Joint type industrial robot adaptive compliant control method based on impedance learning

Abstract

The application discloses a kind of joint type industrial robot adaptive compliant control methods based on impedance learning, it includes the impedance control model of the dynamic relationship between the end of joint type industrial robot and the end position is established to describe the force, the actual contact force of the end and environment and the actual position of the end are obtained to update impedance parameter;After updating impedance parameter, based on the end position control joint type industrial robot movement or based on the end contact force control joint type industrial robot movement.The impedance parameter iterative updating method used in the application, according to the end position control error and the size of contact force, impedance parameter is updated in real time, improve the adaptability, control accuracy, stability and robustness of joint type industrial robot control.

Description

Technical Field

[0001] This invention relates to the field of industrial robot technology, and in particular to a control method for an articulated industrial robot. Background Technology

[0002] With the advent of Industry 4.0, industrial robots have been widely used in various industries, greatly improving productivity. As technology advances, production environments are becoming more complex and dynamic, demanding higher levels of flexibility and intelligence from industrial robots. Traditional error-based PID closed-loop control can no longer meet the force control requirements of current production. Therefore, compliant control of industrial robots based on impedance control models will gradually replace simple closed-loop control. Parameter settings in impedance control models typically require multiple experiments for adjustment, which consumes significant time and manpower in dynamic industrial environments and may even cause damage to the workpiece and end effector.

[0003] Traditional closed-loop position control in industrial robots prioritizes rapid elimination of deviations, resulting in a lack of precise force control or compliance with resistance in industrial scenarios. This can lead to excessive force application, damaging the workpiece or causing wear on the end effector. Currently, conventional impedance control uses a spring-damped-inertia second-order impedance control model to describe the dynamic relationship between the robot's end effector position and the contact force. By setting a desired impedance characteristic, the robot generates a displacement or reaction force proportional to the external force. Adaptive impedance control, on the other hand, is a control strategy that dynamically adjusts impedance parameters. It can adjust the system's impedance characteristics in real time according to environmental changes, task requirements, and robot status to maintain the optimal dynamic relationship between force and displacement. This improves the robot's adaptability in complex and dynamic environments and meets the high flexibility and intelligence requirements of many current production scenarios.

[0004] Currently, there is a large amount of research on adaptive impedance control methods for industrial robots both domestically and internationally, and a variety of effective impedance control methods for industrial robots have been proposed.

[0005] In the paper titled "Impedance Control of a Robotic Arm Based on a Six-Dimensional Force Sensor," author Xinyu Zhao used a genetic algorithm to find the optimal combination of impedance parameters and introduced an adaptive control strategy and an online adjustment method for the adaptive rate to achieve online updates of the impedance parameters. To achieve precise force control of the adaptive impedance parameters, it is first necessary to study the kinematics and dynamics of the robotic arm and establish its kinematic and dynamic models. Simultaneously, methods for end-effector contact force sensing and end-effector collision position detection are needed to ensure the calculation of the difference between the contact force and the desired contact force in the impedance control model. In this paper, torque control is used in the inner-loop control, requiring a precise dynamic model; therefore, load dynamic parameters identification is also necessary under end-effector loading. Regarding the impedance parameter update part, the adaptive damping adjustment strategy proposed by S. Jung et al. in 2004 is referenced. However, this method is outdated and its modeling of the dynamic environment is too simplistic; therefore, its adaptability needs improvement.

[0006] In the article titled "Research on Adaptive Neural Network Impedance Control and Human-Robot Physical Interaction of Robots," author Xinbo Yu proposed an adaptive neural network impedance control algorithm for flexible robot joints. This algorithm integrates the advantages of active compliance control and passive mechanical flexibility, solving the interaction problem of flexible industrial robots under unknown dynamic models. It enables the robot to adjust its compliance and avoid losses from sudden collisions. However, this method uses a neural network to compensate for uncertainties in impedance control, and each adjustment requires a certain amount of computation and convergence time, resulting in a slightly longer robot control cycle. This makes it impossible to achieve real-time updates of adaptive impedance control, thus failing to meet the real-time requirements of industrial environments.

