CN110926377B - Robot and rotation angle measuring method thereof - Google Patents

Robot and rotation angle measuring method thereof Download PDF

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CN110926377B
CN110926377B CN201811103086.5A CN201811103086A CN110926377B CN 110926377 B CN110926377 B CN 110926377B CN 201811103086 A CN201811103086 A CN 201811103086A CN 110926377 B CN110926377 B CN 110926377B
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robot
equal
beacon
angle
rotation
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CN110926377A (en
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崔江伟
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Suzhou Cleva Precision Machinery and Technology Co Ltd
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Suzhou Cleva Precision Machinery and Technology Co Ltd
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
    • G05D1/0234Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using optical markers or beacons
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/26Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes

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  • Electromagnetism (AREA)
  • Aviation & Aerospace Engineering (AREA)
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  • Automation & Control Theory (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a robot and a rotation angle measuring method thereof, the robot comprises a shell, a rotating platform arranged on the shell, an induction component arranged on the rotating platform, and n beacons which are arranged on a working boundary and used for the induction of the induction component and are defined on the working boundaryDuring the steering of the robot, the turntable performs x times of rotation cycles in total, the rotation speed of the turntable is constant, and the azimuth angle recorded by the mth beacon in the ith rotation cycle of the turntable is detected to be
Figure DDA0001807186770000011
Defining a value of angular calculation Δ θ for steering of the robot with reference to the mth beacon m An angle Δ θ for turning the robot, an
Figure DDA0001807186770000012
Wherein m is the mth beacon, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m The effective signal of the mth beacon is obtained for the kth time, j refers to the mth beacon 20 detected for the j times, i is more than or equal to 1 and less than or equal to x, k is more than or equal to 1 and less than or equal to j, j is more than or equal to 1 and less than or equal to x, and the azimuth angle refers to the included angle between the connection line from the rotation center of the robot to the mth beacon and the heading of the robot. The robot calculates the rotation angle more accurately.

Description

Robot and rotation angle measuring method thereof
Technical Field
The invention relates to a robot and a rotation angle measuring method thereof, in particular to a mowing robot and a rotation angle measuring method thereof.
Background
Robot position and state determination is a very important part in robot guidance control. The robot usually completes the in-situ rotation by the differential speed of the left wheel and the right wheel, and the rotation angle can be calculated by the wheel speed and the rotation time, and can also be calculated by a gyroscope. However, the rotation angle is calculated through the rotation speed, and when the wheel slips, the accurate rotation angle cannot be obtained, and the calculation through the gyroscope has accumulated errors, so that the calculated rotation angle is not accurate enough.
Disclosure of Invention
The invention aims to provide a robot and a method for measuring a rotation angle of the robot, wherein the rotation angle calculated by the robot is more accurate.
In order to achieve one of the above objects, according to one embodiment of the present invention, there is provided a robot including a working mechanism, a housing, a traveling mechanism provided in the housing, a turntable rotatably provided in the housing, and a sensing unit provided in the turntable, the robot having a working boundary, the robot including: the robot further comprises n beacons which are arranged on the working boundary and used for sensing the sensing assembly, the rotating table is defined to rotate for x times in the steering process of the robot, the rotating speed of the rotating table is constant, and the m-th beacon recorded in the ith rotating period of the rotating table is detectedIn an azimuth of
Figure GDA0003690234270000011
Defining a calculated value delta theta for the angle at which the robot is steered with reference to the mth beacon m An angle Δ θ for turning the robot, an
Figure GDA0003690234270000012
Wherein m is the mth beacon, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m The effective signal of the mth beacon is obtained for the kth time, j refers to the mth beacon detected for the j times, i is more than or equal to 1 and less than or equal to x, k is more than or equal to 1 and less than or equal to j, j is more than or equal to 1 and less than or equal to x, and the azimuth angle refers to the included angle between the connection line from the rotation center of the robot to the mth beacon and the heading (H0) of the robot.
