-axis and the output value of the acceleration sensor (2).
Similarly, by taking the difference between the acceleration component in the z-axis direction of the instantaneous stationary coordinate system output from the acceleration sensor (2A) and the acceleration component in the z-axis direction of the instantaneous stationary coordinate system output from the acceleration sensor (2B), The angular acceleration around the global coordinate system Y-axis can be calculated. Equation 25 below shows the relationship between the angular acceleration around the global coordinate system Y-axis and the output value of the acceleration sensor (2).

  The relationship between the angular velocity component and the output value of the acceleration sensor (2) is based on the output value related to the acceleration of the acceleration sensor (2) in the x axis direction of the acceleration sensor (2). It can be obtained by taking the difference of the sensor (2B). This relational expression is shown in Expression 26 below. As is apparent from Equation 26, the angular velocity requires a data processing step for integration or differentiation. However, as described above, since there are more relational expressions than necessary, high accuracy can be ensured even if differential calculation processing or integration calculation processing is performed.

6 further shows an operation of rotating around the axis of the measurement object (P) (a line connecting the acceleration sensors (2A, 2B)) with respect to the rotation and tilting operation of the measurement object (P) shown in FIG. The added state is shown.
In the embodiment described with reference to FIGS. 3 to 5, first, the rotation tilt operation around the Y axis of the global coordinate system is considered, and then the rotation tilt operation around the Z axis of the global coordinate system is considered. For the movement of the measurement object (P) shown in FIG. 6, it is necessary to calculate the angle by another method.

FIG. 7 is a diagram for explaining a change in position of the measurement object (P) shown in FIG. The definition of the global coordinate system, the definition of the instantaneous stationary coordinate system, and the definition of the initial position of the measurement object (P) are the same as those described with reference to FIG.
The position of the measurement object (P) shown in FIG. 6 is obtained by rotating the measurement object (P) by an angle α around the Y axis from the initial position (see FIG. 7A), and then measuring object (P). Is coincident with the position rotated around the Y axis by an angle γ (see FIG. 7B).

FIG. 8 shows a state in which the measurement object (P) is rotated around the axis of the measurement object (P). FIG. 8A shows a cross section of the measurement object (P) at the initial position, and FIG. 8B shows the crossing of the measurement object (P) at the position of the measurement object (P) shown in FIG. Show the surface.
As is apparent from FIG. 8, here, it is assumed that the measurement object (P) is rotated about its axis by an angle β while the measurement object (P) moves to the position shown in FIG.

First, also in this embodiment, the relational expression expressed by the above mathematical formula 20 holds.
Next, consider the coordinate transformation of the point G (0, 0, g) on the global coordinates representing acceleration in the same manner as described with reference to FIG. Note that the point G means the gravitational acceleration as in the case described with reference to FIG.
Here, a case is considered in which the point G (0, 0, g) is rotationally transformed from the X axis toward the Z axis around the Y axis of the global coordinate system. The relationship between the coordinates (x _g1 , y _g1 , z _g1 ) after the coordinate conversion is shown in the following Expression 27.

  The gravity acceleration component after coordinate conversion represented by Equation 27 is added to each component of acceleration output by the acceleration sensor (2) represented by Equation 20 above. The addition formula of the gravity acceleration component after the conversion is shown in the following formula 28.

  Next, consider the rotation around the axis of the measurement object (P). Since the instantaneous stationary coordinate system is defined so that the axis of the measuring object (P) coincides with the x axis of the instantaneous stationary coordinate system, the z axis is directed from the z axis to the y axis around the axis of the measuring object (P). Then, the above formula 28 is converted into the following formula 29.

Each component of the instantaneous stationary coordinate system of the acceleration sensor (2A) located at _a distance r _a from the rotation center point (R) is represented by (a _x , a _y , a _z ), and the distance r from the rotation center point (R). _When each component of the instantaneous stationary coordinate system of the acceleration sensor (2B) existing at the position of b is represented by (b _x , b _y , b _z ), the following relational expressions shown in Expressions 30 to 32 can be obtained. Equation 30 below shows the acceleration component in the x-axis direction of the instantaneous stationary coordinate system, Equation 31 below shows the acceleration component in the y-axis direction of the instantaneous stationary coordinate system, and Equation 32 below shows the instantaneous stationary coordinate system. The acceleration component in the z-axis direction is shown.