[0007] In the paper titled "Experimental Study on Adaptive Impedance Control of Collaborative Robotic Arms," ​​author Xu Feixiang addresses the problem that commonly used position-based impedance control algorithms can only be applied to environments with known conditions and constant stiffness, and cannot be applied to unstructured scenarios. By introducing an environmental dynamics model, he analyzes the impact of environmental position estimation errors on the dynamic performance of impedance control and proposes a parameter-adaptive variable impedance control strategy. This method achieves adaptability to different environmental stiffnesses by compensating for damping parameters and realizes accurate force tracking control in various complex environments. However, this method only compensates for the damping matrix in the impedance parameters and does not consider adaptive compensation for the inertia and stiffness matrices, thus limiting its adaptability to dynamic environments. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide an adaptive compliant control method for articulated industrial robots based on impedance learning, so as to solve the problem of tracking control technology for the end effector of articulated industrial robots and realize adaptive compliant control of articulated industrial robots.

[0009] The adaptive compliant control method for articulated industrial robots based on impedance learning of this invention includes the following steps:

[0010] 1) Establish an impedance control model to describe the dynamic relationship between the force and position at the end of an articulated industrial robot. The impedance control model is as follows:

[0011]

[0012] Where M d (t), B d (t) and K d (t) represents the desired inertia matrix, damping matrix, and stiffness matrix, respectively, x d (t) represents the desired position at the end of time t. Let be the expected velocity at the end of time t. Let x(t) be the expected acceleration at the end of time t, and x(t) be the actual position at the end of time t. It is the terminal velocity. It is the terminal acceleration, F d (t) is the desired contact force between the end point and the environment at time t, F e (t) is the actual contact force between the end and the environment at time t;

[0013] 2) The actual contact force F between the end effector and the environment is measured by a force sensor installed at the end effector of the articulated industrial robot. e (t), or the joint driving torque vector τ can be obtained by measuring the joint driving torque vector τ through a joint torque sensor or by reading the current signal of the joint motor and then converting it to obtain the joint driving torque vector τ, and then according to the formula τ = J T ·F e (t) is converted to obtain the end contact force F. e (t), where J is the Jacobian matrix; the joint angle vector q is obtained by measuring the joint angles of the articulated industrial robot using an angle sensor, and the actual position x(t) of the end effector is obtained by solving the forward kinematics based on q, and then the actual contact force F of the end effector is used. e The impedance parameter B is updated based on the actual position x(t) and the position x(t). d (t) and K d The impedance parameter iterative update formula is as follows: (t),

[0014]

[0015]

[0016] Where: e x (t)=x(t)-x d (t), k is the iteration number, β B and β KLet α' be a constant related to the learning rate, and let α' be a constant vector related to the learning rate. Let represent the damping matrix and stiffness matrix obtained in the k-th iteration at time t, respectively; The desired control output y at time t d The first derivative of x(t); y(t) is the iterative output, y(t) = C(t)·x(t), where C(t) = [m1, m2, m3] is a constant vector for adjusting the impedance learning target, and the constants m1, m2, and m3 are adjustable setpoints. It is the first derivative of the output of the (k-1)th iteration; the result is For the next generation Update;

[0017] 3) After updating the impedance parameters, control the motion of the articulated industrial robot based on the end position or the end contact force.

[0018] The motion of the articulated industrial robot based on end-position control includes: applying the desired contact force F at the current moment. d (t) and actual contact force F e The difference between (t) and the input impedance control model are used to output the end position correction amount e. x Then calculate x according to the formula. r (t)=x d (t)+e x Calculate the end position control quantity x r (t), based on the end position control quantity x r (t) Perform inverse kinematics to obtain the joint angle control quantity q at the next moment. r Vector q is controlled by joint angle. r Controlling the movement of articulated industrial robots;

[0019] The method of controlling the motion of an articulated industrial robot based on end-effector contact force includes the following steps:

[0020] a) Obtain the joint angle vector q and joint angular velocity vector of the articulated industrial robot at the current moment.