As a further improvement of an embodiment of the present invention, it is defined that in the steering process of the robot, the sensing component can detect p beacons, where p is greater than or equal to 1 and less than or equal to n, and then the steering angle of the robot is
Figure GDA0003690234270000021
As a further improvement of an embodiment of the present invention, it is defined that during the turning process of the robot, the n beacons are all detected, and the turning angle of the robot is
Figure GDA0003690234270000022
As a further improvement of one embodiment of the present invention, the number of the beacons n is set to 1, and during the turning process of the robot, the beacons are detected x times in total, the azimuth change value at each detection is defined to be constant, and only the recorded azimuth angle of the beacon in the ith rotation period of the turntable is detected to be Δ θ 1i1 Then the angle at which the robot turns is
Figure GDA0003690234270000023
As a further improvement of an embodiment of the present invention, the sensing component includes a laser signal transmitter and a laser signal receiver, and the beacon is an anti-cursor.
As a further improvement of an embodiment of the present invention, the working mechanism is a cutting mechanism for cutting grass.
In order to achieve one of the above objects, an embodiment of the present invention further provides a rotation angle measuring method of a robot, the robot includes a working mechanism, a housing, a traveling mechanism disposed in the housing, and a turntable rotatably disposed in the housing, the rotation angle measuring method includes the steps of:
providing an induction assembly on the turntable;
providing n beacons for the sensing component to sense at a working boundary of the robot;
providing a control module electrically connected with the sensing assembly;
the definition is in the once turns to in-process of robot, the revolving stage carries out x rotation cycle altogether, and the rotational speed of revolving stage is invariable, the response subassembly detects mth beacon at revolving stage ith rotation cycle and record angle signal, the azimuth angle that angle signal was handled through control module is
Figure GDA0003690234270000031
Defining a calculated value Δ θ for an angle at which the robot is steered with the m-th beacon m Is an angle Δ θ by which the robot rotates, an
Figure GDA0003690234270000032
Wherein m is the mth beacon, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m The effective signal of the mth beacon is obtained at the kth time, j refers to the mth beacon detected at the j times, i is larger than or equal to 1 and smaller than or equal to x, k is larger than or equal to 1 and smaller than or equal to j, j is larger than or equal to 1 and smaller than or equal to x, and the azimuth angle refers to the included angle between the connection line from the rotation center of the robot to the mth beacon and the heading (H0) of the robot.
As a further improvement of an embodiment of the invention, it is defined that the sensing component is capable of detecting during a turning of the robotP beacons are reached, wherein p is more than or equal to 1 and less than or equal to n, the steering angle of the robot is
Figure GDA0003690234270000033
As a further improvement of one embodiment of the present invention, the number of the beacons n is set to 1, and during the turning process of the robot, the beacons are detected x times in total, the azimuth change value at each detection is defined to be constant, and only the recorded azimuth angle of the beacon in the ith rotation period of the turntable is detected to be Δ θ 1i1 Then the angle at which the robot turns is
Figure GDA0003690234270000034
As a further improvement of an embodiment of the present invention, the working mechanism is a cutting mechanism for cutting grass.
Compared with the prior art, the invention has the beneficial effects that: the mth beacon is used as a reference, j times of mth beacons can be detected, the azimuth angle detected every time is obtained, and the corresponding steering angle of the robot when the rotary table rotates once is further calculated. And because the rotating speed of the rotary table is constant, the angle of the robot steering corresponding to the rotation of the rotary table for x times, namely the angle of the robot rotating once, is obtained. In conclusion, the rotation angle calculated by the rotation angle measuring method of the robot provided by the invention is more accurate.
Drawings
FIG. 1 is a schematic view of a robot in a rotational state according to an embodiment of the present invention;
fig. 2 is a table showing the rotation angle of the robot according to the embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to specific embodiments shown in the drawings. These embodiments are not intended to limit the present invention, and structural, methodological, or functional changes made by those skilled in the art according to these embodiments are included in the scope of the present invention.
In the various illustrations of the present application, certain dimensions of structures or portions may be exaggerated relative to other structures or portions for ease of illustration and, thus, are provided to illustrate only the basic structure of the subject matter of the present application.
Also, terms used herein such as "upper," "above," "lower," "below," and the like, denote relative spatial positions, and are used for ease of description to describe one element or feature's relationship to another element or feature as illustrated in the figures. The spatially relative positional terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below" or "beneath" other elements or features would then be oriented "above" the other elements or features. Thus, the exemplary term "below" can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
In this context, unless otherwise specified, m, n, x, i, j, k are all positive integers.
As shown in fig. 1, the present invention discloses a robot including a working mechanism (not shown), a housing 10, and a traveling mechanism (not shown) provided in the housing 10. The robot further comprises a turntable rotatably provided in the housing 10 and an electronic sensing assembly provided in the turntable. Generally, the housing 10 includes a base plate on which the traveling mechanism is provided and an upper cover provided on the base plate to cover the working mechanism, and the turntable is rotatably provided on the upper cover.
The walking mechanism comprises four walking wheels, wherein the four walking wheels are rotatably arranged on the chassis. And the four walking wheels are symmetrically arranged.
In the preferred embodiment, the robot is a mowing robot, and specifically, the working mechanism is a cutting mechanism (not shown) for mowing. The cutting mechanism includes a cutting blade or a mowing line. Of course, the robot may be other types of robots such as a sweeping robot. In addition, the working mechanism is arranged on the chassis or the upper cover.
The robot has a working boundary, the preferred embodiment also provides a rotation angle measuring method of the robot, n beacons 20 for induction of the induction component are provided at the working boundary of the robot; typically, n.gtoreq.3; and a control module electrically connected with the sensing assembly is provided; specifically, the sensing assembly includes a laser signal transmitter and a laser signal receiver, and the beacon 20 is an anti-cursor. The sensing assembly transmits laser signals around the robot and receives laser signals reflected back by the beacon 20.
In the working process of the robot, the robot needs to turn in situ due to the influence of obstacles on obstacle avoidance or working requirements. Azimuth angle theta for a certain beacon 20 before robot turns 1 The azimuth angle after the pivot steering action is theta 2 Then the steering angle delta theta of the robot is equal to theta 21 If Δ θ is a positive value, the robot rotates clockwise, specifically as shown in fig. 1, an arrow D1 is a steering direction of the robot, an arrow D2 is a rotating direction of the turntable, H0 is a heading before steering of the robot, and H1 is a heading after steering of the robot; otherwise, the robot rotates anticlockwise. The "azimuth angle for a beacon" as used herein refers to the angle between the line connecting the rotation center of the robot to the beacon and the robot heading H0. The method is characterized in that in the one-time steering process of the robot, the rotary table finishes x rotation periods, namely the rotary table drives the laser signal transmitter and the laser signal receiver to rotate x times.
The control module can record the position of the reflective marker when the laser signal receiver receives the laser signal reflected by the reflective marker, namely the angle between the position of the reflective marker and the direction right ahead of the robot course; specifically, the control module determines that the rotation angle of the turntable is the included angle between the beacon direction and the robot heading when the turntable detects the beacon 20. Here, the rotation angle of the turntable is defined as an angle rotated between an initial position of the turntable to a position at which the beacon 20 is detected. In this embodiment, the initial position of the turntable is the position of the laser transmitter facing the navigation direction of the robot. When the robot turns in place, the azimuth angle formed for a certain cursor will change accordingly. The steering angle of the robot can be obtained by calculating the azimuth angle for a particular cursor.
