Robust Decoupling Control Method for Multilateral Remote Operating Systems Based on Fuzzy Control

Abstract

This invention discloses a robust decoupling control method for a multi-arm teleoperation system based on fuzzy control, comprising: establishing the dynamic equations of the multi-arm teleoperation system; and designing a robust decoupling controller for the multi-arm teleoperation system based on fuzzy control theory. This invention achieves decoupling compensation for multiple coupled manipulators in a multi-arm teleoperation system, thereby ensuring system stability and maintaining system synchronization. It has significant advantages in practical applications with high stability requirements, such as in the medical, aerospace, and marine exploration fields.

Description

Technical Field

[0001] This invention belongs to the field of teleoperation control, specifically a robust decoupling control method for a multilateral teleoperation system based on fuzzy control. Background Technology

[0002] With the development and progress of society, economy, science and technology, the scope of human scientific research is constantly expanding. For some complex and difficult tasks, humans alone cannot complete them. The research and development and production of teleoperated robots can greatly simplify the complexity of these tasks. In recent years, with the expansion of the application fields of teleoperation systems, the requirements for the comprehensive performance of the system have gradually increased. The research object of teleoperation systems has gradually shifted from the traditional single-master-single-slave (SMSS) bilateral structure to a multilateral structure. Based on the number of master and slave robots, multilateral systems are mainly divided into the following categories: single-master-multiple-slaves (SMMS) system, multiple-master-single-slave (MMSS) system, and multiple-master-multiple-slaves (MMMS) system. Reference 1 (Li Zhijun, Su Chunyi. Neural-adaptive control of single-master-multiple-slaves teleoperation for coordinated multiple mobilemanipulators with time-varying communication delays and input uncertainties[J].IEEE Transactions on Neural Networks and Learning Systems,2013,24(9):1400-1413.) studies the coordinated operation of multiple slave robots under unknown input and time-varying delays in a single-master-multiple-slaves teleoperation system. Reference 2 (Ahmad U, Pan YJ and Shen HH. Robust control design for teleoperation of multiple mobile manipulators under time delays[J]. International Journal of Robust and Nonlinear Control,2020,30(16):6454-6472.) designs a robust controller that not only realizes single-master-multiple-slaves synchronous control, but also optimizes the internal force distribution of the object and transmits environmental force feedback through the estimated environmental parameters on the communication channel, thereby maintaining the stability of the entire system.

[0003] While research on the synchronization of multi-side teleoperation systems is increasingly abundant, research on the coupling and decoupling between multiple robotic arms is relatively scarce. Coupling between multiple robotic arms can severely impact the synchronization and stability of bilateral or multilateral systems. Summary of the Invention

[0004] To address the aforementioned technical deficiencies in the prior art, this invention proposes a robust decoupling control method for a multilateral teleoperation system based on fuzzy control.

[0005] The technical solution to achieve the purpose of this invention is: a robust decoupling control method for a multi-sided teleoperation system based on fuzzy control, comprising the following steps:

[0006] Step 1: Establish the dynamic equations of the multi-sided teleoperated robotic arm system;

[0007] Step 2: Design robust decoupling for a multi-sided teleoperated robotic arm system based on fuzzy control theory.

[0008] Preferably, the specific method for establishing the dynamic equations of the multi-sided teleoperated manipulator system is as follows:

[0009] Based on the Euler-Lagrange equations, the dynamic equations of a multilateral teleoperated manipulator system are established. The structure of the multilateral teleoperated manipulator system is a master-slave teleoperation system. The dynamic equations of the multilateral teleoperated manipulator system are as follows:

[0010]

[0011]

[0012] Where m and s represent the master and slave robotic arm systems, respectively; These represent the position vectors of the master and slave robotic arms, respectively. These represent the velocity vectors of the master and slave robotic arms, respectively. These represent the acceleration vectors of the master and slave robotic arms, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. These represent the gravity matrices of the master and slave robotic arms, respectively. These represent the external force acting on the main end and the force exerted by the secondary end on the environment, respectively. These represent the control inputs from the master and slave ends, respectively; i, j represent the slave robot arm serial numbers, c is a constant, and g... ij This represents the coupling coefficient between robotic arms, with 1 for mutual coupling and 0 for no coupling, and n represents the matrix dimension.

[0013] