An output-based cooperative control method for multiple robotic arms

Abstract

The present invention discloses a cooperative control method for multiple robotic arms based on output, comprising the following steps: a) converting the robotic arm dynamics equation into an integral chain form; b) designing a desired reference signal and a formation vector, and calculating the value of the cooperative tracking error between the robotic arm output and the desired reference signal; c) designing a sliding mode error based on the cooperative tracking error value, and on this basis, combining with a fuzzy system to design an observer to estimate the values of each order of the cooperative tracking error; d) designing the control input of the robotic arm from the estimated value of the sliding mode error. The present invention considers unknown non-affine terms in the calculation process, and uses the dynamic equations of each order of the cooperative error to obtain the estimated value of the sliding mode error for controlling the cooperative work of multiple robotic arms, solving the cooperative control problem restricted by the non-affine structure of the input and the uncertainty of the system model. This control method is simple to design and has high precision, and is particularly suitable for cooperative handling and assembly tasks.

Description

Technical Field

[0001] The present invention belongs to the technical field of robotics, and particularly relates to a cooperative control method for multi-robot arms based on output. Background Art

[0002] The cooperative control of robotic arms has been widely used in various industrial fields. Robotic arms can not only replace humans in performing various complex tasks such as stamping, casting, welding, and assembly, but also cooperate to complete tasks under extreme conditions. Although using the cooperative movement of robotic arms for various operations is more efficient than manual operation, when the surrounding environment such as the electric field and magnetic field changes, it will cause the parameters of the robotic arm motors to change. When the input robotic arm is subject to unknown resistance and the voltage is interfered, it will lead to uncertain factors in system modeling (such as parameter uncertainty, structural uncertainty, and the limitation of the unknown non-affine structure of the control input). Therefore, in the design of the control rate (i.e., input control), it is necessary to consider the non-affine form of the input and the uncertainty of the system model. Most current cooperative control methods ignore the non-affine limitations of the system input and the uncertainty of the model. However, during the process of the robotic arm completing tasks, it will inevitably be affected by external unknown resistance, interference, and environmental changes. In fact, most of these changes are unknown, which will not only cause uncertainty in system modeling, but also impose non-affine structure limitations on the system input, thereby affecting the accuracy of cooperative movement and making it impossible to be applied in practice to complete collaborative tasks.

[0003] Currently, almost all the design methods for cooperative control focus on robotic arm systems with affine control inputs and known structures. Existing literature does not consider the case of non-affine structure limitations of the input. The existing design methods are no longer suitable for actual collaborative tasks, and a new cooperative control method needs to be developed to solve the collaborative control problem with non-affine structure of the input and uncertainty limitations of the system model. This case thus arises. Summary of the Invention

[0004] The purpose of the present invention is to provide a cooperative control method for multi-robot arms based on output, which is used to solve the technical problem that in the prior art, the case of non-affine structure limitations is not considered, and under the influence of external unknown resistance, interference, and environmental changes, the accuracy of cooperative movement in the prior art is greatly affected, making it difficult to adapt to actual collaborative tasks.

[0005] The described cooperative control method for multi-robot arms based on output includes the following steps.

[0006] a) Convert the robotic arm dynamics equation into an integral chain form;

[0007] b) Design the desired reference signal and formation vector, and calculate the value of the cooperative tracking error between the manipulator output and the desired reference signal;

[0008] c) Design the sliding mode error from the value of the cooperative tracking error. On this basis, combine the fuzzy system to design an observer to estimate the values of each order of the cooperative tracking error;

[0009] d) Design the control input of the manipulator from the estimated value of the sliding mode error.

[0010] 2. A cooperative control method for multi-manipulators based on output according to claim 1, wherein: said step a) includes the following steps:

[0011] a1) Transform the manipulator dynamic model into the form of a first-order differential equation;

[0012] a2) According to the mean value theorem, transform the first-order differential equation in step a2) into an integral chain form.

[0013] 3. A cooperative control method for multi-manipulators based on output according to claim 2, wherein: in said step a), the manipulator dynamic model is

[0014]

[0015] wherein, i represents the i-th manipulator system, q i 、 respectively represent the angular position, angular velocity and angular acceleration, τ i is the motor armature current, y i is the system output, M i is the armature inductance, H i is the armature resistance, K m，i is the back electromotive force coefficient, J i is the moment of inertia of the motor rotor, m i is the link mass, M 0.i is the load mass, d i is the link length, δ i is the load radius, g is the acceleration due to gravity, B 0.i is the viscous friction coefficient of the link, K r，i is the motor torque coupling coefficient, is the uncertain term, u i is the control input, f i (u i ) is the unknown non-affine term;

[0016] In step a1), define a new set of variables x i，1 = q i , x i，3 = τ i In step a2), a new set of variables z is defined i，1 = x i，1 , The integral chain form of the manipulator dynamics model transformation is

[0017]

[0018] where F i (x i，1 , x i，2 , x i，3 ) and G i (x i，1 , x i，2 , x i，3 ) are unknown non-linear functions generated by the system transformation without the control variable u i .

