Control method, control device and program

Abstract

A method for controlling a model of a control object in which a trajectory is an energy storage system including the steps of: calculating mechanical energy of the control object; determining a constraint condition of the trajectory leading to a posture in which the control object is desired to be moved; deriving an equation of motion from the constraint condition of the trajectory; and calculating force to be applied to the control object on the basis of the derived equation of motion.

Description

Control method, control device, and program

[0001] The present invention relates to a control method, a control device, and a program. This application claims priority under Japanese Patent Application No. 2024-168529, filed on 27 September 2024, the contents of which are incorporated herein by reference.

[0002] For example, in the control of bipedal robots, whole-body control and low-dimensional models have been considered. Whole-body control is computationally expensive, making online planning difficult. On the other hand, low-dimensional models are simpler than whole-body control, and for example, a linear inverted pendulum model (LIP) has been proposed in which the height of the center of gravity is constant, i.e., the trajectory is constrained to be linear. Furthermore, control methods using a nonlinear inverted pendulum model with a variable center of gravity have also been proposed (see, for example, Patent Document 1).

[0003] In the linear and nonlinear inverted pendulum models described above, various methods have been proposed for obtaining analytical solutions in motion planning for control. Conventional methods propose conditions under which the solution to the differential equation becomes closed form by introducing a specific external force into the equation of motion. Note that the energy in the equation of motion includes an integral term. Therefore, in the linear inverted pendulum model, the constraint condition that the trajectory of the center of mass is linear results in an analytical solution without a remaining integral term. Furthermore, the method described in Patent Document 1 determines the swing leg trajectory during walking from the external force conditions under which the integral of the motion can be determined. Note that a system energy expression without an integral term is called a conservative system. A system being a conservative system is a sufficient condition for the system's motion to be determined analytically.

[0004] Patent Application No. 2024-040334

[0005] However, with conventional techniques, the trajectories that can serve as constraints to prevent the integral term from remaining are limited, making it difficult to control the trajectory using an arbitrary trajectory.

[0006] The present invention has been made in view of the above-mentioned problems, and aims to provide a control method, a control device, and a program that can realize any trajectory.

[0007] To achieve the above objective, the control method, control device, and program according to this invention employ the following configuration: (1) A control method according to one aspect of the present invention is a control method for a model of a controlled object in which the trajectory is an energy conservation system, comprising the steps of: calculating the mechanical energy of the controlled object; determining constraint conditions for the trajectory to reach the desired attitude of the controlled object; deriving equations of motion from the constraint conditions of the trajectory; and calculating the force to be applied to the controlled object based on the derived equations of motion.

[0008] (2) In the control method according to one embodiment of (1) above, the constraint conditions for the trajectory may be determined by determining the points through which the trajectory passes and the target acceleration at each point, and calculating the target trajectory from the points through which it passes.

[0009] (3) In the control method according to one embodiment of (1) or (2) above, the constraint conditions of the trajectory may be calculated from the resultant force of vectors calculated from the trajectories projected onto the control target plane, respectively.

[0010] (4) In any one embodiment of the control method described in (1) to (3) above, the model of the object to be controlled, or the medium that applies force to the model of the object to be controlled, may have a plurality of movable parts, and the force to be applied to the object to be controlled may be a resultant force, which is decomposed into the forces of each of the plurality of movable parts for control.

[0011] (5) In a control method according to one embodiment of (1) or (2) above, the constraint conditions for the trajectory are determined by projecting the calculated three-dimensional target trajectory of the controlled object onto two two-dimensional planes, and determining the first trajectory of the projected first plane (for example, T ｘｙ ) and the second trajectory of the second plane (for example, T ｘｚ ) may be a constraint force (for example, f) that is generated at the center of gravity of the controlled object in order to achieve the target motion. ｎｏｒ ) may be determined using the first and second orbitals.

[0012] (6) In any one embodiment of the control method described in (1) to (5) above, for the center of gravity of the controlled object to be constrained to the target trajectory of the center of gravity of the controlled object, when the external force acting on the point mass of the controlled object is decomposed into a normal component and a tangential component in the target trajectory, the normal component is constrained to the constraint condition (for example, constraint force f nor ) is equal to and, in order for the trajectory to be an energy conservation system, a tangential force (for example f) acts in the tangential direction to the center of mass of the controlled object. ｔａｎ ) may be a preservative.

[0013] (7) A control device according to one aspect of the present invention is a control device that performs a control method for a model of a controlled object in which the trajectory is an energy conservation system, and comprises a control unit, the control unit calculates the mechanical energy of the controlled object, determines the constraint conditions of the trajectory to reach the desired attitude of the controlled object, derives the equation of motion from the constraint conditions of the trajectory, and calculates the force to be applied to the controlled object based on the derived equation of motion.

[0014] (8) A program according to one aspect of the present invention causes a computer of a control device that executes a control method for a model of a controlled object whose trajectory is an energy conservation system to calculate the mechanical energy of the controlled object, determine the constraint conditions of the trajectory to reach the desired attitude of the controlled object, derive the equation of motion from the constraint conditions of the trajectory, and calculate the force to be applied to the controlled object based on the derived equation of motion.

[0015] According to the embodiments described in (1) to (8) above, control in any trajectory becomes easier.

[0016] This figure shows an example of an arbitrary nonlinear position orbit. This figure shows an example of a model that satisfies a conservative system. This figure shows an example of projecting the orbit onto the xy-plane and the xz-plane. f ｍｏｄｅｌ , restraining force f ｎｏｒIt is a diagram showing relationships such as etc. It is a diagram for explaining the equation of motion in the tangent direction. It is a diagram showing a configuration example of the control system of the embodiment. It is a flowchart of the processing procedure by the control device of the embodiment. It is a flowchart of the calculation procedure of the force to be applied to the target object in the control according to the embodiment. It is a diagram showing an example of the trajectory control of the center-of-gravity position during the walking of the robot. It is a diagram showing an example of moving the target object in a non-linear position trajectory with a multi-fingered hand.

[0017] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings used in the following description, the scales of each member are appropriately changed in order to make each member recognizable. In all the drawings for explaining the embodiments, those having the same function are denoted by the same reference numerals, and repeated explanations are omitted. Also, as used in the present application, "based on XX" means "based at least on XX", and includes cases based on other elements in addition to XX. Also, "based on XX" is not limited to the case of directly using XX, and includes cases based on those obtained by performing operations or processing on XX. "XX" is an arbitrary element (for example, arbitrary information).

[0018] <Explanation of the control method> FIG. 1 is a diagram showing an example of an arbitrary non-linear position trajectory. In FIG. 1, the symbol p ｃ is the center-of-gravity position of the control target object. The dashed line g1 is an example of an arbitrary non-linear position trajectory represented by the function f(p ｃ ). In the present embodiment, the control target is, for example, the torso of a walking robot, an object held by a hand, or the like. Also, in FIG. 1, the trajectory example is represented by the xz plane in the floor surface direction (x-axis direction) and the direction perpendicular to the floor (z-axis direction). Also, the trajectory example in FIG. 1 is a holonomic trajectory example whose constraint conditions can be described only by coordinates and time.

[0019] The equation of motion of the model (centroid dynamics model) obtained by applying an external force and a moment to the mass point of the pendulum is as shown in the following equation (1). In equation (1), m ｃ is the mass of the control target, I ｃ is the moment of inertia of the control target, θ ｃ is the inclination angle with respect to the coordinate system of the control target, g is the gravitational acceleration, fｅ τ is the external force applied to the controlled object. ｅ This is the torque applied to the controlled object. Also, superscript “ ・・ The symbol " represents the second derivative.

[0020]

[0021] Here, the energy E in the equation of motion ａｌｌ This can be expressed as shown in equation (2). In equation (2), T represents the transpose, and the superscript " ・ The symbol " represents the first derivative.

[0022]

[0023] Energy E of the linear model in the xz plane ａｌｌ This can be expressed as shown in equation (3) below.

