A compliant control method and system for robot skill reproduction

Abstract

The application discloses a kind of compliant control method and system for robot skill reproduction, belong to human-computer interaction technical field.Control method includes obtaining the original desired trajectory that robot needs to reproduce, input pre-constructed impedance control model, control robot to complete skill reproduction;Wherein, the construction process of impedance control model includes: constructing the dynamics model of robot;Based on the dynamics model of robot, the desired trajectory of robot is revised, and dynamic force tracking equation between the revised desired trajectory and actual trajectory is constructed;Based on dynamic force tracking equation, Lyapunov equation is constructed, and the stability of impedance control model is verified by Lyapunov equation, and the impedance control model that meets stability condition is obtained.The application makes robot more stable to realize skill reproduction, improves safety and environmental adaptability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of human-computer interaction, and particularly relates to a compliant control method and system for robot skill reproduction. BACKGROUND

[0002] When human-computer collaboration is performed, humans can exert their wisdom and flexibility, and robots can complete some complex high-precision and high-load tasks in cooperation with humans by virtue of high precision and high reliability. In current industrial production, industrial robots are widely used to replace manual work to complete some simple and repetitive single tasks by virtue of high repeat positioning precision and high reliability.

[0003] However, with the continuous improvement of production requirements, robots exhibit certain limitations in the process of implementing human skill reproduction: (1) the working area of the robot needs to be strictly specified during work, and good human-robot collaboration is difficult to achieve; (2) the movement process of the robot is rigid, and the safety and robustness are low, and the robot cannot be humanized, and the accuracy is low; (3) the traditional skill reproduction method assumes that the robot has no contact force or the contact force can be ignored during work, and it is difficult to be applied to some work that requires the robot to generate interaction force with the environment, such as constant force polishing, polishing, zero force dragging, etc., and the application range is small. SUMMARY

[0004] The purpose of the application is to overcome the deficiencies in the prior art, and provide a compliant control method and system for robot skill reproduction, so that the robot can more stably implement skill reproduction and improve safety and environmental adaptability.

[0005] The application provides the following technical solutions:

[0006] In a first aspect, a compliant control method for robot skill reproduction is provided, comprising: obtaining an original desired trajectory that needs to be reproduced by a robot, inputting a pre-constructed impedance control model, and controlling the robot to complete skill reproduction; wherein the construction process of the impedance control model comprises: constructing a dynamic model of the robot to obtain dynamic parameters of the robot; based on the dynamic model of the robot and different environment models, correcting the desired trajectory of the robot, and constructing a dynamic force tracking equation between the corrected desired trajectory and an actual trajectory; based on the dynamic force tracking equation, constructing a Lyapunov equation, and verifying the stability of the impedance control model through the Lyapunov equation to obtain the impedance control model that meets the stability condition.

[0007] As an optional technical solution of the application, the construction of the dynamic model of the robot comprises:

[0008] The dynamics of the robot is modeled by the Lagrange method, and the dynamic parameters are expressed as: (1) wherein, t represents the joint torque of the robot at time step t , represents the joint angular displacement of the robot at time step t , represents the joint angular velocity of the robot at time step t , represents the joint angular acceleration of the robot at time step t , represents the joint angular acceleration of the robot at time step t , , and are obtained by encoders in the joints of the robot, represents the mass matrix, represents the centripetal force and Coriolis force, represents the gravity.

[0009] As an optional technical solution of the present application, at time step t , the joint angular displacement of the robot is mapped to the robot end through the pose transformation matrix , and the robot end generates displacement ;

[0010] At time step t , the joint angular velocity of the robot is mapped to the robot end through the Jacobian matrix , and the robot end generates velocity ;

[0011] At time step t , the joint angular velocity of the robot and the joint angular acceleration are mapped to the robot end through the Jacobian matrix and , and the robot end generates acceleration .