[0021] b) Obtain the actual end position x(t) by performing forward kinematics calculation based on the joint angle vector q;

[0022] c) According to the formula Calculated velocity According to the formula Acceleration was calculated Where J is the Jacobian matrix;

[0023] d) The difference between x(t) and the desired position xd (t), With expected speed difference, With acceleration The difference between the two values ​​serves as the input to the impedance control model, which outputs the desired contact force F between the end and the environment. d (t);

[0024] e) According to the formula τ=J T ·F d The joint driving torque vector τ is obtained by conversion, and the motion of the articulated industrial robot is controlled by the joint driving torque vector τ.

[0025] Furthermore, the environmental dynamics model described in step 2) is as follows:

[0026]

[0027] Where M e B e and K e These are the inertia matrix, damping matrix, and stiffness matrix of the environmental dynamics, respectively. e This represents the initial location of the environment.

[0028] The beneficial effects of this invention are:

[0029] 1. Traditional closed-loop position control in articulated industrial robots aims for rapid elimination of deviations, resulting in a lack of precise force control or compliance with resistance in industrial scenarios. This leads to excessive force application, damaging the workpiece or wearing out the end effector. This invention establishes an impedance control model to describe the dynamic relationship between the force and position at the end of the articulated industrial robot, achieving precise control of the force at the end, which can effectively reduce workpiece damage or end effector wear.

[0030] 2. Conventional impedance control uses fixed impedance parameters, requiring manual adjustment to achieve different control effects. This approach cannot guarantee consistent control performance in real-time for unknown or relatively unstable environments, resulting in poor adaptability. The impedance parameter iterative update method employed in this invention updates the impedance parameters in real-time based on the end-effector position control error and contact force magnitude, improving the adaptability, control accuracy, stability, and robustness of articulated industrial robot control. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of some joint connections of an industrial robot.

[0032] Figure 2 This is a model of robot-environment contact in impedance control.

[0033] Figure 3 This is the impedance parameter update process.

[0034] Figure 4 This is a block diagram illustrating the principle of location-based adaptive impedance control.

[0035] Figure 5 This is a block diagram of the principle of force-based adaptive impedance control. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] For articulated industrial robots, their dynamic model can be established using the Newton-Euler method. Figure 1 The diagram shows a partial joint of an articulated industrial robot. A corresponding coordinate system is established at each link node, and the transformation matrix between adjacent coordinate systems is obtained using the MDH modeling method. This enables the kinematic association between links in an articulated industrial robot system.

[0038] According to Newton's third law, the net force f acting on the center of mass of link i in an articulated industrial robot is... ic for:

[0039] f ic =m i a ic (1)

[0040] Where: m is the mass of the connecting rod; a ic Let be the linear acceleration at the center of mass of link i.

[0041] According to Euler's equations, the net torque on the center of mass of link i in an articulated industrial robot is... c n ic for:

[0042]

[0043] in: c I i Let ω be the inertial tensor in the coordinate system {c} established with the center of mass as the origin for robot link i; i Let be the angular velocity of robot link i relative to the base coordinate system; Let be the angular acceleration of robot link i relative to the polar coordinate system.

[0044] By using the Newton-Euler method in a forward recursive manner, the angular velocity of the i-th link of the articulated industrial robot arm relative to coordinate system i can be obtained. i ω i angular acceleration Linear acceleration i a i The iterative relationship between the i-1 rod and the i-1 rod.

[0045] angular velocity i ω i Iteration relationship:

[0046]

[0047] angular acceleration Iteration relationship:

[0048]

[0049] Linear acceleration i a i Iteration relationship:

[0050]

[0051] in: The rotation matrix between coordinate system i-1 and coordinate system i illustrates the transformation relationship between the two coordinate systems; This represents the joint angular velocity of link i in the robot; Represents the projection onto the Z-axis of the coordinate system; This represents the joint angular acceleration of link i in the robot. i-1 P i This represents the vector from the origin of coordinate system i-1 to the origin of coordinate system i.

[0052] By using the Newton-Euler method in reverse recursion, the resultant torque at joint i of the robot link can be determined. i n i Resultant torque at link i+1 i+1 n i+1 Inter-iterational relationship:

[0053]

[0054] The resulting resultant torque i n i Projecting the torque τ of link i of the industrial robot onto the Z-axis in coordinate system i, we can obtain the torque τ. i :

[0055]

[0056] By combining equations (1)-(7), the dynamic equations of the robot are established:

[0057]

[0058] Taking a six-joint industrial robot as an example, where: τ=[τ1,τ2,τ3,τ4,τ5,τ6] TLet θ be the joint driving torque vector of the robot, and q = [θ1, θ2, θ3, θ4, θ5, θ6] be the joint angle vector. The joint angular velocity vector. This is the joint angular acceleration vector.

[0059] M(q) is the robot's inertia matrix, specifically represented as follows:

[0060]

[0061] in 0 A k Let be the transformation matrix from system k to system 0.

[0062] The Coriolis force and centrifugal force matrix of an industrial robot is specifically represented as follows:

[0063]

[0064] in Each component is a quadratic form of the generalized velocity, containing The term is centrifugal force, containing The term is Coriolis force. This is the gravity term.

[0065] The dynamic model described in equation (8) is an ideal model that does not consider the interaction forces generated by contact with the environment. Adding the interaction force term F with the environment... e Then, a complete dynamic model of the industrial robot is obtained:

[0066]

[0067] Where J is the Jacobian matrix, used for the mutual conversion between joint velocity, acceleration, torque and end velocity, acceleration, and force.

[0068] The goal of impedance control for articulated industrial robots is to control the dynamic relationship between the interaction forces between the robot and its environment and its end effector position, such as... Figure 2 As shown. The environmental dynamics model of the articulated industrial robot in contact with the environment is as follows:

[0069]

[0070] Where M e B e and K e These are the inertia matrix, damping matrix, and stiffness matrix of the environmental dynamics, respectively. e This represents the initial location of the environment.

[0071] The adaptive compliant control method for articulated industrial robots based on impedance learning in this embodiment includes the following steps:

[0072] 1) Establish an impedance control model to describe the dynamic relationship between the force and position at the end of an articulated industrial robot. The impedance control model is as follows:

[0073]

[0074] Where M d (t), B d (t) and K d (t) represents the desired inertia matrix, damping matrix, and stiffness matrix, respectively, x d (t) represents the desired position at the end of time t. Let be the expected velocity at the end of time t. Let x(t) be the expected acceleration at the end of time t, and x(t) be the actual position at the end of time t. It is the terminal velocity. It is the terminal acceleration, F d (t) is the desired contact force between the end point and the environment at time t, F e (t) is the actual contact force between the end and the environment at time t.

[0075] 2) The actual contact force F between the end effector and the environment is measured by a force sensor installed at the end effector of the articulated industrial robot. e (t), or the joint driving torque vector τ can be obtained by measuring the joint driving torque vector τ through a joint torque sensor or by reading the current signal of the joint motor and then converting it to obtain the joint driving torque vector τ, and then according to the formula τ = J T ·F e (t) is converted to obtain the end contact force F. e (t), where J is the Jacobian matrix; the joint angle vector q is obtained by measuring the joint angles of the articulated industrial robot using an angle sensor, and the actual position x(t) of the end effector is obtained by solving the forward kinematics based on q, and then the actual contact force F of the end effector is used. e The impedance parameter B is updated based on the actual position x(t) and the position x(t). d (t) and K d The impedance parameter iterative update formula is as follows: (t),

[0076]

[0077] Where: e x (t)=x(t)-x d (t), k is the iteration number, β B and β K Let α be a constant related to the learning rate, and α' be a constant vector related to the learning rate. Let represent the damping matrix and stiffness matrix obtained in the k-th iteration at time t, respectively; The desired control output y at time t d The first derivative of x(t); y(t) is the iterative output, y(t) = C(t)·x(t), where C(t) = [m1, m2, m3] is a constant vector for adjusting the impedance learning target, and the constants m1, m2, and m3 are adjustable setpoints. It is the first derivative of the output of the (k-1)th iteration; the result is For the next generation Update.

[0078] The following describes the damping matrix B in this embodiment. d and stiffness matrix K d The derivation process of the learning law. For the damping matrix B... d and stiffness matrix K d The learning pattern of iterative updates is as follows:

[0079]

[0080] Where: constant β B β K These are the damping learning rate and the stiffness learning rate, respectively; Γ k (t) represents the cost function, which measures the interaction between the articulated industrial robot and its environment. This cost function is related to the previously established environmental dynamics model. Since the parameters in the environmental dynamics model are unknown, the gradient of the cost function with respect to the current impedance parameter is obtained through the interaction force. As an intermediate variable, it is transformed. From equation (13), we can obtain:

[0081]

[0082] Where e x (t)=x(t)-x d (t). For equations (16) and (17) The environmental dynamics state equation is used to solve the problem. The environmental dynamics model in equation (12) is expressed using the following state equation:

[0083]

[0084] Where: the state variable is chosen as x1(t) = Δx e (t)=x e (txt), and Where s is an intermediate variable. Where E n It is an n-dimensional identity matrix;

[0085] The gradient relationship between the substitution function and the contact force is determined using the following lemma.

[0086] Lemma 1: For the linear time-varying system described by equation (18), in order to satisfy the control output y(t), the control input u(t) can be adjusted by the following iterative law:

[0087]

[0088] Where k is the iteration number, y d (t) represents the desired control output, and α is a constant vector that satisfies the following inequality:

[0089] ||E-α'B(t)C(t)|| ∞ <1 (22)

[0090] Where E is the identity matrix.

[0091] The environmental dynamics state equation (19) can then be expressed as:

[0092]

[0093] The input is the contact force F. e (t), then its update process is as follows:

[0094]

[0095] If we consider the above equation as a gradient method for adjusting the contact force, then...

[0096]

[0097] Where β is the contact force learning rate. Finally, by combining equations (24) and (25), the gradient relationship between the cost function and the terminal interaction force is obtained:

[0098]

[0099] The output y(t) = C(t)·x(t) can be the target of the impedance learning process, which can be the end position, velocity, contact force integral or a combination of the three. The learning target can be adjusted by selecting different C(t). For example, if the target of impedance learning is the end contact force integral, then C(t) = [0,0,m3].

[0100] Substituting the above equation into equations (16) and (17), we finally obtain the impedance learning law as follows:

[0101]

[0102] In this embodiment, the impedance learning method equates the cost function in the interaction force adjustment process of the environmental dynamics model with the cost function in the damping matrix and stiffness matrix adjustment process of the impedance control model; both are cost functions Γ. k (t), because both aim to adjust the dynamic relationship between the position of the robot's end effector and the contact force, thus avoiding the measurement of unknown environments and enhancing the adaptability of impedance control to the environment.

[0103] 3) After updating the impedance parameters, control the motion of the articulated industrial robot based on the end position or the end contact force.

[0104] like Figure 4 As shown, the motion control of the articulated industrial robot based on the end-effector position includes: controlling the desired contact force F at the current moment. d (t) and actual contact force F e The difference between (t) and the input impedance control model are used to output the end position correction amount e. x Then calculate x according to the formula. r (t)=x d (t)+e x Calculate the end position control quantity x r (t), based on the end position control quantity x r (t) Perform inverse kinematics to obtain the joint angle control quantity q at the next moment. r Vector q is controlled by joint angle. r Controlling the movement of articulated industrial robots.

[0105] like Figure 5 As shown, the motion control of the articulated industrial robot based on end-effector contact force includes the following steps:

[0106] a) Obtain the joint angle vector q and joint angular velocity vector of the articulated industrial robot at the current moment.