[0024]

[0025] Here, in many cases where an analytical solution exists for an orbit, when the energy is transformed to the Cartesian coordinate system, the energy can be reduced to the form of equation (4) below. In equation (4), a and b are predetermined constants.

[0026]

[0027] In conventional techniques, the energy of the entire system can be determined if it can be decomposed into a point mass that behaves like an inverted pendulum and into point masses whose behavior can be defined by an affine transformation. However, conventional techniques had the constraint that the point masses must be "point masses whose behavior can be defined by an affine transformation." Furthermore, conventional techniques took an approach of "decomposing the point mass" from the "orbit" and then "decomposing the point mass" to determine the "energy of the system."

[0028] In contrast, this embodiment employs an approach of "system energy" from the "orbit" and "constraint force decomposition (contact point decomposition)" from the "system energy". In this embodiment, by first deriving the energy of the entire system so that it is a conservative system, the need to decompose it into "point masses whose behavior can be defined by affine transformations" in order to make it a conservative system is eliminated.

[0029] Any trajectory in three-dimensional space can be expressed using two constraints. For example, a straight line passing through the origin and (1,1,1) can be expressed using two constraints as shown in equation (5).

[0030]

[0031] In the following, any trajectory in three-dimensional space will be expressed by the constraint equations for x and y and the constraint equations for x and z. In this case, the physical quantity relating to the energy of the entire system (corresponding to the Lagrangian of the system) is given by the following equation (7), where m is the mass and the constraint conditions are given by the following equation (6). Note that in equation (7), λ ｘｙ and λ ｘｚ This represents an unknown constant.

[0032]

[0033]

[0034] Since the physical quantities relating to the energy of this system satisfy the Euler-Lagrange equations, substituting equation (7) into the Euler-Lagrange equations yields the equation of motion shown in equation (8) below (same as the method of Lagrangian multipliers). Note that in equation (8), i = 1, 2, ..., p ｃ = {q １ ,q ２ ,...} Ｔ That is the case.

[0035]

[0036] As long as the constraint forces obtained here are followed, the above target attitude and target motion will be achieved passively. In the embodiment, these are called models. In the first equation of equation (8), equation (9), obtained from the right-hand side, corresponds to the constraint force on the constrained trajectory.

[0037]

[0038] Therefore, from the system of equations (8), λ ｘｙ and λ ｘｚ Taking into consideration that the following can be determined, the normal constraint force f that must be generated at the center of gravity in order to achieve the target motion is ｎｏｒ This can be found as shown in equation (10).

[0039]

[0040] In this embodiment, as shown in Figure 2, the force that must be generated at the center of gravity to achieve the target motion is f. ｍｏｄｅｌ , force f ｍｏｄｅｌ The component in the normal direction of the trajectory of the centroid position is f. ｔａｎ Figure 2 shows an example model that satisfies the requirements for a conservative system. In Figure 2, p ｄ The target position of the center of gravity on the target trajectory, l ｔａｎ l is the tangential direction at the center of gravity. ｎｏｒ The applied force f ｍｏｄｅｌ This is the normal direction at the center of gravity position passing through the endpoint position. The control device 3 (Figure 6) controls the three-dimensional target trajectory p ｄ point p on the orbit １ , p ２ , p ３ This can be calculated by interpolation, for example, using a spline curve or a higher-order function.

[0041] Equation (1) will be further explained using Figure 3. Figure 3 shows an example of projecting the trajectory onto the xy-plane and the xz-plane. As shown in Figure 3, the constrained trajectory T is realized by the constraint conditions. ｄ Let this be the following equation (11).

[0042]

[0043] At this time, T ｘｙ is the constrained trajectory T ｄ This is the orthogonal projection of T onto the xy-plane. ｘｚ is the constrained trajectory T ｄ This is the orthogonal projection onto the xz-plane. Furthermore, the constrained trajectory T ｄ The tangential direction at the point mass position is l ｄ Toshi, T ｘｙ and T ｘｚ The tangential direction at the point mass position is l ｘｙ ,l ｘｚ Therefore, these are in the tangential direction l ｄ This is an orthogonal projection. Therefore, each is in the tangential direction l. ｄ It lies on the same plane as shown in Figure 3, ▽T ｘｙ is T ｘｙ This represents the gradient, ▽T ｘｚ is Tｘｚ This represents the gradient. Therefore, these relationships can be expressed by the following equation (12).