The angular velocity component or the angular acceleration component is removed from the pair of relational expressions shown in Equations 30 to 32 by the following procedure similar to the procedure described above.
(1) The distance from the rotation center point (R) to the acceleration sensor (2B) is integrated with respect to the output value of the acceleration sensor (2A).
(2) The distance from the rotation center point (R) to the acceleration sensor (2A) is added to the output value of the acceleration sensor (2B).
(3) The difference between the integrated values obtained from the procedures (1) and (2) is taken, and the angular velocity component or angular acceleration component of the measurement object (P) is removed.
A set of relational expressions obtained according to this procedure is shown in Equation 33 below.

As is apparent from the above equation 33, the sine function value of the rotational tilt angle around the global coordinate system Y-axis can be calculated from the data related to the instantaneous stationary coordinate system x-axis. Also, based on this sine function value, the cosine function value is also known. Therefore, this known cosine function value and the rotation angle β around the x axis of the instantaneous stationary coordinate system can be calculated.
Therefore, the calculation of the rotational tilt angle around the global coordinate system Y-axis and the rotational tilt angle around the instantaneous stationary coordinate system x-axis can be performed only by algebraic computation without requiring an integral computation process.

Subsequently, the rotation around the instantaneous stationary coordinate system z-axis is considered, and then this is coordinate-converted onto the global coordinate system (X, Y, Z) to calculate the rotational tilt angle around the global coordinate system Z-axis.
First, a difference between acceleration components obtained from the acceleration sensors (2A, 2B) is calculated. This calculation process is shown in Equation 34 below.

By combining the relational expression relating to the y-axis component and the z-axis component shown in the mathematical formula 34, the angular acceleration around the y-axis and the angular acceleration around the z-axis of the instantaneous stationary coordinate system can be calculated.
A determinant for converting the angular acceleration around the y-axis and the angular acceleration around the z-axis of the instantaneous stationary coordinate system calculated in the following Equation 35 into the overall coordinate system (X, Y, Z) is shown. In this conversion, the direction from the X axis to the Z axis is positive. Further, the acceleration component along the x axis of the instantaneous stationary coordinate system is “0”.

  Based on Equation 35 above, an angular acceleration component of the global coordinate system (X, Y, Z) can be obtained, and an angular velocity component can be obtained by integrating these. A relational expression of angular velocity components obtained by this integration calculation is shown in the following Expression 36.

  In the above equation 34, the relational expression of the acceleration output in the instantaneous stationary coordinate system x-axis direction is a function of the acceleration component related to the rotation around the instantaneous stationary coordinate system y-axis and the z-axis. A relational expression between the rotational speed around the Y axis and the rotational speed around the Z axis in the global coordinate system can be obtained. By using this relational expression to integrate the angular velocity around the global coordinate system Z-axis, the rotational tilt angle γ around the global coordinate system Z-axis can be calculated while suppressing the integration error.

FIG. 9 shows an application example of the calculation method of the tilt angle estimation system (1) described with reference to FIGS. In the example shown in FIG. 9, two measurement objects (P1, P2) are connected at one rotation center point (R). In addition, the two measurement objects (P1, P2) are rotating and tilting about the rotation center point (R) independently of each other.
Two acceleration sensors (2A1, 2B1) are attached to the measurement object (P1), and two acceleration sensors (2A2, 2B2) are attached to the measurement object (P2). Distance from the rotation center point (R) to the acceleration sensor (2A1) is represented by _{r a1,} the distance from the rotation center point (R) to the acceleration sensor (2B1) is represented by _{r b1,} the center of rotation (R) distance from to the acceleration sensor (2A2) is represented by _{r a2,} the distance from the rotation center point (R) to the acceleration sensor (2B2) is expressed by _{r a2.}