[0012] As an optional technical solution of the present application, the original desired trajectory is input into a pre-obtained impedance controller, and the trajectory deviation is converted into a force deviation, represented as: (2) wherein, represents the stiffness matrix of the impedance controller, represents the damping matrix of the impedance controller, represents the inertia matrix of the impedance controller, represents the original desired trajectory of the robot, represents the actual trajectory of the robot at time step t , represents the original desired velocity of the robot, represents the actual velocity of the robot at time step t , represents the original desired acceleration of the robot, represents the actual acceleration of the robot at time step t , represents the force bias at time step t , , and are orthogonal matrices;

[0013] the force bias at time step t is represented as: (3) wherein, represents the robot end-effector contact force at the previous time step , represents the robot desired end-effector contact force at the previous time step ;

[0014] the force bias at time step t is input into the robot joint controller to obtain the robot end-effector contact force at time step based on equation (1) t , is represented as: (4) wherein, represents the pseudo-inverse of the force Jacobian matrix represents the joint torques of the robot at time step t , represents the joint angular displacement of the robot at time step t , represents the gravity.

[0015] As an optional technical solution of the present application, the method for correcting the desired trajectory of the robot comprises:

[0016] constructing an impedance control model in a single direction;

[0017] the actual force bias in the single direction at time step t is represented as: (5)

[0018] wherein, m represents the mass coefficient of the single-direction impedance control model, k represents the stiffness coefficient of the single-direction impedance control model, b represents the damping coefficient. ​​​

[0019] Based on equation (5), the time step t The modified desired trajectory is expressed as: (6) wherein, represents the position compensation term at the time step t , represents the fixed offset of the robot desired trajectory at the time step t , represents the offset caused by , represents the offset caused by , represents the first derivative of .

[0020] As an optional technical solution of the present application, the dynamic force tracking equation between the modified desired trajectory and the actual trajectory comprises:

[0021] Based on equation (6), the force tracking error dynamic equation of the single direction impedance control model is expressed as: (7) wherein, represents the environmental stiffness, represents the environmental position, m represents the mass coefficient of the single direction impedance control model, k represents the stiffness coefficient of the single direction impedance control model, b represents the damping coefficient, represents the second derivative of , represents the desired force in the single direction;

[0022] Based on equation (7), let:

[0023] (8) The second order ideal force tracking error dynamic equation of the single direction impedance control model is expressed as: (9) wherein, represents the desired force deviation at the time step t , represents the first derivative of , represents the second derivative of , , both represent parameters;

[0024] Based on equations (7)-(9), let , The dynamic force tracking equation between the modified desired trajectory and the actual trajectory is expressed as: (10).

[0025] As an optional technical solution of the present application, the Lyapunov equation is constructed based on the dynamic force tracking equation, and the stability of the impedance control model is verified through the Lyapunov equation, which comprises:

[0026] Based on formula (10), the Lyapunov equation is constructed, which is expressed as: (11) Wherein, and Both represent a second-order positive definite real symmetric matrix, , , and satisfy , , x represents any non-zero vector, , , All represent constants;

[0027] For non-zero and , always holds, and only when and are both 0, ;

[0028] Derive formula (11) to obtain: (12) Wherein, , , All represent symmetric positive definite matrices, represents the first derivative of , represents the first derivative of b , represents the first derivative of c , represents a fixed offset of the robot desired trajectory;

[0029] By adjusting the parameters in formula (12) so that always holds, the impedance control model that meets the stability condition is obtained.

[0030] In the second aspect, a compliant control system for robot skill reproduction is provided, comprising: a reproduction module for obtaining an original desired trajectory of a robot to be reproduced, inputting a pre-constructed impedance control model, and controlling the robot to complete skill reproduction;

[0031] A construction module for constructing the impedance control model, comprising:

[0032] constructing a dynamic force tracking equation between the corrected expected trajectory and the actual trajectory based on the dynamic model of the robot;

[0033] correcting the expected trajectory of the robot based on the dynamic model of the robot, and constructing a dynamic force tracking equation between the corrected expected trajectory and the actual trajectory;

[0034] constructing a Lyapunov equation based on the dynamic force tracking equation, and verifying the stability of the impedance control model through the Lyapunov equation to obtain the impedance control model meeting the stability condition.