[0044]

[0045] Furthermore, in the tangential direction l ｘｙ ,l ｘｚ Each is in the tangential direction l ｄ Since it lies on the same plane, ▽T ｘｙ ,▽T ｘｚ , l ｘｙ ,l ｘｚ The relationship is given by the following equation (13).

[0046]

[0047] From the above, the constraint force on an arbitrary trajectory (the second line of equation (10)) is given by the constraint trajectory T ｄ Given as such, it is the force generated in the direction of the normal vector. Also, the constraint force f in the direction of the normal vector. ｎｏｒ Since the energy contribution by is always zero, it is also guaranteed that the system will be a conservative system.

[0048] Thus, for the center of gravity to be constrained to the target trajectory, when the external force acting on the point mass is decomposed into a normal component and a tangential component in the target trajectory, the normal component is the constraining force f. ｎｏｒ It is a necessary and sufficient condition that it is equal to the external force f, which is the resultant force in the tangential direction. ｍｏｄｅｌ The endpoint is the line l in Figure 4. ｍｏｄｅｌ It can be said that it is good if it is at the top. Figure 4 is f ｍｏｄｅｌ , restraining force f ｎｏｒ This diagram shows the relationships between these factors.

[0049] Furthermore, according to the embodiment, the independently acting tangential force f ｔａｎ By designing the system to be a conservative system, it becomes possible to arbitrarily design the acceleration of movement on the constrained trajectory while keeping the system a conservative system. Note that the acceleration a in the tangential direction is ｔａｎ If we want to achieve this, the equation of motion in the tangential direction is given by equation (14) as shown in Figure 5. Figure 5 is a diagram illustrating the equation of motion in the tangential direction. In equation (14), ||・|| is the norm of "・", and <α,β> is a subgroup. Also, a ｔａｎThis represents the target acceleration of the trajectory. The target acceleration can be predetermined by the user, for example.

[0050]

[0051] The tangential external force component f that should be generated ｔａｎ This is given by the following equation (15).

[0052]

[0053] Note that the tangential direction l ｄ From the relationship in equation (13), it can be expressed as equation (16).

[0054]

[0055] Furthermore, the tangential external force component f that should occur when the following conditions are met is ｔａｎ This is a conservative force. Here, the target acceleration a ｔａｎ p is as shown in equation (17) below. ｃ Assume it is a function that depends on [something].

[0056]

[0057] By adding the following equation (18) to the center of gravity, the initially set holonomic constrained trajectory T is obtained. ｘｙ , T ｘｚ While satisfying the set target acceleration a ｔａｎ This model satisfies the requirements and also serves as a conservation system.

[0058]

[0059] In the example above, the target trajectory T ｄ Projecting T onto the xy-plane ｘｙ We find and project it onto the xz plane to get T ｘｚ The example of how to calculate this is explained, but it is not limited to this; two orthogonal planes, such as the xy-plane and the zy-plane, may also be used. In other words, in this embodiment, it is calculated from the resultant force of the vectors calculated from the trajectories projected onto the controlled plane.

[0060] <System Configuration Example> Figure 6 shows an example of the configuration of the control system of this embodiment. The control system 1 includes, for example, a robot 2 and a control device 3. The control device 3 may also be provided by the robot 2. The robot 2 includes, for example, a first leg portion 21, a second leg portion 22, a first end effector 23, a second end effector 24, a sensor 25, an actuator 26, a body 27, a communication unit 28, and a storage unit 29. The robot 2 may also be equipped with a power supply and a head, etc. The control device 3 includes, for example, an acquisition unit 31, a control unit 32, an output unit 33, and a storage unit 34.

[0061] (Robot) Robot 2 is, for example, a bipedal robot and has two end effectors. Robot 2 transmits and receives information with the control device 3 via a wired or wireless network NW.

