JP2012024872A - Legged walking robot and method for determining foot trajectory of the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for determining the foot trajectory of a legged robot so as to prevent the load on an actuator from becoming excessive.SOLUTION: The method for determining the foot trajectory of a legged walking robot, includes a path determination step and a one step time determination step. The path determination step determines a motion path of a foot from a takeoff position to a landing position along which the foot moves. The one step time determination step evaluates a value as an one step time necessary for the foot to takeoff and land by dividing the length of the motion path by an average motion speed of the foot. The determined motion path and the one step time correspond to the foot trajectory.

Description

  The present invention relates to a legged walking robot. In particular, the present invention relates to a technique for determining a foot trajectory of a legged walking robot.

  A legged walking robot, particularly a biped robot, will fall down unless the landing position and landing timing of the foot are properly determined. Hereinafter, in this specification, “walking without falling” is expressed as “walking stably”. “Stable” here means different from “stable” in control theory. “Stable” in the walking of a legged walking robot is calculated (simulated) that the position and speed of the center of gravity of the legged walking robot stay within a predetermined range at least one step or several steps ahead. Means that

  For simplicity, the legged walking robot may be simply referred to as “robot” below. A ZMP equation is often used to determine the landing position and landing timing of a foot for stable walking. Also, the landing timing corresponds to the time required from the time when the foot leaves the ground until the landing. Hereinafter, in this specification, the time required for the foot to take off and land is sometimes referred to as “one step time”. Since the one-step time corresponds to the walking speed, keeping the walking speed constant is essentially equivalent to keeping the one-step time constant. In normal walking, it is desirable to keep the walking speed constant.

  When there is an unscheduled obstacle on the walking route, it may be required to appropriately change the landing position and landing timing from the original schedule. However, changing the landing position and landing timing immediately before landing of the free leg may impair stability. Thus, for example, Patent Document 1 discloses a technique for gradually decreasing the walking speed (one step time) according to the distance to the obstacle. Patent Document 1 discloses a technique for reducing the stride of a robot according to not only the walking speed but also the distance to the obstacle. Japanese Patent Application Laid-Open No. 2004-228688 discloses a technique for making the landing timing earlier than planned when the robot is further tilted forward than the planned posture. Advancing the landing timing is equivalent to shortening the one-step time.

JP 2007-160438 A JP-A-5-254465

  There is a possibility that inconvenience may occur if only one step time is changed depending on the situation. For example, shortening the one-step time may impose a high load on the actuator. This is because shortening the one-step time leads to an increase in the moving speed of the foot, which in turn requires a high output from the actuator. Also, if the foot movement path is made longer than planned in order to cross over the detected obstacle, the foot movement speed will be excessive if the one-step time is constant, which will also apply a high load to the actuator. It might be. The present specification provides a technique for determining a step time so that a load on an actuator is not excessive in a legged walking robot.

  From the above facts, it is understood that the load on the actuator in the swing leg depends on the relationship between the foot movement path from the takeoff position to the landing position and the time of one step. The inventor of the present application has obtained the idea of determining the one-step time based on the movement path of the foot from the takeoff position to the landing position from the above knowledge. It should be noted that the “movement path” means a path through which the foot passes and is a concept that does not depend on the moving speed (that is, time). Furthermore, it should be noted that the “trajectory” described later is a concept including a “movement path” and a passing time of each point on the movement path.

  One of the techniques disclosed in this specification provides a method for determining a foot trajectory of a legged walking robot. The method includes a route determination step and a one-step time determination step. The route determination step determines a foot movement route from a foot separation position to a landing position in walking. In the one-step time determination step, a time required for the foot to take off after landing (that is, one step time) is determined. Specifically, the one-step time is obtained by dividing the length of the foot movement path by a predetermined average foot movement speed. The average moving speed is determined in advance from physical constraints such as the maximum output of a motor provided in the leg joint. Also, typically, when the travel route becomes longer than the planned length, the one-step time is made longer than the planned length.

  Various variations can be assumed for the movement route from the takeoff position to the landing position. Therefore, in order to uniquely determine the movement route, the route determination step preferably includes the following passage position setting step, interpolation step, and integral calculation step. The passing position setting step sets a scheduled passing position that the foot should pass from the takeoff position to the landing position. In addition, what is necessary is just to determine a plan passage position according to the height from a road surface (an obstacle is included), for example. In the interpolation step, a movement route from the takeoff position to the landing position through the planned passing position is obtained by an interpolation formula of the variable τ. Further, in the interpolation step, after setting as a constraint condition that the value of the interpolation equation corresponds to the expected passing position when the variable τ takes a specific value, the coefficient of the interpolation equation is determined so as to satisfy the constraint condition. In the integral calculation step, the length of the moving path is obtained by integrating the norm of the derivative of the interpolation formula.