Each acceleration sensor (2A1, 2B1, 2A2, 2B2) includes the acceleration in the axial direction of the measurement object (P1, P2), the acceleration in the direction orthogonal to the axis of the measurement object (P1, P2), and the measurement object. The acceleration relating to the rotation around the axis (P1, P2) can be measured. Thereby, the acceleration vector which consists of three components in each acceleration measuring point of a measuring object (P1, P2) can be obtained. Since the acceleration vector at each measurement point can be obtained from the acceleration sensor (2A1, 2B1, 2A2, 2B2), the acceleration vector at the rotation center point (R) of the measurement object (P1, P2) can be calculated.
The calculation formula of the acceleration vector at the rotation center point (R) is shown below. The following formula 37 is for the measurement object (P1), and the following formula 38 is for the measurement object (P2).

  The acceleration vector at the rotation center point (R) of the measurement object (P1) represented by the mathematical formula 37 is rotated by an angle α around the Y axis of the global coordinate system (X, Y, Z), and an angle γ around the Z axis. When the rotation angle is rotated by an angle β around the axis of the measurement object (P1) (see FIGS. 7 and 8), the case where it coincides with the acceleration vector of the other measurement object (P2) is considered. By obtaining such angles (α, β, γ) by numerical calculation, the relative angular position of the measurement object (P2) with respect to the measurement object (P1) can be calculated.

FIG. 10 is a conceptual diagram when three measurement objects (P1, P2, P3) arranged so as to be orthogonal to each other are considered. The three measurement objects (P1, P2, P3) intersect with each other at one point, and perform a rotational tilt motion with this one intersection as the rotation center point (R). An acceleration sensor (2) for measuring the acceleration component in the axial direction of each measurement object (P1, P2, P3) is attached to the rotation center point (R). Further, one acceleration sensor is attached to each measurement object (P1, P2, P3).
If one of the measurement objects (P1, P2, P3) is defined as the x direction, the axes of the other measurement objects (P1, P2, P3) are naturally defined as the y direction and the z direction. . As a result, the relational expression shown in the following mathematical formula 39 can be obtained.

  The absolute values of the three angular velocities can be calculated by combining the relational expressions related to the axial direction components of the mathematical formula 39. Regarding two directions of the three axes, since the angular velocities are obtained by measurement, the signs are determined. For the other axis, the acceleration in the direction parallel to the axis whose angular velocity is determined by measurement is simultaneously measured, whereby the sign of the acceleration of the other axis is also determined.

  The present invention can be suitably used for human walking motion analysis research, human balance function evaluation, robot movement motion analysis research, sports training such as golf, and development of medical welfare equipment.

It is a schematic block diagram of the inclination-angle estimation system which concerns on this invention. It is a figure explaining the coordinate system of a motion of the measuring object of the inclination-angle estimation system shown in FIG. It is a figure explaining the coordinate system of the motion of the measuring object rotated in solid space. It is a figure explaining the concept of the coordinate transformation used for the inclination-angle estimation of the measuring object rotated in solid space. It is a figure explaining the concept of the coordinate transformation used for the inclination-angle estimation of the measuring object rotated in solid space. It is a figure explaining the coordinate system of a motion of the measuring object rotated about an axis. It is a figure explaining the coordinate system of a motion of the measuring object rotated about an axis. It is a figure explaining the coordinate system of a motion of the measuring object rotated about an axis. It is a model figure of the measuring object whose relative angle is estimated by the relative angle estimation system concerning the present invention. It is a model figure of the measuring object whose angular velocity is estimated by the angular velocity estimation system concerning the present invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Inclination angle estimation system 2 ... Acceleration sensor 3 ... Arithmetic processing unit

Claims (36)