[0035] Compared with the prior art, the present application has the following beneficial effects:

[0036] The compliant control method for robot skill reproduction provided by the present application improves the stability and anti-interference ability of the robot, and when the external environment changes, the robot can exhibit certain compliance according to the expected performance, the robot exhibits better compliance in the trajectory reproduction process, and the adaptability of the robot to the external dynamic environment is improved; the working area of the robot does not need to be strictly specified, and the applicability is more extensive, and good human-machine cooperation is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a schematic diagram of the compliant control method in the embodiment of the present application;

[0038] Figure 2 is a schematic diagram of the impedance control model in the embodiment of the present application. DETAILED DESCRIPTION

[0039] The present application will be further described below in conjunction with the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0040] Embodiment 1

[0041] The present embodiment provides a compliant control method for robot skill reproduction, which is a control method based on force control. As shown in Figure 1 , the deviation between the actual trajectory and the expected trajectory of the robot end is converted into joint driving to adjust the contact force between the robot end and the environment. It includes: obtaining the original expected trajectory that the robot needs to reproduce, inputting the pre-constructed impedance control model, and controlling the robot to complete skill reproduction.

[0042] As shown in Figure 2 , the construction process of the impedance control model specifically includes the following steps:

[0043] Step 1: Constructing a dynamic model of the robot. Specifically, it includes:

[0044] Step 1.1, modeling the dynamics of the robot by Lagrange method, the dynamics parameters are represented as: wherein, t represents the joint torque of the robot at time step t , represents the joint angular displacement of the robot at time step t , represents the joint angular velocity of the robot at time step t , represents the joint angular acceleration of the robot at time step t , represents the joint angular jerk of the robot at time step t , , and are obtained by the encoders in the joints of the robot, represents the mass matrix, represents the centripetal force and Coriolis force, represents the gravity.

[0045] Step 1.2, at time step t , the joint angular displacement of the robot is mapped to the robot end by the pose transformation matrix , and the robot end generates displacement .

[0046] At time step t , the joint angular velocity of the robot is mapped to the robot end by the Jacobian matrix , and the robot end generates velocity .

[0047] At time step t , the joint angular velocity and the joint angular acceleration of the robot are mapped to the robot end by the Jacobian matrix and , and the robot end generates acceleration .

[0048] Step 2: based on the dynamics model of the robot, correcting the expected trajectory of the robot, and constructing the dynamic force tracking equation between the corrected expected trajectory and the actual trajectory. Specifically includes:

[0049] Step 2.1, inputting the original expected trajectory into the pre-obtained impedance controller, converting the trajectory deviation into force deviation, represented as: (2) wherein, represents the stiffness matrix of the impedance controller, This is represented as the damping matrix of the impedance controller. Represented as the inertia matrix of the impedance controller, This represents the robot's original desired trajectory. Indicates at time step t The actual trajectory of the robot. This represents the robot's original expected speed. Indicates at time step t The actual speed of the robot This represents the robot's initial expected acceleration. Indicates at time step t The actual acceleration of the robot, Indicates at time step t The reaction force of the downward deviation, , and All are orthogonal matrices.

[0050] At time step t Force deviation Represented as: (3) Among them, Indicates the previous time step The contact force at the end of the robot. Indicates the previous time step The robot expects to have contact force.

[0051] Time step t Force deviation Input the robot joint controller, and obtain the time step based on equation (1). t The robot end contact force , represented as: (4) Among them, Representing the Lijacobi matrix The pseudo-inverse matrix, Indicates at time step t The torque of each joint of the robot, Indicates at time step t Lower robot joint angular displacement, It represents gravity.

[0052] Step 2.2, the correction of the robot's desired trajectory includes:

[0053] because , and All are orthogonal matrices, and the impedance controller will not be coupled in any direction in Cartesian space, so only an impedance control model in a single direction needs to be constructed.