[0019] 4. A cooperative control method for multiple manipulators based on output according to claim 3, characterized in that: said step b) comprises the following steps:

[0020] b1) Determine the desired reference signal by inverse kinematics solution;

[0021] b2) Determine the formation vector of the manipulator according to the task requirements;

[0022] b3) Obtain the cooperative tracking error equation from the manipulator output, reference signal and formation vector.

[0023] 5. A cooperative control method for multiple manipulators based on output according to claim 4, characterized in that: in said step b), the manipulator output y i = z i，1 , the desired reference signal y r , the formation vector of the manipulator Δ = [Δ 1 ,..., Δ N T , and the cooperative tracking error is designed as

[0024]

[0025] 6. A cooperative control method for multiple manipulators based on output according to claim 5, characterized in that: said step c) comprises the following steps:

[0026] c1) Calculate the values of each order of the cooperative tracking error using the cooperative error equation;

[0027] c2) Define the sliding mode error using the cooperative error and its values of each order and calculate its value; ​

[0028] c3) Construct a fuzzy system using the system state to estimate the unknown non - linear function in the system;

[0029] c4) Estimate the values of all orders of the cooperative error by constructing an observer through the fuzzy system and the cooperative error.

[0030] 7. A cooperative control method for multiple robotic arms based on output according to claim 6, characterized in that: in the step c), the dynamic equations of all orders of the cooperative error are:

[0031]

[0032] Define the sliding - mode error as

[0033] S i =λ 1 e i，1 +λ 2 e i，2 +e i，3 ,

[0034] where e i，1 , e i，2 and e i，3 represent the cooperative error and all orders of the cooperative error between the i - th robotic arm and its neighbors, and λ 1 , λ 2 are the coefficients of e i，1 and e i，2 in the sliding - mode error;

[0035] The unknown non - linear functions F i and G i are approximated by the following fuzzy system:

[0036]

[0037]

[0038] where, θ fi and λ gi are update parameters, and are fuzzy basis functions; the observer is

[0039]

[0040] where, l 1 , l 2 and l 3 are observer gain coefficients.

[0041] 8. A cooperative control method for multiple robotic arms based on output according to claim 7, characterized in that: the step d) includes the following steps:

[0042] d1) Calculate the estimated value of the sliding mode error based on the collaborative error and the values of each order of the collaborative error estimated by the observer.

[0043] d2) Design the control input of the robotic arm using the estimated value of the sliding mode error.

[0044] d3) Finally, the host computer sends the calculated control input of the robotic arm to the lower computer, and the motion is completed through the servo system.

[0045] 9. A collaborative control method for multiple robotic arms based on output according to claim 8, wherein in step d), the estimated value of the sliding mode error is

[0046] The control input of each robotic arm is where α i and are adaptive parameters;

[0047] Use the Nussbaum function to stabilize the problem that the control direction is unknown at some moments caused by the unknown nonlinear function G i , and design the update law as

[0048]

[0049] where, γ i , σ i , η fi , η gi , are positive design parameters and are arbitrary positive constants.

[0050] The present invention has the following advantages: The above control process includes unknown non-affine terms and dynamic equations of each order of the collaborative error in the calculation process. The sliding mode error is designed through the collaborative tracking error value, and the observer is designed in combination with the fuzzy system to estimate the values of each order of the collaborative tracking error, thereby obtaining the estimated value of the sliding mode error for controlling the collaborative work of multiple robotic arms, thus overcoming the defect in the prior art that the case with non-affine structure limitations is not considered, solving the collaborative control problem with non-affine structure of the input and uncertainty limitations of the system model. This control method is simple to design and has high precision, and is especially suitable for collaborative handling and assembly tasks. Description of the Drawings

[0051] Figure 1 is a flowchart of a collaborative control method for multiple robotic arms based on output of the present invention.

[0052] Figure 2 is a system block diagram of the robotic arm in the present invention.