[0062] Each of the first leg 21 and the second leg 22 is connected to the body at the hip via a joint. Each of the first leg 21 and the second leg 22 is, for example, a lower limb comprising a thigh, lower leg, and foot, and has joints at the hip, knee, and ankle. Each joint is also equipped with a sensor 25. Furthermore, each of the first leg 21 and the second leg 22 is equipped with an actuator 26 at each joint.

[0063] Each of the first end effector 23 and the second end effector 24 includes, for example, an arm and, for example, two or more finger parts. Each joint of the arm and finger parts is equipped with a sensor 25. Each joint of the arm and finger parts is also equipped with an actuator 26.

[0064] Sensor 25 includes, for example, encoders attached to each joint, acceleration sensors, force sensors, and gyro sensors attached to the legs and end effectors. Sensor 25 detects, for example, the posture of the waist link, ground reaction force, joint angles, acceleration, and the force applied when gripping an object. Sensor 25 is also an RGBD imaging device that can obtain depth information. The imaging device is attached, for example, to the head or the hand of the end effector.

[0065] The actuator 26 controls the operations of the joints of the first leg portion 21, the second leg portion 22, the first end effector 23, and the second end effector 24 according to a control command or a driving vibration output from the communication unit 28. Note that the actuator 26 may include a driving unit such as a driving circuit.

[0066] The first leg portion 21, the second leg portion 22, the first end effector 23, and the second end effector 24 are connected to the body 27. A head may be connected to the body 27.

[0067] The communication unit 28 outputs the detection value (including the captured image) detected by the sensor 25 to the control device 3. The communication unit 28 acquires a control value, a control command, or a driving signal output from the control device 3.

[0068] The storage unit 29 stores, for example, programs, threshold values, mathematical formulas, and the like.

[0069] (Control Device) The control device 3 is, for example, a personal computer or the like.

[0070] The acquisition unit 31 acquires the detection value output from the robot 2. Note that the acquisition unit 31 may acquire operation instructions or the like set or input by the operator of the robot 2.

[0071] The control unit 32 sets a passing point that is a target trajectory and a target acceleration. The control unit 32 complements the passing points with a spline curve or a higher-order function to generate a three-dimensional target trajectory T ｄ The control unit 32 projects the generated three-dimensional target trajectory T ｄ onto, for example, the xy plane to obtain T ｘｙ and projects the generated three-dimensional target trajectory T ｄ onto, for example, the xz plane to obtain T ｘｚ The control unit 32 uses T ｘｙ and T ｘｚ to obtain a constraint force f ｍｏｄｅｌTo obtain it. In order to achieve the target constraint force as the resultant force, the control unit 32 decomposes it, for example, into multiple fingers of the end effector and generates a control command. The control unit 32 performs well-known image processing on the captured image included in the detection value to estimate, for example, information regarding the gripped target object (type, size, position, etc. of the object). Note that the weight, etc. of the target object may be acquired or stored in advance, or may be input by the user.

[0072] The output unit 33 outputs a control value or a control command or a drive signal to the robot 2.

[0073] The storage unit 34 stores, for example, programs, threshold values, expressions, etc. used by each part of the control device 3.

[0074] <Example of Control Procedure> Next, an example of the control procedure will be described. FIG. 7 is a flowchart of the processing procedure by the control device of the present embodiment.

[0075] (Step S1) The acquisition unit 31 acquires the detection value output by the robot 2.

[0076] (Step S2) The control unit 32 sets the passing points that are the target trajectories, and sets the target acceleration a ｔａｎ at the set passing points.

[0077] (Step S3) The control unit 32 complements the passing points with a spline curve or a higher-order function to generate a three-dimensional target trajectory T ｄ .

[0078] (Step S4) The control unit 32 projects the generated three-dimensional target trajectory T ｄ onto, for example, the xy plane to obtain T ｘｙ , and projects the generated three-dimensional target trajectory T ｄ onto, for example, the xz plane to obtain T ｘｚ .