A system for estimating an inclination angle of an object having one rotation center point and tilting while rotating in one plane around the rotation center point,
At least two acceleration sensors attached to the object;
An arithmetic processing unit that receives outputs from the at least two acceleration sensors and calculates an inclination angle of the object based on the outputs;
The at least two acceleration sensors are aligned on one line, and a line connecting the at least two acceleration sensors passes through the rotation center point.   The tilt angle estimation system according to claim 1, wherein distances of at least two acceleration sensors from the rotation center point are different from each other.   The tilt angle estimation system according to claim 2, wherein a position of one of the at least two acceleration sensors coincides with the rotation center point. In the arithmetic processing unit, a first reference axis that defines the one plane and passes through the rotation center point is defined,
Of the at least two acceleration sensors, one acceleration sensor and the other acceleration sensor each output a first acceleration in a direction along a line connecting the at least two acceleration sensors.
The arithmetic processing unit integrates a distance from the rotation center point to the one acceleration sensor with respect to an output value from the other acceleration sensor, and calculates a first integrated value;
Integrating a distance from the rotation center point to the other acceleration sensor with respect to an output value from the one acceleration sensor, and calculating a second integrated value;
A step of calculating a sine function value of an included angle between the first reference axis and a line connecting the at least two acceleration sensors is executed based on a difference value between the first integrated value and the second integrated value. The tilt angle estimation system according to claim 1. In the arithmetic processing unit, a first reference axis that defines the one plane and passes through the rotation center point is defined,
Of the at least two acceleration sensors, one acceleration sensor and the other acceleration sensor are second in a direction perpendicular to a line connecting the at least two acceleration sensors and parallel to the moving plane of the object. Output the acceleration of
The arithmetic processing unit integrates a distance from the rotation center point to the one acceleration sensor with respect to an output value from the other acceleration sensor, and calculates a third integrated value;
Integrating a distance from the rotation center point to the other acceleration sensor with respect to an output value from the one acceleration sensor, and calculating a fourth integrated value;
A step of calculating a cosine function value of an included angle between the first reference axis and a line connecting the at least two acceleration sensors is executed based on a difference value between the third integrated value and the fourth integrated value. The tilt angle estimation system according to claim 1. In the arithmetic processing unit, a first reference axis that defines the one plane and passes through the rotation center point is defined,
Among the at least two acceleration sensors, one acceleration sensor is orthogonal to a first acceleration in a direction along a line connecting the at least two acceleration sensors and a line connecting the at least two acceleration sensors, and A second acceleration in a direction parallel to the moving plane of the object is output, and another acceleration sensor includes a first acceleration in a direction along a line connecting the at least two acceleration sensors, and the at least two acceleration sensors. A third acceleration in a direction orthogonal to a line connecting the two and parallel to the moving plane of the object, and a line orthogonal to a line connecting the at least two acceleration sensors and the moving plane of the object Outputs the fourth acceleration in the parallel direction,
The arithmetic processing unit calculates a distance from the rotation center point to the one acceleration sensor with respect to an output value of acceleration in a direction along a line connecting the at least two acceleration sensors output by the other acceleration sensor. Integrating and calculating a first integrated value;
The distance from the rotation center point to the other acceleration sensor is integrated with the acceleration output value in the direction along the line connecting the at least two acceleration sensors output by the one acceleration sensor, and the second Calculating the integrated value;
A distance from the rotation center point to the one acceleration sensor is added to an acceleration output value in a direction orthogonal to a line connecting the at least two acceleration sensors output by the other acceleration sensor; Calculating the integrated value of
A distance from the rotation center point to the other acceleration sensor is added to an acceleration output value in a direction orthogonal to a line connecting the at least two acceleration sensors output by the one acceleration sensor; Calculating the integrated value of
Calculating a sine function value of an included angle between the first reference axis and a line connecting the at least two acceleration sensors based on a difference value between the first integrated value and the second integrated value;
A step of calculating a cosine function value of an included angle between the first reference axis and a line connecting the at least two acceleration sensors is executed based on a difference value between the third integrated value and the fourth integrated value. The tilt angle estimation system according to claim 1. The arithmetic processing unit has a first upper limit value incremented by a predetermined angle with respect to an odd multiple of π / 2 and a first lower limit decremented by a predetermined angle with respect to the odd multiple of π / 2. Recognizing a first threshold region defined between values,