  The interpolation formula may typically be a polynomial (interpolation polynomial) having a variable τ as a parameter. By introducing a “interpolation equation having a parameter τ” and a constraint condition related to a planned passing position, a preferable movement route can be determined prior to determining the one-step time.

  A preferred embodiment of the interpolation step is as follows. First, the distance of each line segment of the broken line that connects the planned passing positions to the landing position in the order of planned passing from the takeoff position is obtained. Next, the specific value of the variable τ at each position is determined in accordance with the ratio between the partial sum of the distances of the line segments from the takeoff position to each position and the sum of the distances of the line segments from the takeoff position to the landing position.

  As described above, the one-step time is determined by dividing the length of the moving route by a predetermined average moving speed of the foot. The estimated required time to reach each planned passing position is preferably determined to be a value obtained by dividing the length of the moving route from the take-off position to the planned passing position by the average moving speed of the foot. If the time is determined as such, the speed of the foot moving along the movement path can be suppressed to be approximately equal to or less than the average movement speed, so that an excessive load on the actuator can be suppressed.

  Another technique disclosed in the present specification provides a legged walking robot including a controller that executes the above-described foot trajectory determination method. The robot typically includes an obstacle sensor, and when changing the landing position based on the sensor data of the obstacle sensor, the step time is determined by the above-described foot trajectory determination method.

  According to the present invention, in the legged walking robot, one step time can be determined so that the load on the actuator is not excessive.

A schematic side view of a legged walking robot is shown. The flowchart of a leg trajectory determination process is shown. An example of a foot movement path is shown. The relationship between the line segment connecting the movement route and the planned passing position is shown.

  FIG. 1 shows a schematic side view of a legged walking robot 10. Hereinafter, for the sake of simplicity, the legged walking robot 10 is simply referred to as the robot 10. The robot 10 imitates a human structure and is a biped walking robot having a head 12, a trunk 14, and two legs 16L (left leg) and 16R (right leg). The leg has a multi-link multi-joint structure composed of a plurality of joints and links. The leg also resembles a human leg, with a thigh link connected to the lower part of the trunk by a joint equivalent to a hip joint, a lower leg link connected to a lower end of the thigh link by a joint equivalent to a knee, and a lower end of the lower leg link It has a foot link connected by a joint corresponding to the ankle. The robot 10 walks by appropriately controlling each joint of the leg. When walking, the robot 10 must determine the trajectory of the foot. The “foot trajectory” means a change with time of the foot position from the takeoff position to the landing position. In other words, the “foot trajectory” is represented by the foot movement path from the take-off position to the landing position and the time passing through each position on the movement path.

  The head 12 of the robot 10 includes a controller and an obstacle sensor. The obstacle sensor detects an obstacle ahead. Based on the sensor data of the obstacle sensor, the controller determines the trajectory of the foot so as to avoid the detected obstacle.

  FIG. 1 shows a moment when the right foot (right leg 16R) has just taken off. The robot 10 determines the trajectory of the foot before the right foot takes off. The trajectory of the foot here is the movement path Path that leaves the takeoff position P0 at the timing t0, passes through the planned passing positions P1 and P2, and finally reaches the landing position P3, and the time and landing that passes through each planned passing position. The time to reach position P3 is determined. The robot 10 has a feature in the process of determining the trajectory of the foot.

  FIG. 2 shows a flowchart of processing for determining the foot trajectory. First, the robot 10 determines scheduled passing positions P1 and P2 that a foot should pass between the take-off position P0 and the landing position P3 (S2). The planned passing position is appropriately determined according to, for example, the horizontal distance from the landing position P0 and the height from the floor (including obstacles). For example, the height of the planned passing position changes according to the height of the obstacle. As described above, the robot 10 detects an obstacle ahead by the obstacle sensor built in the head 12, and the controller determines the scheduled passage position based on the sensor data. There are various methods for determining the expected passing position.

  Next, the robot 10 determines a movement path Path from the takeoff position P0 through the scheduled passage positions P1 and P2 to the landing position P3 (S3). The robot 10 determines the movement path Path by interpolation processing. At this time, the robot 10 determines the movement path Path using an interpolation formula (interpolation polynomial) having the variable τ as a parameter. Now, in order to simplify the description, the description will be continued by limiting the movement path to the XZ plane of FIG. The X axis is determined along the traveling direction of the robot 10, and the Z axis is determined in a direction perpendicular to the walking surface. An example of the interpolation polynomial is given by the following (Equation 1). (Equation 1) is a cubic polynomial with respect to the variable τ.