[0107] b) Obtain the actual end position x(t) by performing forward kinematics calculation based on the joint angle vector q;

[0108] c) According to the formula Calculated velocity According to the formula Acceleration was calculated Where J is the Jacobian matrix of the articulated industrial robot;

[0109] d) The difference between x(t) and the desired position x d (t), With expected speed difference, With acceleration The difference between the two values ​​serves as the input to the impedance control model, which outputs the desired contact force F between the end and the environment. d (t);

[0110] e) According to the formula τ=J T ·F d The joint driving torque vector τ is obtained by conversion, and the motion of the articulated industrial robot is controlled by the joint driving torque vector τ.

[0111] Both of the above control methods can achieve adaptive compliant control, avoiding the estimation of environmental dynamic parameters and achieving high adaptability to unknown environments.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An adaptive compliant control method for articulated industrial robots based on impedance learning, characterized in that: Includes the following steps: 1) Establish an impedance control model to describe the dynamic relationship between the force and position at the end of an articulated industrial robot. The impedance control model is as follows: Where M d (t), B d (t) and K d (t) represents the desired inertia matrix, damping matrix, and stiffness matrix, respectively, x d (t) represents the desired position at the end of time t. Let be the expected velocity at the end of time t. Let x(t) be the expected acceleration at the end of time t, and x(t) be the actual position at the end of time t. It is the terminal velocity. It is the terminal acceleration, F d (t) is the desired contact force between the end point and the environment at time t, F e (t) is the actual contact force between the end and the environment at time t; 2) The actual contact force F between the end effector and the environment is measured by a force sensor installed at the end effector of the articulated industrial robot. e (t), or the joint driving torque vector τ can be obtained by measuring the joint driving torque vector τ through a joint torque sensor or by reading the current signal of the joint motor and then converting it to obtain the joint driving torque vector τ, and then according to the formula τ = J T ·F e (t) is converted to obtain the end contact force F. e (t), where J is the Jacobian matrix; the joint angle vector q is obtained by measuring the joint angles of the articulated industrial robot using an angle sensor, and the actual position x(t) of the end effector is obtained by solving the forward kinematics based on q, and then the actual contact force F of the end effector is used. e The impedance parameter B is updated based on the actual position x(t) and the position x(t). d (t) and K d The impedance parameter iterative update formula is as follows: (t), Where: e x (t)=x(t)-x d (t), k is the iteration number, β B and β K Let α be a constant related to the learning rate, and let α' be a constant vector related to the learning rate. Let represent the damping matrix and stiffness matrix obtained in the k-th iteration at time t, respectively; Let y be the desired control output at time t. d The first derivative of x(t); y(t) is the iterative output, y(t) = C(t)·x(t), where C(t) = [m1, m2, m3] is a constant vector for adjusting the impedance learning target, and the constants m1, m2, and m3 are adjustable setpoints. It is the first derivative of the output of the (k-1)th iteration; the result is For the next generation Update; 3) After updating the impedance parameters, control the motion of the articulated industrial robot based on the end position or the end contact force. The motion of the articulated industrial robot based on end-position control includes: applying the desired contact force F at the current moment. d (t) and actual contact force F e The input impedance control model is based on the difference between (t) and the output end position correction amount e. x Then calculate x according to the formula. r (t)=x d (t)+e x Calculate the end position control quantity x r (t), based on the end position control quantity x r (t) Perform inverse kinematics to obtain the joint angle control quantity q at the next moment. r Vector q is controlled by joint angle. r Controlling the movement of articulated industrial robots; The method of controlling the motion of an articulated industrial robot based on end-effector contact force includes the following steps: a) Obtain the joint angle vector q and joint angular velocity vector of the articulated industrial robot at the current moment. b) Obtain the actual end-effector position x(t) by performing forward kinematics calculation based on the joint angle vector q; c) According to the formula Calculated velocity According to the formula Acceleration was calculated Where J is the Jacobian matrix; d) The difference between x(t) and the desired position x d (t), With expected speed difference, With acceleration The difference between the two values ​​serves as the input to the impedance control model, which outputs the desired contact force F between the end and the environment. d (t); e) According to the formula τ=J T ·F d The joint driving torque vector τ is obtained by conversion, and the motion of the articulated industrial robot is controlled by the joint driving torque vector τ.

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