[0053] Parameter descriptions of the markings in the attached drawings: M i : Armature inductance of the i-th robotic arm; H i : Armature resistance of the i-th robotic arm; K m，i : Back electromotive force coefficient of the i-th robotic arm; J i : Moment of inertia of the motor rotor of the i-th robotic arm; m i : Link mass of the i-th robotic arm; M 0.i : Load mass of the i-th robotic arm; d i : Link length of the i-th robotic arm; δ i : Load radius of the i-th robotic arm; g: Acceleration due to gravity; B 0.i : Viscous friction coefficient of the link of the i-th robotic arm; K r，i : Motor torque coupling coefficient of the i-th robotic arm; u i : Input control voltage of the i-th robotic arm. Detailed implementation manners

[0054] The following further elaborates on the specific implementation manners of the present invention by describing the embodiments with reference to the attached drawings, so as to help those skilled in the art have a more complete, accurate, and in-depth understanding of the inventive concept and technical solution of the present invention.

[0055] The meanings of the parameter symbols in this article are shown in Table 1.

[0056] Table 1: Meanings of each parameter symbol in this article

[0057]

[0058]

[0059]

[0060] As Figure 1 、 Figure 2 shown, the present invention provides a collaborative control method for multi-robotic arms based on output, which considers the case where the dynamic equation of the robotic arm contains unknown dynamics and non-affine forms of control inputs, and is particularly suitable for solving the control problem of the robotic arm to complete collaborative handling and assembly tasks in an unknown changing environment.

[0061] The dynamic equation of the i-th robotic arm is as follows:

[0062]

[0063] where q i 、 respectively represent angular position, angular velocity, and angular acceleration, τ i is the motor armature current, y i is the system output, Mi is the armature inductance, H i is the armature resistance, K m，i is the back electromotive force coefficient J i is the moment of inertia of the motor rotor, m i is the connecting rod mass, M 0.i is the load mass, d i is the connecting rod length, δ i is the load radius, g is the acceleration due to gravity, B 0.i is the viscous friction coefficient of the connecting rod, K r，i is the motor torque coupling coefficient is the uncertainty term, u i is the control input (which can be the input control voltage), f i (u i ) is the unknown non - affine term.

[0064] The control objective is: Given a desired reference signal y r , given the formation vector Δ = [Δ 1 ,..., Δ N T , design the control input for each robotic arm system so that the formation of the robotic arms remains unchanged, that is

[0065] In the present invention, a desired reference signal is set as the leader and all robotic arm systems are regarded as followers. Each robotic arm realizes cooperative control by obtaining the position information of its neighbors through one - way communication. Here, a one - way graph is used to describe the constructed leader and followers, where is the node set, the 0 - node represents the leader, and the nodes from 1 to N represent each follower robotic arm system respectively, is the set of directed edges. If there exists a directed edge from node q to p, it indicates that robotic arm p can receive the information of robotic arm q, and robotic arm p is called a neighbor of robotic arm q. When there exists a directed path between any two nodes in the graph, then the graph has a directed spanning tree. The adjacency matrix A = [a pq can be defined as: when and only when , a pq = 1, and the others are a pq = 0. Use the directed graph G=(V, E) to describe N followers, where V = {1, 2,..., N} is the set of follower nodes, is the set of directed edges of the followers. Define B = diag{b 1 , b 2 ,..., b N}, where bi = 1 (i = 1,..., N) indicates that the i-th follower can obtain the information of the leader, otherwise b i = 0. Similarly, let A = [a ij represent the adjacency matrix of graph G.

[0066] Based on the above design idea, this method includes the following steps.

[0067] 1) Step P1: Convert the dynamic equation of the robotic arm into an integral chain form.

[0068] The present invention is a cooperative control method for multi-robotic arms based on output, considering the situation where the dynamic equation of the robotic arm contains unknown dynamics and non-affine control inputs. Therefore, it is necessary to establish the dynamic equation of the robotic arm according to the system framework of the robotic arm (as Figure 2 shown), design the desired reference signal and formation vector; gradually calculate the control input signal based on the available information such as the system output, reference signal, and formation vector, so that the robotic arm can complete the cooperative movement driven by the control input signal. The specific steps are as follows:

[0069] The first step: Establish the traditional mathematical model of the robotic arm according to the system framework of the robotic arm

[0070]

[0071] Among them, i represents the i-th robotic arm system, q i , respectively represent the angular position, angular velocity, and angular acceleration, τ i is the motor armature current, y i is the system output, M i is the armature inductance, H i is the armature resistance, K m，i is the back electromotive force coefficient, J i is the moment of inertia of the motor rotor, m i is the mass of the connecting rod, M 0.i is the load mass, d i is the length of the connecting rod, δ i is the load radius, g is the acceleration due to gravity, B 0.i is the viscous friction coefficient of the connecting rod, K r，i is the motor torque coupling coefficient, is the uncertainty term, u i is the control input, f i (u i ) is the unknown non-affine term.