In the above (Equation 1), f _x1 (τ) and f _z1 (τ) are interpolation polynomials for determining a partial movement path from the takeoff position P0 to the first planned passing position P1. _{Here, a x1, b x1, c} x1, d x1, a z1, b z1, c z1, d z1 are the coefficients of the interpolating polynomial are determined to satisfy the constraint condition to be described later. Similar to (Equation 1), interpolation polynomials f _x2 (τ), f _z2 (τ), and f _z2 (τ) for determining a partial movement path between the first planned passage position P1 and the second planned passage position P2, and Interpolation polynomials f _x3 (τ) and f _z3 (τ) for determining a partial movement path between the second planned passing position P2 and the landing position P3 are prepared in advance. Like (Equation 1), each interpolation polynomial has its own coefficient. Dividing the movement path Path from the takeoff position P0 to the landing position P3 into a plurality of partial paths, and expressing each partial path with different interpolation polynomials is called piecewise polynomial approximation (Piecewise-Polynomial Approximation). This is a well-known technique. In FIG. 3, the interpolating polynomials f _x1 (τ), f _x2 (τ), f _x3 (τ), f _z1 (τ), f _z2 (τ), and f _z3 (τ) of the _parameter τ are represented. An example of the movement route Path is shown. In FIG. 3 and the following description, the coordinates of the landing position P0, the first planned passing position P1, the second planned passing position P2, and the landing position P3 are respectively (x ₀ , z ₀ ), (x ₁ , z ₁ ), (x ₂ , z ₂ ), (x ₃ , z ₃ ). These coordinates are obtained when the takeoff position P0, the landing position P3, and the planned passing positions P1 and P2 are determined.

The movement path Path must be determined unless the coefficient (a _x1 etc.) of the interpolation polynomial is determined. Next, a process for determining the coefficient a _{x1 of the} interpolation polynomial will be described. The coefficient a _{x1 and the} like can be determined by giving some constraint condition to the interpolation polynomial. First, each partial polynomial must be contiguous with the adjacent partial interpolation polynomial at its ends. That is, the value of the derivative at the end of f _x1 (τ) must match the value of the first derivative of the start of f _x2 (τ). These give boundary conditions to be continuous.

  A condition is added that the value of the first derivative of the interpolation polynomial at the takeoff position P0 and the landing position P3 is zero. In other words, the condition that the first derivative is zero at both ends is given as the boundary condition of the interpolation polynomial. Specifically, this boundary condition is given by the following (Equation 2). This condition ensures that the foot is stationary at the takeoff position P0 and the landing position P3.

Next, a value (specific value) to be taken by the parameter τ at the scheduled passage positions P1 and P2 is determined. In other words, the constraint condition is that the value of the interpolation polynomial corresponds to the expected passing position when the parameter τ takes a specific value. The robot 10 determines the coefficient so as to satisfy the above-described boundary condition and the constraint condition that the value of the interpolation polynomial corresponds to the planned passing positions P1, P2 and the landing position P3 when the variable τ is a specific value.

  Next, the process until the coefficient is determined will be specifically described. The robot 10 obtains the distances D1, D2, and D3 of the broken line connecting the planned passing positions P1, P2 to the landing position P3 in the order of planned passing from the takeoff position P0, and from the takeoff position P0 to each position. The specific value at each position is determined according to the ratio between the partial sum of the distances of the line segments and the sum of the distances of the line segments from the takeoff position P0 to the landing position P3. FIG. 4 shows the relationship between the movement path Path and the line segment connecting each position. Reference sign D1 indicates the distance of a line segment connecting the takeoff position P0 and the first planned passing position P1. Reference sign D2 indicates the distance of a line segment connecting the first planned passage position P1 and the second planned passage position P2. Reference sign D3 indicates the distance of a line segment connecting the second planned passing position P2 and the landing position P3. The partial sum of the distance from the takeoff position P0 to the first planned passage position P1 is represented by D1. The partial sum of the distance from the takeoff position P0 to the second planned passing position P2 is represented by D1 + D2. The total distance from the takeoff position P0 to the landing position P3 is represented by D1 + D2 + D3. Therefore, the specific value τ1 that the parameter τ should take when the value of the interpolation polynomial corresponds to the first passage position P1, the specific value τ2 that the parameter τ should take when it corresponds to the second passage position P2, and the landing The specific value τ3 to be taken by the parameter τ when it corresponds to the position P3 is expressed by the following (Equation 3).