At m thFor the beacon 20 as a reference, for the m (1 ≦ m ≦ n) th beacon 20, during one turning of the robot, the turntable totally completes x rotation periods, that is, the beacon 20 can be detected at most x times, that is, the m-th beacon 20 can be detected at most x times. Thus, x azimuthal variation values can be theoretically obtained: delta theta m1 ,Δθ m2 ,…,Δθ mx . According to the algorithm, the azimuth angle change value refers to the difference value between the current azimuth angle and the last azimuth angle. But due to obstacles or other reasons the beacon 20 will not be detected and the corresponding azimuth angle will not be available each time during the turn of the robot. Since the rotating speed of the turntable and the rotating speed of the robot in one turning process are both basically constant, the sensing assembly detects that the mth beacon 20 obtains the laser signal reflected by the beacon 20 in the ith rotating period of the turntable. According to the laser signal, the control module processes the laser signal to obtain an azimuth angle
Figure GDA0003690234270000061
The calculated value of the steering angle of the robot by the mth beacon 20
Figure GDA0003690234270000062
1≤i≤x,1≤k m J is more than or equal to x. Wherein m is the mth beacon 20, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m Means that the k-th time a valid signal from the mth beacon 20 is obtained, and j means that j times of the mth beacon 20 are detected in total in one robot turning process.
As specifically illustrated below, further reference is made to an embodiment set forth in fig. 2, wherein,
i columns: confirming that the rotary table is in the ith rotation period when the specific beacon signal is obtained;
k m the method comprises the following steps: recording the number of sequences confirming receipt of a reflected signal from the m-th beacon;
Δθ mx the method comprises the following steps: a theoretical azimuthal variation value;
Figure GDA0003690234270000063
the method comprises the following steps: the theoretical azimuth angle is obtained in the table according to the following algorithm
Figure GDA0003690234270000064
In this embodiment, during a turning process of the robot, the turntable drives the laser signal transmitter and the laser signal receiver to complete 10 rotation cycles, that is, x is 10. With reference to the 1 st beacon 20, that is, m is 1, the laser signal receiver thereof confirms that the 1 st beacon 20 is detected in the 2 nd, 5 th, 7 th and 8 th rotation periods of the turntable, so that the laser signal receiver detects the signal of the 1 st beacon 20 4 times, that is, k is 1 when i is 2, k is 2 when i is 5, k is 3 when i is 7, and k is 4 when i is 8; and measure
Figure GDA0003690234270000065
Then
Figure GDA0003690234270000066
Therefore, the estimated steering angle of the robot is 100.007 degrees with reference to the 1 st beacon 20.
With reference to the 2 nd beacon 20, that is, x is 10 and m is 2, the laser signal receiver thereof detects the 2 nd beacon 20 in the 3 rd, 4 th and 10 th rotation periods of the turntable, so that the laser signal receiver detects the signal of the 2 nd beacon 20 3 times, that is, k is 1 when i is 3, k is 2 when i is 4, and k is 3 when i is 10; and measure
Figure GDA0003690234270000071
Then
Figure GDA0003690234270000072
Therefore, the estimated steering angle of the robot is 100.001 degrees with reference to the 2 nd beacon 20.
With reference to the 3 rd beacon 20, that is, x is 10, m is 3, the laser signal receiver thereof detects the 3 rd beacon 20 in the 1 st, 2 nd, 5 th, 6 th and 9 th rotation periods of the turntable, so that the laser signal receiver detects the signal of the 3 rd beacon 20 for 5 times, that is, k is 1 when i is 1, and k is 2 when i is 22, k is 3 when i is 5, k is 4 when i is 6, and k is 5 when i is 9; and measure
Figure GDA0003690234270000073
Figure GDA0003690234270000074
Then
Figure GDA0003690234270000075
Therefore, the estimated steering angle of the robot is 100.013 degrees with reference to the 3 rd beacon 20.