[0054] At time stept Actual force deviation in single direction is expressed as: (5)

[0055] wherein, m denotes the mass coefficient of the single direction impedance control model, k denotes the stiffness coefficient of the single direction impedance control model, b denotes the damping coefficient;

[0056] Based on equation (5), the time step t Modified desired trajectory is expressed as: (6) wherein, denotes the position compensation term at the time step t , denotes the fixed offset of the robot desired trajectory at the time step t , denotes the offset caused by , denotes the offset caused by , denotes the first derivative of .

[0057] Further, in order to adapt to different working environment stiffness while taking into account the accuracy of the robot trajectory reproduction, a position compensation term is added to the original desired trajectory. At the same time, the influence of the actual force deviation in a single direction and the first derivative of the force deviation on the robot desired trajectory is considered.

[0058] Step 2.3, the dynamic force tracking equation between the constructed modified desired trajectory and the actual trajectory, comprising:

[0059] Based on equation (6), the force tracking error dynamic equation of the impedance control model in a single direction is expressed as: (7) wherein, denotes the environment stiffness, denotes the environment position, m denotes the mass coefficient of the single direction impedance control model, k denotes the stiffness coefficient of the single direction impedance control model, b denotes the damping coefficient, denotes the second derivative of , denotes the desired force in a single direction.

[0060] Based on formula (7), let

[0061] (8) The second-order ideal force tracking error dynamic equation of the impedance control model in a single direction is expressed as: (9) wherein, represents the expected force deviation at the time step t , represents the first-order derivative of , represents the second-order derivative of , , all represent parameters.

[0062] Based on formula (7)~(9), let , The dynamic force tracking equation between the modified expected trajectory and the actual trajectory is expressed as: (10).

[0063] Step 3: Based on the dynamic force tracking equation, a Lyapunov equation is constructed, and the stability of the impedance control model is verified through the Lyapunov equation, to obtain the impedance control model meeting the stability condition. Specifically, it includes:

[0064] Based on formula (10), a Lyapunov equation is constructed and expressed as: (11) wherein, and all represent second-order positive definite real symmetric matrices, , , and satisfy , , x represents an arbitrary non-zero vector, , , all represent constants.

[0065] For non-zero and , is always true, and only when and are both 0, .

[0066] Derive formula (11) to obtain: (12) wherein, , , all represent symmetric positive definite matrices, a first derivative of a first derivative of b a first derivative of c represents a fixed offset of the robot desired trajectory.

[0067] By adjusting the parameters in equation (12) so that is always true, the impedance control model that meets the stability condition is obtained.

[0068] In this embodiment, the impedance control model includes an external loop and an internal loop. The external loop converts the trajectory deviation into force deviation through the impedance controller, and the internal loop adopts the PID method to perform closed-loop control of the joint driving torque.

[0069] Embodiment 2

[0070] The embodiment provides a compliant control system for robot skill reproduction, comprising: a reproduction module, configured to acquire an original desired trajectory of a robot to be reproduced, input a pre-constructed impedance control model, and control the robot to complete skill reproduction;

[0071] a construction module, configured to construct the impedance control model, comprising:

[0072] constructing a dynamics model of the robot.

[0073] Based on the dynamics model of the robot, the desired trajectory of the robot is corrected, and a dynamic force tracking equation between the corrected desired trajectory and an actual trajectory is constructed.

[0074] Based on the dynamic force tracking equation, a Lyapunov equation is constructed, and the stability of the impedance control model is verified through the Lyapunov equation, so that the impedance control model that meets the stability condition is obtained.

[0075] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0076] ​​​The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0077] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0078] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks. Figure 1 one or more flow or blocks.

[0079] The above only is the preferred embodiment of the present application, it should be pointed out that, for those skilled in the technology in the art, without departing from the technical principles of the present application, can also make a number of improvements and variations, these improvements and variations should also be considered as the protection scope of the present application.