The coefficient a _x1 of the interpolation polynomial of (Equation 1) can be determined using (Equation 3), the constraint condition, and the previous boundary condition. That is, the polynomial f _x1 (τ) of the parameter τ is determined. The graph of FIG. 3 is a graph determined by the determined coefficient a _x1 or the like. Thus, the movement path Path is determined.

  Returning to FIG. 2, the description of the process of determining the foot trajectory will be continued. After determining the movement path Path, the robot 10 calculates the length of the movement path Path (S4 in FIG. 2). Specifically, the length of the movement path Path is obtained by integrating the norm of the derivative of the interpolation formula. This process will be specifically described. Hereinafter, for the sake of explanation, the section between the takeoff position P0 and the first planned passage position P1 is section 1, the section between the first planned passage position P1 and the second planned passage position P2 is section 2, and the second planned passage A section between the position P2 and the landing position P3 is referred to as a section 3. The length L1 of the section 1 is obtained by integrating the norm of the derivative of the interpolation polynomial whose coefficient is obtained (Equation 4). Note that the length L2 of the section 2 and the length L3 of the section 3 are also obtained in the same manner as (Expression 4).

By calculating the integral calculation regarding L1 (and L2, L3) by numerical integration, it is possible to calculate the length (L1 etc.) of the foot movement path in each section. Numerical integration can be performed at high speed by using a known calculation method such as trapezoidal rule or Simpson rule. However, it is preferable to use a value that is sufficiently smaller than the interval between τ ₁ , τ ₂ , and τ ₃ previously calculated for the integral step size. According to the above calculation, the length of the smooth curve (that is, the movement path Path) is obtained in which the speed becomes zero at the takeoff position P0 and the landing position P3 and passes through all the planned passing positions.

Next, the robot 10 calculates the one-step time T using the calculated length (path length) of the movement path Path (S5 in FIG. 2). The one-step time T means a required time from the foot taking off until landing. The robot 10 obtains the required time from the takeoff timing to each scheduled passing position point and the required time to landing based on the predetermined average moving speed v _av of the foot and the path length. Then, the robot 10 employs a trajectory determined by the determined moving path Path and the required time to each scheduled passing position as the foot trajectory (S9).

The process for determining the required time (one step time) will be specifically described. The one-step time T is determined so as to increase in proportion to the length of the movement route. Here, the average moving speed v _av of the foot is used as the proportionality constant. The average moving speed v _av is determined in advance from physical restrictions such as the maximum output of the motor of the robot 10. The timing t1 for passing through the first scheduled passage position P1, the timing t2 for passing through the second scheduled passage position P2, and the timing for reaching the landing position P3 (ie, one step time T) are obtained by the following (Equation 5). .

As is clear from (Equation 5), the robot 10 determines a value obtained by dividing the length of the movement path by the average movement speed v _av of the foot as one step time. In addition, the robot 10 determines a value obtained by dividing the length of the moving path from the takeoff position P0 to each planned passing position by the average foot movement speed v _av as the planned passing time of each planned passing position.

  Finally, the robot 10 determines whether or not the one-step time T obtained in (Equation 5) is greater than a predetermined threshold Th (FIG. 2, S6). The threshold value Th is equivalent to one step time for steady walking. When the one-step time T is smaller than the threshold value Th, the robot 10 adopts the threshold value Th as a required time required for movement of the movement path Path (S7), and when the one-step time T is larger than the threshold value Th, the one-step time calculated in step S5. T is adopted as the required time (S8). This process is predetermined when the calculated one-step time T is smaller than the threshold Th, that is, when it is possible to move from the take-off position P0 to the landing position P3 earlier than the one-step time Th during normal walking. Means to move from the takeoff position P0 to the landing position P3 at the time Th. On the other hand, when it is not possible to move from the takeoff position P0 to the landing position P3 without taking a longer time than the one-step time Th of the normal walking (in this case, the calculated length of the movement path Path is the initial expected length) This corresponds to a case where the movement is determined from the take-off position P0 to the landing position P3 over the calculated one-step time T instead of the predetermined one-step time Th.

(Equation 5) means that the time required for the foot to move from the takeoff position P0 to the landing position P1 (one step time) is determined in proportion to the length of the movement path Path. The proportionality constant is given by the reciprocal of the average movement speed v _av of the foot. The movement path Path thus obtained and the passage times t1, t2, and T at each scheduled passage position are employed as the movement trajectory of the leg of the free leg. During walking, the robot 10 generates time-series data of the angles of the joints so that the feet move along the movement trajectory, and controls the joints.