[0079] (Step S5) The control unit 32 uses T ｘｙ , T ｘｚ etc. to obtain the constraint force f ｍｏｄｅｌ .

[0080] (Step S6) The control unit 32 generates control commands by decomposing them into, for example, the multiple fingers of the end effector in order to achieve the target restraining force as a resultant force. That is, in this embodiment, the model to be controlled, or the control device 3 (medium) that applies force to the model to be controlled, has a plurality of movable parts (e.g., legs, end effector, etc.), and the force to be applied to the model to be controlled is taken as a resultant force and controlled by decomposing it into the forces of each of the plurality of movable parts.

[0081] (Step S7) The control unit 32 controls the operation of the robot 2 by outputting the generated control instructions to the robot 2 via the output unit 33.

[0082] (Step S8) The control unit 32 determines whether or not a disturbance has occurred. If no disturbance has occurred (Step S7; No), the control unit 32 continues the current operation control. If a disturbance has occurred (Step S7; Yes), the control unit 32 repeats the processes of Steps S1 to S7.

[0083] <Calculation of Force to be Applied to the Target Object> Next, an example of the procedure for calculating the force to be applied to the target object will be further explained. Figure 8 is a flowchart of the procedure for calculating the force to be applied to the target object in the control according to this embodiment.

[0084] (Step S11) The control unit 32 uses equation (7) to calculate the total mechanical energy of the controlled object, which depends on the target, rather than the equation of motion.

[0085] (Step S12) The control unit 32 uses equation (18) to determine the constraint conditions (constraint force f) for the trajectory that will lead to the desired orientation of the object to be controlled. ｍｏｄｅｌ ) will be decided.

[0086] (Step S13) The control unit 32 derives the equation of motion in the tangential direction from the constraint conditions of the trajectory, as shown in equation (15).

[0087] (Step S14) The control unit 32 substitutes equation (18) into equation (1) and calculates the force to be applied to the controlled object based on the derived equation of motion.

[0088] Step S12 corresponds to the process of step S5 in Figure 7. Therefore, in Figure 7, the control unit 32 performs the process of step S11 in Figure 8 before the process of step S5. Also, the control unit 32 performs the processes of steps S13 and S14 before the process of step S6 in Figure 7.

[0089] The processing content and procedures described using Figures 7 and 8 are examples only and are not limited to them. For example, several processing procedures may be performed simultaneously, and other processes may also be performed.

[0090] <First Embodiment> The first embodiment is an example of reducing a 3D coordinate system model to 2D. In the first embodiment, we consider the case where the motion takes place on a plane parallel to the xz plane, that is, y = C (C: Constant). In this case, we get equation (19) below.

[0091]

[0092] Substituting equation (19) into equation (8) yields equation (20).

[0093]

[0094] From the fourth equation of equation (20), y = C, therefore y ・・ = 0, and substituting this into the second equation of equation (20), we get λ ｘｙ = 0. Therefore, the motion in the xz plane is ultimately reduced to equation (21).

[0095]

[0096] First, the force f in the normal direction. ｎｏｒ This will be explained. The component of the force in the normal direction is the constraint force necessary to restrain the center of mass to the target trajectory. Of the components in equation (21), λ ｘｚ The terms marked with an asterisk (f) are the constraint forces that constrain the target trajectory. Therefore, this constraint force f ｎｏｒ The vector representing is given by equation (22), and its magnitude can be expressed by equation (23).

[0097]

[0098]

[0099] Next, the component f of the external force applied tangentially to the target trajectory. ｔａｎ Let's explain how to derive this f. ｔａｎ The magnitude of determines the acceleration in the direction of the target trajectory, and by adjusting this, the target velocity can be achieved. Here, from the relationship in equation (24), the vector representing the tangential direction can be expressed as equation (25) by substituting it into equation (16).

[0100]

[0101]

[0102] Substitute equation (25) into equation (15) to obtain the acceleration a in the tangential direction. ｔａｎ The tangential external force component f to achieve this ｔａｎ This is given by equation (26).