[0072] Define a new set of variables x i，1 = q i , x i，3 = τ i , the established kinetic equation (1) is rewritten in the form of a first-order differential equation

[0073]

[0074] Step 2: Define a new set of variables z i，1 = x i，1 , The first-order differential equation model (2) is transformed into the following form

[0075]

[0076] where, T i (x i，1 , x i，2 , x i，3 , u i ) is an unknown nonlinear function of x i，1 , x i，2 , x i，3 and u i .

[0077] Using the mean value theorem, the control variable u i is separated from T i (x i，1 , x i，2 , x i，3 , u i ), that is

[0078]

[0079] where,[[]] is an unknown constant between 0 and u i . Then the system (3) is rewritten in the integral chain form explicitly containing the control variable (control input) u i :

[0080]

[0081] where, F i (x i，1 , x i，2 , x i，3 ) and G i (x i，1 , x i，2 , x i，3 ) are unknown nonlinear functions generated by the system transformation and do not contain the control variable u i .

[0082] 2) Step P2: Design the desired reference signal and formation vector, and calculate the value of the cooperative tracking error between the manipulator output and the desired reference signal.

[0083] Step 1: Determine the desired reference signal y by inverse kinematics r .

[0084] Step 2: Determine the formation vector Δ = [Δ 1 ,..., Δ N of the robotic arm according to the task requirements T .

[0085] Step 3: Obtain the cooperative tracking error as

[0086]

[0087] 3) Step P3: Design the sliding mode error based on the cooperative tracking error value. On this basis, design an observer in combination with a fuzzy system to estimate the values of each order of the cooperative tracking error.

[0088] Step 1: Use the cooperative error equation (6) to establish the dynamic equations of each order of the cooperative error as

[0089]

[0090] Step 2: Use the dynamic equations of each order of the cooperative error (7) to define the sliding mode error as

[0091] S i = λ 1 e i，1 + λ 2 e i，2 + e i，3 , (8)

[0092] Step 3: Approximate the unknown nonlinear functions F i and G i through the following fuzzy system

[0093]

[0094]

[0095] where, θ fi and θ gi are update parameters, and are fuzzy basis functions.

[0096] Step 4: Since only the system output y i = z i，1 is available, that is, the cooperative error e i，1 is available, e i，2 and e i，3 depend on the unknown nonlinear functions F i and Gi is unavailable. Therefore, by using the fuzzy systems (9) and (10), the following observer is constructed to simultaneously estimate the values of e i，1 , e i，2 and e i，3 . The observer is

[0097]

[0098] where l 1 , l 2 and l 3 are the observer gain coefficients.

[0099] 4) Step P4: Design the control input of the robotic arm from the estimated value of the sliding mode error.

[0100] First step: Calculate the estimated value of the sliding mode error as

[0101] Second step: Design the control input of each robotic arm according to the estimated value of the sliding mode error as

[0102]

[0103] where is the Nussbaum function, which is used to stabilize the problem that the control direction is unknown at some moments caused by the unknown nonlinear function G j . The update law is designed as

[0104]

[0105] where γ i , σ i , η fi , η gi , are positive design parameters and can be any positive constants.

[0106] Third step: Finally, the upper computer sends the calculated control input u i of the robotic arm to the lower computer, and the motion is completed through the servo system. If the desired control objective is not achieved at one time, the calculation and control can be looped from step P2 to P4 until the control objective is reached and then the calculation and control process stops.