In the preferred embodiment, the mth beacon 20 is defined as a reference, and j times of the mth beacon 20 can be detected, and the angle change value detected each time is obtained, so that the corresponding robot steering angle when the turntable rotates once is calculated. And because the rotating speed of the rotary table is constant, the angle of the robot steering corresponding to the rotation of the rotary table for x times, namely the angle of the robot rotating once, is obtained. In conclusion, the rotation angle calculated by the rotation angle measuring method provided by the robot is more accurate.
Further, defining that the sensing component can detect p beacons 20 in one steering process of the robot, wherein p is more than or equal to 1 and less than or equal to n, and the steering angle of the robot is
Figure GDA0003690234270000076
That is, the steering angle values calculated with reference to each beacon 20 are averaged to obtain the steering angle value of the robot. Thus, the calculated rotation angle of the robot is more accurate. Specifically, in the present embodiment, if 3 beacons 20 of the 1 st, 2 nd and 3 rd are detected in total as an example, the steering angle value of the robot is
Figure GDA0003690234270000077
A second preferred embodiment of the present invention is a specific case of the first preferred embodiment, and in this embodiment, p is n, x is 1, i is 1, and k is 1. When the robot is turning in place, the azimuth angle formed for the mth beacon 20 will followThe angle change value Delta theta can be obtained for the beacon 20 on the basis of keeping the identification of the beacon 20 m . In particular, in the embodiment defined in the present invention, in one pivot steering of the robot, n beacons 20 can be detected once, that is, x is 1, so that an angle change value Δ θ can be obtained for each beacon 20 m Then the robot rotates by an angle of
Figure GDA0003690234270000081
A third preferred embodiment of the present invention is another specific aspect of the first preferred embodiment, and in this preferred embodiment, n-1, m-1, k-1, and j-1. And in one pivot turning of the robot, the turntable drives the beacon 20 to complete x rotation cycles, so that the beacon 20 is still detected x times, and the rotation rate of the turntable is set to be constant, so that the angle change is uniform within equal time intervals, namely, the angle change values within the same time interval are the same. When detecting the change of the rotation angle in the rotation process by adopting a certain equal interval frequency, it is assumed that the beacon 20 can be identified only at a certain detection moment in the whole rotation process, that is, only the azimuth recorded by the beacon 20 in the ith rotation period of the turntable is detected and recorded as delta theta 1i1 . And because the azimuth angle change value in each detection is constant, the rotation angle of the robot is
Figure GDA0003690234270000082
Wherein Δ θ 1i1 The leftmost 1 in the subscript of (a) refers to a beacon 20, i refers to the i-th rotation period of the turntable at which the particular beacon signal is acknowledged, and the rightmost 1 refers to the resulting primary valid signal.
For example, if the beacon 20 is detected 10 times during one turn of the robot, 10 angular variations will theoretically be generated. However, only the first detection can determine that the signal angle change value comes from the beacon 20, and the following 9 times cannot determine whether the signal angle change comes from the beacon 20. The change in angle at the time of the first discernment can be recorded as delta theta 111 . And because it is known that x is experienced in totalAnd (5) secondary detection. From the previous setting, assuming that the angle change value at each subsequent detection is constant and the same as the first change value, the rotation angle of the robot can be finally estimated as,
Figure GDA0003690234270000083
it should be understood that although the present description refers to embodiments, not every embodiment contains only a single technical solution, and such description is for clarity only, and those skilled in the art should make the description as a whole, and the technical solutions in the embodiments can also be combined appropriately to form other embodiments understood by those skilled in the art.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.