[0103]

[0104] <Energy Contribution Due to External Forces> Next, we will explain the energy contribution due to external forces. First, the constraint force f in the normal direction. ｎｏｒ The energy contribution is calculated. The constraint force f in the normal direction. ｎｏｒ The energy contribution by is given by equation (27) below, and is always zero regardless of the orbit.

[0105]

[0106] Next, the tangential component f ｔａｎ We calculate the energy contribution. From equation (15) above, we obtain the following equation (28).

[0107]

[0108] Here, equations (19) and (20), and ∂T ｄ / ∂x and ||l ｄ Since || depends only on position and not on time, equation (28) becomes equation (29).

[0109]

[0110] <Second Embodiment> In the second embodiment, the constraint force when the target orbit is an elliptical orbit will be explained. The orbital constraint for an elliptical orbit is given by the following equation (30) from the formula for ellipses. Herein, a and b are the radii of the major axis and minor axis b, respectively.

[0111]

[0112] From equations (30) and (7), the Lagrangian in this case is given by equation (31). Note that in equation (31), λ ｐ This represents an unknown constant.

[0113]

[0114] Using the method of Lagrange multipliers, we obtain equation (32).

[0115]

[0116] From the third equation of equation (32), we can express it as equation (33).

[0117]

[0118] Substituting equation (33) into the first and second equations of the following equation (32), we obtain equation (34). Note that double-headed arrows represent equivalent values.

[0119]

[0120] From equation (34), θ ・・ This can be found as shown in equation (35).

[0121]

[0122] According to equation (35), θ ・・ Because it can eliminate λ ｐ This is given by the following equation (36).

[0123]

[0124] As a result, the x-component of the constraint force is given by equation (37), the y-component of the constraint force is given by equation (38), and its magnitude is given by equation (39).

[0125]

[0126]

[0127]

[0128] Figure 9 shows an example of trajectory control of the center of gravity position during robot walking. Conventional technology could only control the trajectory in a limited range, such as a straight line for bipedal walking, but this embodiment allows control in linear and arbitrary nonlinear position trajectories.

[0129] In the example described above, we explained using the center of gravity trajectory for walking of a bipedal robot as shown in Figure 8, but this is not the only example. In this way, the controlled object and the controlling entity may be the same, or they may be different. For example, when manipulating an object obj with a multi-fingered hand as shown in Figure 10, the constraint force calculated above can be applied to the object using the multi-fingered hand. Figure 10 shows an example of moving an object in a nonlinear position trajectory with a multi-fingered hand. In this case, the center of gravity position is the center of gravity position of the object obj, and the operation of the end effector is controlled so that this object obj moves in a nonlinear trajectory.

[0130] Another example is when several robot arms are used to manipulate the same object; the constraint force calculated above can be added as the combined force from the multiple robot arms.

[0131] As described above, in this embodiment, by changing the derivation method from "ideal motion" to "energy" and from "energy" to "equation of motion", an analytical solution model for any positional trajectory without constraints (constraint force f) can be obtained. ｍｏｄｅｌ This allows for easy derivation of the analytical solution model. In this embodiment, the trajectory of the center of gravity of the target object to be controlled is controlled using the analytical solution model derived in this way.

[0132] As a result, according to this embodiment, any trajectory can be realized. Furthermore, according to this embodiment, control along any trajectory is easy, and the effort of integral calculations during derivation is eliminated, making implementation easy. Moreover, according to this embodiment, since any trajectory can be designed, it can be adapted to the manipulation of various objects, so not only walking control but also, for example, in-hand object manipulation is possible.