  Through the above processing, the robot 10 sets a longer time for the movement as the moving path of the leg of the free leg becomes longer. By setting in such a manner, the robot 10 avoids the generation of a moving trajectory that has to move along a long moving path at an excessive speed. That is, the robot 10 can determine the foot trajectory so that the load of the actuator that drives the joint of the leg is not excessive.

  Points to be noted in the foot trajectory determination process of the embodiment will be described. Step S2 in FIG. 2 corresponds to a scheduled passage position setting step. Step S3 in FIG. 2 corresponds to an interpolation step. Step S4 in FIG. 2 corresponds to an integration calculation step. The processing from step S2 to S4 in FIG. 2 corresponds to a route determination step. Step S5 in FIG. 2 corresponds to a one-step time determination step.

  In the embodiment, the leg movement path is limited to the XZ plane in order to simplify the explanation. It should be noted that the movement path Path can actually be determined in a three-dimensional space. Further, the above-described processing is executed by a controller built in the head 12 of the robot 10.

  1 and 4, the position of the foot is represented by a point fixed to the tip of the foot, and the movement path of the foot is represented by a path along which the representative position of the foot moves. Any point may be selected as long as it is a point representing the position of the foot or a point on the coordinate system fixed to the foot. In the embodiment, two scheduled passage positions P1 and P2 are assumed. The number of scheduled passage positions to be set may be less than two or more than two.

  In the embodiment, the one-step time T is determined simply in proportion to the length of the leg movement path Path. The load applied to the leg joint depends on the distance (height) from the floor of the foot trajectory. That is, the higher the movement path, the greater the load on the leg joint. Therefore, when calculating the length of each section, it is also preferable to add a weight kz in the z direction of the foot position as represented by the following (Equation 6).

  (Equation 6) is an expression for determining a virtual section length for determining one step time, not the actual length of each section of the movement route. By adopting (Equation 6) instead of (Equation 4), the one-step time (and the time until it passes through each scheduled passage position) is set longer as the height of the movement route is higher.

The process for obtaining the one-step time according to (Equation 5) can be expressed as follows. That is, the one-step time determination step includes a required time determination step and a foot trajectory determination step. The required time determining step is based on the predetermined average moving speed v _av of the foot and the length of the moving path Path, and the required time (t1, t2) from the take-off timing to the scheduled passing position and the landing The required time (T) is obtained. In the foot trajectory determination step, a trajectory determined by the determined travel route Path and the required time (t1, t2, T) to each planned passing position is adopted as the foot trajectory.

  Specific examples of the present invention have been described in detail above, but these are merely examples and do not limit the scope of the claims. The technology described in the claims includes various modifications and changes of the specific examples illustrated above. The technical elements described in this specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the technology exemplified in this specification or the drawings can achieve a plurality of objects at the same time, and has technical usefulness by achieving one of the objects.

10: Legged walking robot 12: Head 14: Trunk 16R, 16L: Leg

Claims (4)

It is a method for determining the leg trajectory of a legged walking robot,
A route determining step for determining a moving route of the foot from the foot landing position to the landing position;
One step time determination step for obtaining a value obtained by dividing the length of the moving route by a predetermined average moving speed of the foot as a step time required for the foot to take off after landing.
A foot trajectory determination method comprising: The route determining step includes:
A passing position setting step for setting a planned passing position where the foot should pass between the takeoff position and the landing position;
An interpolation step for obtaining a movement route from the takeoff position through the planned passing position to the landing position by an interpolation formula of the variable τ,
An integration calculation step of obtaining the length of the movement path by integrating the norm of the derivative of the interpolation formula;
Contains
In the interpolation step, after setting as a constraint condition that the value of the interpolation equation corresponds to the expected passing position when the variable τ takes a specific value, a coefficient of the interpolation equation is determined so as to satisfy the constraint condition. The foot trajectory determination method according to claim 1.   The interpolation step calculates the distance of each line segment of the broken line connecting the planned passing position to the landing position in the order of planned passing from the takeoff position, and calculates the partial sum of the distance of the line segment from the takeoff position to each position and the takeoff position. The trajectory determination method according to claim 2, wherein the specific value at each position is determined according to a ratio to a sum of distances of line segments to the landing position.   A legged walking robot comprising a controller for executing the trajectory determination method according to any one of claims 1 to 3.

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