Claims

1. A compliant control method for reproducing robot skills, characterized in that, include: Obtain the original expected trajectory that the robot needs to reproduce, input the pre-built impedance control model, and control the robot to complete the skill reproduction; The process of constructing the impedance control model includes: Construct a dynamic model of the robot; Based on the robot's dynamic model, the desired trajectory of the robot is corrected, and a dynamic force tracking equation is constructed between the corrected desired trajectory and the actual trajectory, including: The original desired trajectory is input into a pre-acquired impedance controller, and the trajectory deviation is converted into a force deviation, expressed as: (2) Among them, Represented as the stiffness matrix of the impedance controller. This is represented as the damping matrix of the impedance controller. Represented as the inertia matrix of the impedance controller, This represents the robot's original desired trajectory. Indicates at time step t The actual trajectory of the robot. This represents the robot's original expected speed. Indicates at time step t The actual speed of the robot This represents the robot's initial expected acceleration. Indicates at time step t The actual acceleration of the robot, Indicates at time step t The reaction force of the downward deviation, , and All are orthogonal matrices; At time step t Force deviation Represented as: (3) Among them, Indicates the previous time step The contact force at the end of the robot. Indicates the previous time step The robot's expected contact force; Time step t Force deviation Input the robot joint controller, and obtain the time step based on equation (1). t The robot end contact force , is represented as: (4) Among them, Representing the Lijacobi matrix The pseudo-inverse matrix, Indicates at time step t The torque of each joint of the robot, Indicates at time step t Lower robot joint angular displacement, Represents gravity; Construct an impedance control model in a single direction; At time step t Actual force deviation in the next single direction Represented as: （5） in, m This represents the quality coefficient of the unidirectional impedance control model. k This represents the stiffness coefficient of the unidirectional impedance control model. b Indicates the damping coefficient; Based on equation (5), time step t Lowered expected trajectory Represented as: （6） in, Indicates time step t The following position compensation item, Indicates time step t The fixed offset of the robot's desired trajectory. Indicates by The resulting offset Indicates by The resulting offset express The first derivative; Based on equation (6), the dynamic equation for the force tracking error of the impedance control model in a single direction is expressed as: （7） in, Indicates environmental stiffness. Indicates environmental location, m This represents the quality coefficient of the unidirectional impedance control model. k This represents the stiffness coefficient of the unidirectional impedance control model. b Indicates the damping coefficient. express The second derivative, Represents the expected force in one direction; Based on equation (7), let: （8） The dynamic equation for the second-order ideal force tracking error of the impedance control model in a single direction is expressed as: (9) Among them, Indicates time step t The expected force deviation, Represented as The first derivative, Represented as The second derivative, , All represent parameters; Based on equations (7) to (9), let , The dynamic force tracking equation between the corrected desired trajectory and the actual trajectory is expressed as follows: （10）； Based on the dynamic force tracking equation, the Lyapunov equation is constructed, and the stability of the impedance control model is verified by the Lyapunov equation, thus obtaining the impedance control model that meets the stability condition.

2. The compliant control method for robot skill reproduction according to claim 1, characterized in that: The dynamic model of the constructed robot includes: The robot's dynamics are modeled using the Lagrange method, and the dynamic parameters are expressed as follows: （1） in, t Indicates at time step t Down, Indicates at time step t The torque of each joint of the robot, Indicates at time step t Lower robot joint angular displacement, Indicates at time step t Lower the angular velocity of the robot joints. Indicates at time step t Lowering the joint angular acceleration of the robot, , and All data is obtained from encoders in the robot's joints. Represents the mass matrix, Representing centripetal force and Coriolis force, It represents gravity.

3. The compliant control method for robot skill reproduction according to claim 2, characterized in that: At time step t Below, the robot's joint angular displacement Through pose transformation matrix Mapped to the robot's end effector, the robot's end effector generates displacement. ; At time step t Below, the robot joint angular velocity Through the Jacobian matrix Mapped to the robot's end effector, the robot's end effector generates velocity. ; At time step t Below, the robot joint angular velocity and joint angular acceleration Through the Jacobian matrix and Mapped to the robot's end effector, the end effector generates acceleration. .