When the included angle value obtained from the sine function value and the cosine function value is within the range of the first threshold region, an integrated value or a divided value of the sine function and the cosine function is calculated as the included angle. The tilt angle estimation system according to claim 6, wherein the tilt angle estimation system is used in a system. The arithmetic processing unit has a first upper limit value incremented by a predetermined angle with respect to an odd multiple of π / 2 and a first lower limit decremented by a predetermined angle with respect to the odd multiple of π / 2. Recognizing a first threshold region defined between values,
When the included angle value obtained from the sine function value and the cosine function value is within the first threshold region, the arithmetic processing unit outputs the included angle calculated based on the cosine function value. The tilt angle estimation system according to claim 6. The arithmetic processing unit is defined between a second upper limit value incremented by a predetermined angle with respect to a multiple value of π and a second lower limit value decremented by a predetermined angle with respect to the multiple value of π. Recognizing a second threshold region to be
When the included angle value obtained from the sine function value and the cosine function value is within the range of the second threshold region, an integrated value or a divided value of the sine function and the cosine function is calculated as the included angle. The tilt angle estimation system according to claim 6, wherein the tilt angle estimation system is used in a system. The arithmetic processing unit is defined between a second upper limit value incremented by a predetermined angle with respect to a multiple value of π and a second lower limit value decremented by a predetermined angle with respect to a multiple value of π. Recognizing a second threshold region,
When the value of the included angle obtained from the sine function value and the cosine function value is within the range of the second threshold region, the arithmetic processing unit outputs the included angle calculated based on the sine function value. The tilt angle estimation system according to claim 6.   The tilt angle estimation system according to claim 1, wherein the rotation center point moves linearly within the one plane.   12. The tilt angle estimation system according to claim 11, wherein the linear movement speed of the rotation center point changes with time. In the arithmetic processing unit, a first reference axis that defines the one plane, passes through the rotation center point, and is parallel to the gravitational acceleration vector, and a second reference axis orthogonal to the first reference axis Is defined,
The rotation center point moves linearly within the one plane,
A linear moving speed of the rotation center point is defined by a component along the first reference axis and a component along the second reference axis;
The linear movement speed of the rotation center point changes with time, and the component along the first reference axis and the component along the second reference axis of the time change amount are known. 12. The tilt angle estimation system according to 12. Of the at least two acceleration sensors, one acceleration sensor and the other acceleration sensor each output a first acceleration in a direction along a line connecting the at least two acceleration sensors.
The arithmetic processing unit integrates a distance from the rotation center point to the one acceleration sensor with respect to an output value from the other acceleration sensor, and calculates a first integrated value;
Integrating a distance from the rotation center point to the other acceleration sensor with respect to an output value from the one acceleration sensor, and calculating a second integrated value;
The step of calculating an included angle between the first reference axis and a line connecting the at least two acceleration sensors based on a difference value between the first integrated value and the second integrated value is performed. The tilt angle estimation system according to claim 13. Of the at least two acceleration sensors, one acceleration sensor and the other acceleration sensor are second in a direction perpendicular to a line connecting the at least two acceleration sensors and parallel to the moving plane of the object. Output the acceleration of
The arithmetic processing unit integrates a distance from the rotation center point to the one acceleration sensor with respect to an output value from the other acceleration sensor, and calculates a third integrated value;
Integrating a distance from the rotation center point to the other acceleration sensor with respect to an output value from the one acceleration sensor, and calculating a fourth integrated value;
The step of calculating an included angle between the first reference axis and a line connecting the at least two acceleration sensors based on a difference value between the third integrated value and the fourth integrated value is performed. The tilt angle estimation system according to claim 13. In the one plane, the rotation center point linearly moves in a direction orthogonal to the direction of the gravitational acceleration vector, and the movement acceleration of the rotation center point is an unknown.
The arithmetic processing unit recognizes the movement locus of the rotation center point as a first reference axis,
Of the at least two acceleration sensors, one acceleration sensor has a first acceleration in a direction along a line connecting the at least two acceleration sensors and a direction orthogonal to a line connecting the at least two acceleration sensors. The second acceleration is output, and the other acceleration sensor is orthogonal to the first acceleration in the direction along the line connecting the at least two acceleration sensors and the line connecting the at least two acceleration sensors, and the object And outputs a third acceleration in a direction parallel to the moving plane and a fourth acceleration in a direction perpendicular to the line connecting the at least two acceleration sensors and parallel to the moving plane of the object. ,