Claims (10)

1. The utility model provides a robot, the robot includes operating device, casing, locates the running gear of casing, rotationally locate the revolving stage of casing with locate the response subassembly of revolving stage, the robot has work boundary, its characterized in that: the robot further comprises n beacons which are arranged on the working boundary and used for sensing the sensing assembly, the rotating table is defined to rotate for x times in the steering process of the robot, the rotating speed of the rotating table is constant, and the azimuth angle recorded by the mth beacon in the ith rotating period of the rotating table is detected to be
Figure FDA0003690234260000011
Defining a calculated value Δ θ for an angle of steering of the robot with reference to the m-th beacon m An angle Δ θ for turning the robot, an
Figure FDA0003690234260000012
Wherein m is the mth beacon, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m The effective signal of the mth beacon is obtained for the kth time, j refers to the mth beacon detected for the j times, i is more than or equal to 1 and less than or equal to x, k is more than or equal to 1 and less than or equal to j, j is more than or equal to 1 and less than or equal to x, and the azimuth angle refers to the included angle between the connection line from the rotation center of the robot to the mth beacon and the heading (H0) of the robot.
2. The robot of claim 1, wherein: defining that in the steering process of the robot, the sensing assembly can detect p beacons, wherein p is more than or equal to 1 and less than or equal to n, and the steering angle of the robot is
Figure FDA0003690234260000013
3. The robot of claim 1, wherein: defining that the n beacons are all detected in the steering process of the robot, and the steering angle of the robot is
Figure FDA0003690234260000014
4. The robot of claim 1, wherein: the number of the beacons n is set to be 1, the beacons are detected x times in the steering process of the robot, the change value of the azimuth angle in each detection is defined to be constant, and only the fact that the azimuth angle recorded in the ith rotation period of the rotary table of the beacon is delta theta is detected 1i1 Then the angle at which the robot turns is
Figure FDA0003690234260000015
5. A robot as claimed in any of claims 1 to 4, characterized in that: the sensing assembly comprises a laser signal transmitter and a laser signal receiver, and the beacon is a cursor reflecting body.
6. A robot as claimed in any of claims 1 to 4, characterized in that: the working mechanism is a cutting mechanism for mowing.
7. A rotation angle measuring method of a robot comprises a working mechanism, a shell, a traveling mechanism arranged on the shell and a rotary table rotatably arranged on the shell, and comprises the following steps:
providing an induction assembly on the turntable;
providing n beacons for the sensing component to sense at a working boundary of the robot;
providing a control module electrically connected with the sensing assembly;
the method is characterized in that in the process of one-time steering of the robot, the rotary table performs x rotation periods in total, the rotation speed of the rotary table is constant, the sensing assembly detects that the mth beacon is in the ith rotation period of the rotary table and records an angle signal, and the azimuth angle of the angle signal processed by the control module is
Figure FDA0003690234260000021
Defining a calculated value delta theta for the angle at which the robot is steered with reference to the mth beacon m Is an angle Delta theta of rotation of the robot, an
Figure FDA0003690234260000022
Wherein m is the mth beacon, m is more than or equal to 1 and less than or equal to n, i is the i-th rotation period of the rotary table when the specific beacon signal is confirmed, k is m The effective signal of the mth beacon is obtained for the kth time, j refers to the mth beacon detected for the j times, i is more than or equal to 1 and less than or equal to x, k is more than or equal to 1 and less than or equal to j, j is more than or equal to 1 and less than or equal to x, and the azimuth angle refers to the included angle between the connection line from the rotation center of the robot to the mth beacon and the heading (H0) of the robot.
8. The rotation angle measuring method of a robot according to claim 7, characterized in that: is defined inIn the steering process of the robot, the sensing assembly can detect p beacons, wherein p is more than or equal to 1 and less than or equal to n, and the steering angle of the robot is
Figure FDA0003690234260000023
9. The rotation angle measuring method of a robot according to claim 7, characterized in that: the number of the beacons n is set to be 1, the beacons are detected x times in the steering process of the robot, the change value of the azimuth angle in each detection is defined to be constant, and only the fact that the azimuth angle recorded in the ith rotation period of the rotary table of the beacon is delta theta is detected 1i1 Then the angle at which the robot turns is
Figure FDA0003690234260000031
10. The rotation angle measuring method of a robot according to any one of claims 7 to 9, characterized in that: the working mechanism is a cutting mechanism for mowing.
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