4. The compliant control method for robot skill reproduction according to claim 1, characterized in that: The process of constructing the Lyapunov equation based on the dynamic force tracking equation and verifying the stability of the impedance control model using the Lyapunov equation includes: Based on equation (10), the Lyapunov equation is constructed, expressed as: （11） in, and Both represent second-order positive definite real symmetric matrices. , And satisfy , , x Represent any non-zero vector. , , Both represent constants; For nonzero and , It holds true if and only if and When both are 0, ; Differentiating equation (11), we get: （12） in, , , Both represent symmetric positive definite matrices. express The first derivative, express b The first derivative, express c The first derivative, This represents a fixed offset from the robot's desired trajectory. By adjusting the parameters in equation (12) to make If the condition is always met, the impedance control model that satisfies the stability condition is obtained.

5. A compliant control system for reproducing robot skills, characterized in that, include: The reproduction module is used to obtain the original expected trajectory that the robot needs to reproduce, input a pre-built impedance control model, and control the robot to complete the skill reproduction. A building module for constructing the impedance control model includes: Construct a dynamic model of the robot; Based on the robot's dynamic model, the desired trajectory of the robot is corrected, and a dynamic force tracking equation is constructed between the corrected desired trajectory and the actual trajectory, including: The original desired trajectory is input into a pre-acquired impedance controller, and the trajectory deviation is converted into a force deviation, expressed as: (2) Among them, Represented as the stiffness matrix of the impedance controller. This is represented as the damping matrix of the impedance controller. Represented as the inertia matrix of the impedance controller, This represents the robot's original desired trajectory. Indicates at time step t The actual trajectory of the robot. This represents the robot's original expected speed. Indicates at time step t The actual speed of the robot This represents the robot's initial expected acceleration. Indicates at time step t The actual acceleration of the robot, Indicates at time step t The reaction force of the downward deviation, , and All are orthogonal matrices; At time step t Force deviation Represented as: (3) Among them, Indicates the previous time step The contact force at the end of the robot. Indicates the previous time step The robot's expected contact force; Time step t Force deviation Input the robot joint controller, and obtain the time step based on equation (1). t The robot end contact force , is represented as: (4) Among them, Representing the Lijacobi matrix The pseudo-inverse matrix, Indicates at time step t The torque of each joint of the robot, Indicates at time step t Lower robot joint angular displacement, Represents gravity; Construct an impedance control model in a single direction; At time step t Actual force deviation in the next single direction Represented as: （5） in, m This represents the quality coefficient of the unidirectional impedance control model. k This represents the stiffness coefficient of the unidirectional impedance control model. b Indicates the damping coefficient; Based on equation (5), time step t Lowered expected trajectory Represented as: （6） in, Indicates time step t The following position compensation item, Indicates time step t The fixed offset of the robot's desired trajectory. Indicates by The resulting offset Indicates by The resulting offset express The first derivative; Based on equation (6), the dynamic equation for the force tracking error of the impedance control model in a single direction is expressed as: (7) Among them, Indicates environmental stiffness. Indicates environmental location, m This represents the quality coefficient of the unidirectional impedance control model. k This represents the stiffness coefficient of the unidirectional impedance control model. b Indicates the damping coefficient. express The second derivative, Represents the expected force in one direction; Based on equation (7), let: （8） The dynamic equation for the second-order ideal force tracking error of the impedance control model in a single direction is expressed as: (9) Among them, Indicates time step t The expected force deviation, Represented as The first derivative, Represented as The second derivative, , All represent parameters; Based on equations (7) to (9), let , The dynamic force tracking equation between the corrected desired trajectory and the actual trajectory is expressed as follows: （10）； Based on the dynamic force tracking equation, the Lyapunov equation is constructed, and the stability of the impedance control model is verified by the Lyapunov equation, thus obtaining the impedance control model that meets the stability condition.

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