The arithmetic processing unit calculates a distance from the rotation center point to the one acceleration sensor with respect to an output value of acceleration in a direction along a line connecting the at least two acceleration sensors output by the other acceleration sensor. Integrating and calculating a first integrated value;
The distance from the rotation center point to the other acceleration sensor is integrated with the acceleration output value in the direction along the line connecting the at least two acceleration sensors output by the one acceleration sensor, and the second Calculating the integrated value;
The acceleration in the direction parallel to the moving plane of the object and perpendicular to the line connecting the at least two acceleration sensors output by the other acceleration sensors, and the distance from the rotation center point to the one acceleration sensor Calculating a third integrated value by integrating the output values of
Acceleration in a direction perpendicular to the line connecting the at least two acceleration sensors output from the one acceleration sensor and parallel to the moving plane of the object, with the distance from the rotation center point to the other acceleration sensor Calculating a fourth integrated value by integrating the output values of:
A first difference value obtained by calculating a difference between the first integrated value and the second integrated value, and a second value obtained by calculating a difference between the third integrated value and the fourth integrated value. 2. The tilt angle estimation system according to claim 1, wherein the step of removing an acceleration component of linear movement of the rotation center point along the first reference axis is executed using a difference value. Among the acceleration components output by the at least two acceleration sensors, the arithmetic processing unit outputs an output value of one acceleration sensor and another acceleration sensor for an acceleration component in a direction parallel to a line connecting the at least two acceleration sensors. And calculating the difference between the distance between one of the at least two acceleration sensors and the rotation center point and the distance between the other acceleration sensor and the rotation center point. Calculate the difference
3. The tilt angle estimation system according to claim 2, wherein the angular velocity of the object is calculated by dividing the difference between the output values by the difference in distance. Among the acceleration components output by the at least two acceleration sensors, the arithmetic processing unit calculates one of the acceleration components in a direction perpendicular to a line connecting the at least two acceleration sensors and parallel to the moving plane of the object. The difference between the output value of the other acceleration sensor and the output value of the other acceleration sensor is calculated, the distance between one of the at least two acceleration sensors and the rotation center point, and the other acceleration sensor And calculate the difference in distance between the rotation center point and
The tilt angle estimation system according to claim 2, wherein the angular acceleration of the object is calculated by dividing the difference between the output values by the difference in distance. In a three-dimensional space defined by three orthogonal coordinate axes, with the intersection point of the orthogonal coordinate axes as the rotation center point, the rotational angle of the object having a tilt posture is estimated by rotating around two coordinate axes of the three orthogonal coordinate axes. A system that
At least two acceleration sensors attached to the object;
An arithmetic processing unit that receives outputs from the at least two acceleration sensors and calculates an inclination angle of the object based on the outputs;
The at least two acceleration sensors are aligned on one line, and a line connecting the at least two acceleration sensors passes through the rotation center point.   The at least two acceleration sensors have a first acceleration component parallel to a line connecting the two acceleration sensors and a first orthogonal component in a direction orthogonal to the line connecting the two acceleration sensors and the plane of movement of the object. 20. The tilt angle estimation system according to claim 19, wherein the second acceleration component and a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component are output. The arithmetic processing unit integrates the distance between the other acceleration sensor and the rotation center point with respect to the three output values of the acceleration output from one of the at least two acceleration sensors. A first integrating step for obtaining two integrated values;
A second integration step of integrating the distance between the one acceleration sensor and the rotation center point with respect to the three output values of the acceleration output by the other acceleration sensor, and obtaining three integrated values;
For each of the three integrated values obtained from the first integrating step, execute a difference step for calculating a difference using the integrated value of the acceleration component in the corresponding direction obtained from the second integrating step,