[0133] Furthermore, a program to implement all or part of the functions of the control device 3 in this invention may be recorded on a computer-readable recording medium, and all or part of the processing performed by the control device 3 may be performed by loading the program recorded on this recording medium into a computer system and executing it. Herein, "computer system" includes hardware such as an OS and peripheral devices. Furthermore, "computer system" also includes a WWW system equipped with a homepage provisioning environment (or display environment). Furthermore, "computer-readable recording medium" refers to portable media such as flexible disks, magneto-optical disks, ROMs, CD-ROMs, and storage devices such as hard disks built into a computer system. Moreover, "computer-readable recording medium" also includes volatile memory (RAM) inside a computer system that acts as a server or client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line, which holds the program for a certain period of time. Alternatively, some or all of these components may be implemented by hardware (including circuitry) such as LSI (Large Scale Integration), ASIC (Application Specific Integrated Circuit), FPGA (Field-Programmable Gate Array), GPU (Graphics Processing Unit), or SOC (System On Chip), or by the collaboration of software and hardware.

[0134] Furthermore, the above program may be transmitted from a computer system that stores the program in a memory device or the like to another computer system via a transmission medium or by transmission waves within the transmission medium. Here, the "transmission medium" for transmitting the program refers to a medium that has the function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. Also, the above program may be for the purpose of realizing a part of the functions described above. Furthermore, it may be a so-called differential file (differential program) that can realize the above functions in combination with a program already recorded in the computer system.

[0135] Although embodiments for carrying out the present invention have been described above using examples, the present invention is not limited in any way to these embodiments, and various modifications and substitutions can be made without departing from the spirit of the present invention.

[0136] 1...Control system, 2...Robot, 3...Control device, 21...First leg, 22...Second leg, 23...First end effector, 24...Second end effector, 25...Sensor, 26...Actuator, 27...Body, 28...Communication unit, 29...Storage unit, 31...Acquisition unit, 32...Control unit, 33...Output unit, 34...Storage unit

Claims

1. A control method for a model of a controlled object whose trajectory is an energy conservation system, comprising: a step of calculating the mechanical energy of the controlled object; a step of determining constraint conditions for the trajectory that leads to the desired attitude of the controlled object; a step of deriving equations of motion from the constraint conditions of the trajectory; and a step of calculating the force to be applied to the controlled object based on the derived equations of motion.

2. The control method according to claim 1, wherein the constraint conditions of the trajectory are determined by determining the points the trajectory passes through and the target acceleration at each point, and calculating the target trajectory from the points the trajectory passes through.

3. The control method according to claim 1 or 2, wherein the constraint conditions of the trajectory are calculated from the resultant force of vectors calculated from the trajectories projected onto the control target plane of the trajectory.

4. The control method according to claim 1 or claim 2, wherein the model to be controlled, or the medium that applies force to the model to be controlled, has a plurality of movable parts, and the force to be applied to the model to be controlled is taken as a resultant force and decomposed into the forces of each of the plurality of movable parts for control.

5. The constraint conditions for the trajectory are the first trajectory in the first plane and the second trajectory in the second plane obtained by projecting the calculated three-dimensional target trajectory of the controlled object onto two two-dimensional planes, and the constraint force to be generated at the center of gravity of the controlled object in order to achieve the target motion is determined using the first trajectory and the second trajectory, as described in claim 1 or claim 2.

6. For the center of gravity of the controlled object to be constrained to lie on a target trajectory at the position of the center of gravity of the controlled object, the control method according to claim 1 or claim 2, wherein when the external force acting on a point mass of the controlled object is decomposed into a normal component and a tangential component in the target trajectory, the normal component is equal to the constraint condition, and for the trajectory to be an energy-conserving system, the tangential force acting tangentially to the position of the center of gravity of the controlled object is a conservation system.

7. A control device for executing a control method for a model of a controlled object whose trajectory is an energy conservation system, comprising a control unit, the control unit calculating the mechanical energy of the controlled object, determining constraint conditions for the trajectory to reach the desired attitude of the controlled object, deriving equations of motion from the constraint conditions for the trajectory, and calculating the force to be applied to the controlled object based on the derived equations of motion.

8. A program that causes the computer of a control device, which executes a control method for a model of a controlled object whose trajectory is an energy conservation system, to calculate the mechanical energy of the controlled object, determine the constraint conditions of the trajectory that lead to the desired attitude of the controlled object, derive the equations of motion from the constraint conditions of the trajectory, and calculate the force to be applied to the controlled object based on the derived equations of motion.

Images