[0107] The present invention has been described exemplarily above with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited by the above-mentioned manner. As long as various non-substantive improvements are made by adopting the inventive concept and technical solution of the present invention, or the inventive concept and technical solution of the present invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A collaborative control method for multiple robotic arms based on output, characterized in that: It includes the following steps: a) Convert the robotic arm dynamics equation into an integral chain form; b) Design a desired reference signal and a formation vector, and calculate the value of the collaborative tracking error between the robotic arm output and the desired reference signal; c) Design a sliding mode error based on the collaborative tracking error value. On this basis, combine a fuzzy system to design an observer to estimate the values of each order of the collaborative tracking error; d) Design the control input of the robotic arm based on the estimated value of the sliding mode error; Define the sliding mode error as S i = λ 1 e i,1 + λ 2 e i,2 + e i,3 , where e i,1 , e i,2 and e i,3 represent the cooperation error and its various orders between the i-th robotic arm and its neighbors, and λ 1 , λ 2 are the coefficients of e i,1 and e i,2 in the sliding mode error; In the step d), the estimated value of the synovial error is The control inputs of each robotic arm are is the Nussbaum function, where α i and are adaptive parameters; x i,1 = q i , x i,3 = τ i , q i represents the angular position, represents the angular velocity, τ i represents the motor armature current, θ fi and θ gi are update parameters, and are fuzzy basis functions; Using the Nussbaum function to stabilize the system affected by an unknown nonlinear function G i which causes the problem that the control direction is unknown at some moments, the update law is designed as Among them, γ i , σ i , η fi , η gi , are positive design parameters and are any positive constants.

2. A collaborative control method for multiple robotic arms based on output according to claim 1, characterized in that: The step a) includes the following steps: a1) Transform the robotic arm dynamics model into the form of a first-order differential equation; a2) According to the mean value theorem, transform the first-order differential equation in step a2) into an integral chain form.

3. A collaborative control method for multiple robotic arms based on output according to claim 2, characterized in that: In the step a), the robotic arm dynamics model is where i represents the i-th robotic arm system, q i , represent the angular position, angular velocity, and angular acceleration respectively, τ i is the motor armature current, y i is the system output, M i is the armature inductance, H i is the armature resistance, K m,i is the back electromotive force coefficient, J i is the moment of inertia of the motor rotor, m i is the link mass, M 0.i is the load mass, d i is the link length, δ i is the load radius, g is the acceleration due to gravity, B 0.i is the viscous friction coefficient of the link, K r,i is the motor torque coupling coefficient, is the uncertainty term, u i is the control input, f i (u i ) is the unknown non-affine term; In step a1), a new set of variables x is defined i,1 = q i , x i,3 = τ i In step a2), another new set of variables z is defined i,1 = x i,1 , The integral chain form of the transformation of the robotic arm dynamics model is Among them, F i (x i,1 , x i,2 , x i,3 ) and G i (x i,1 , x i,2 , x i,3 ) are unknown nonlinear functions generated by system transformation without the control variable u i .

4. A collaborative control method for multiple robotic arms based on output according to claim 3, characterized in that: The step b) includes the following steps: b1) Determine the desired reference signal by inverse kinematics; b2) Determine the formation vector of the robotic arm according to the task requirements; b3) Obtain the collaborative tracking error equation from the robotic arm output, reference signal, and formation vector.

5. A collaborative control method for multiple robotic arms based on output according to claim 4, characterized in that: In step b), the robotic arm outputs y i = z i,1 , the desired reference signal y r , the formation vector of the robotic arm Δ = [Δ 1 ,..., Δ N T , and the cooperative tracking error is designed as​ 6. A collaborative control method for multiple robotic arms based on output according to claim 5, characterized in that: The step c) includes the following steps: c1) Calculate the values of each order of the collaborative tracking error using the collaborative error equation; c2) Define the sliding mode error using the collaborative error and its values of each order and calculate its value; c3) Construct a fuzzy system using the system state to estimate the unknown nonlinear function in the system; c4) Estimate the values of each order of the collaborative error by constructing an observer through the fuzzy system and the collaborative error.

7. A collaborative control method for multiple robotic arms based on output according to claim 6, characterized in that: In the step c), the dynamic equations of each order of the collaborative error are: Define the sliding mode error as S i = λ 1 e i,1 + λ 2 e i,2 + e i,3 , where e i,1 , e i,2 and e i,3 represent the collaborative error and its various orders between the i-th robotic arm and its neighbors, and λ 1 , λ 2 are the coefficients of e i,1 and e i,2 in the sliding mode error; Unknown non - linear functions F i and G i are approximated by the following fuzzy system: where, θ fi and θ gi are update parameters, and are fuzzy basis functions; The observer is where, l 1 , l 2 and l 3 are observer gain coefficients.

8. A collaborative control method for multiple robotic arms based on output according to claim 7, characterized in that: The step d) includes the following steps: d1) Calculate the estimated value of the sliding mode error according to the collaborative error and the values of each order of the collaborative error estimated by the observer; d2) Design the control input of the robotic arm using the estimated value of the sliding mode error; d3) Finally, the upper computer sends the calculated control input of the robotic arm to the lower computer, and the motion is completed through the servo system.

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