21. The tilt angle estimation system according to claim 20, wherein a step of calculating a tilt angle component with respect to an axis serving as a center of the rotational motion of the object is executed based on a difference value obtained from the difference step. The arithmetic processing unit calculates a difference between an output value of one acceleration sensor and an output value of another acceleration sensor for the second acceleration component among the acceleration components output by the at least two acceleration sensors. Calculating a difference between a distance between one of the at least two acceleration sensors and the rotation center point and a distance between the other acceleration sensor and the rotation center point;
21. The tilt angle estimation system according to claim 20, wherein the angular acceleration of the object is calculated by dividing the difference between the output values by the difference in distance.   The tilt angle estimation system according to claim 19, wherein the object further rotates about an axis connecting the at least two acceleration sensors. The three orthogonal coordinate axes are a first coordinate axis in a direction parallel to the gravity vector, a second coordinate axis in a direction orthogonal to the first coordinate axis, the first coordinate axis, and the second coordinate axis. A third coordinate axis perpendicular to the coordinate axis,
The arithmetic processing unit integrates the distance between the other acceleration sensor and the rotation center point with respect to the three output values of the acceleration output from one of the at least two acceleration sensors. A first integrating step for obtaining two integrated values;
A second integration step of integrating the distance between the one acceleration sensor and the rotation center point with respect to the three output values of the acceleration output by the other acceleration sensor, and obtaining three integrated values;
A difference between an integrated value from the first integrating step and an integrated value from the second integrating step regarding an acceleration component in a direction parallel to a line connecting the at least two acceleration sensors, and the one acceleration sensor; Inclination by rotation about the second coordinate axis or the third coordinate axis based on the difference between the distance between the rotation center point and the distance between the other acceleration sensor and the rotation center point The tilt angle estimation system according to claim 23, wherein a sine function value of an angular component is calculated. The arithmetic processing unit is configured to calculate the second coordinate axis or the third coordinate axis based on the calculated second coordinate axis or a sine function value of a tilt angle component by rotation about the third coordinate axis. Calculate the cosine function value of the tilt angle component by rotation around
The calculated cosine function value and the integrated value from the first integrating step and the integrated value from the second integrating step regarding the acceleration component in the direction parallel to the axis orthogonal to the rotational movement plane of the object. The at least two acceleration sensors based on a difference with an integrated value and a difference between a distance between the one acceleration sensor and the rotation center point and a distance between the one acceleration sensor and the rotation center point. 25. The tilt angle estimation system according to claim 24, wherein a cosine function value of a tilt angle related to a rotation operation about a line connecting the two is calculated. The arithmetic processing unit is configured to calculate the second coordinate axis or the third coordinate axis based on the calculated second coordinate axis or a sine function value of a tilt angle component by rotation about the third coordinate axis. Calculate the cosine function value of the tilt angle component by rotation around
The calculated cosine function value, acceleration in a direction parallel to an axis orthogonal to an axis orthogonal to the rotational movement plane of the object and an axis parallel to a line connecting the at least two acceleration sensors The difference between the integrated value from the first integrating step and the integrated value from the second integrating step, the distance between the one acceleration sensor and the rotation center point, the other acceleration sensor, 25. A sine function value of an inclination angle related to a rotation operation with a line connecting the at least two acceleration sensors as an axis is calculated based on a difference from a distance from the rotation center point. The described tilt angle estimation system. The arithmetic processing unit further includes a difference between an output value of the one acceleration sensor and an output value of the other acceleration sensor with respect to an acceleration component in a direction parallel to an axis orthogonal to the rotational movement plane of the object. ,
The output of the one acceleration sensor relating to the acceleration component in the direction parallel to the axis orthogonal to the axis perpendicular to the rotational movement plane of the object and the axis parallel to the line connecting the at least two acceleration sensors. The difference between the value and the output value of the other acceleration sensor,
Based on the difference between the distance between the rotation center point and the one acceleration sensor and the distance between the rotation center point and the other acceleration sensor, a direction parallel to an axis orthogonal to the rotational movement plane of the object is set. The angular acceleration in the direction parallel to the axis orthogonal to the axis orthogonal to the rotational movement plane of the object and the axis parallel to the axis connecting the at least two acceleration sensors. 27. The tilt angle estimation system according to claim 25 or 26, wherein the tilt angle estimation system is calculated.   The arithmetic processing unit further integrates and calculates an angular acceleration whose axis is parallel to an axis orthogonal to the rotational movement plane of the object, and is defined by the second coordinate axis and the third coordinate axis. 28. The tilt angle estimation system according to claim 27, wherein the tilt angle in a plane to be calculated is calculated. One object having one rotation center point and rotating about the one rotation center point, and connected to the one object at the one rotation center point and rotating about the one rotation center point A system for estimating the relative angle between other moving objects,
A first acceleration sensor group comprising at least two acceleration sensors attached to the one object;
A second acceleration sensor group comprising at least two acceleration sensors attached to the other object;
Comprising an arithmetic processing unit that receives outputs from the acceleration sensors of the first and second acceleration sensor groups and calculates an inclination angle of the object based on the outputs;
The at least two acceleration sensors of the first acceleration sensor group are aligned on the one object;
The at least two acceleration sensors of the second acceleration sensor group are aligned on the one object;
A line connecting the at least two acceleration sensors constituting the first acceleration sensor group and a line connecting the at least two acceleration sensors constituting the second acceleration sensor group both pass through the one rotation center point. A relative angle estimation system characterized by that.   The at least two acceleration sensors of the first acceleration sensor group are orthogonal to a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors and a rotational movement plane of the object. 30. An output relating to acceleration comprising a second acceleration component in a direction and a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component is output. Relative angle estimation system.   The at least two acceleration sensors of the second acceleration sensor group are orthogonal to a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors and a rotational movement plane of the object. 30. An output relating to acceleration comprising a second acceleration component in a direction and a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component is output. Relative angle estimation system.   31. The arithmetic processing unit calculates a first acceleration vector at a rotation center point of the one object based on an output from an acceleration sensor that constitutes the first acceleration sensor group. Relative angle estimation system.   32. The arithmetic processing unit calculates a second acceleration vector at a rotation center point of the other object based on an output from an acceleration sensor that constitutes the second acceleration sensor group. Relative angle estimation system. The at least two acceleration sensors of the first acceleration sensor group are orthogonal to a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors and a rotational movement plane of the object. A second acceleration component in a direction, and an output relating to an acceleration composed of a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component,
The at least two acceleration sensors of the second acceleration sensor group are orthogonal to a first acceleration component in a direction parallel to a line connecting the at least two acceleration sensors and a rotational movement plane of the object. A second acceleration component in a direction, and an output relating to an acceleration composed of a third acceleration component in a direction orthogonal to the first acceleration component and the second acceleration component,
The arithmetic processing unit calculates a first acceleration vector at a rotation center point of the one object based on an output from an acceleration sensor constituting the first acceleration sensor group, and sets the second acceleration sensor group. Based on the output from the constituting acceleration sensor, a second acceleration vector at the rotation center point of the other object is calculated,
30. The relative angle estimation according to claim 29, wherein a relative angle between the one object and the other object is estimated from a difference between the first acceleration vector and the second acceleration vector. system. One acceleration sensor arranged at the center of rotation of the rotating object;
Three acceleration sensors arranged apart from the one acceleration sensor;
An arithmetic processing unit that receives outputs from the one acceleration sensor and the three acceleration sensors,
The lines connecting the one acceleration sensor and the three acceleration sensors are orthogonal to each other,
The one acceleration sensor outputs an acceleration component in a direction parallel to a line connecting the one acceleration sensor and each of the three acceleration sensors;
Each of the three acceleration sensors outputs an acceleration component in a direction parallel to a straight line toward the one acceleration sensor,
At least one of the three acceleration sensors outputs an acceleration component in a direction parallel to a line connecting the other acceleration sensor and the one acceleration sensor,
An angular velocity estimation system that estimates an angular velocity of a rotational motion of the object based on a relationship between outputs of the one acceleration sensor and the three acceleration sensors. A system for estimating an inclination angle of an object having one rotation center point and tilting while rotating in one plane around the rotation center point,
At least one acceleration sensor attached to the object;
An arithmetic processing unit that receives an output from the at least one acceleration sensor and calculates an inclination angle of the object based on the output;
An inclination angle estimation system, wherein one of the at least one acceleration sensors is arranged on the rotation center point.

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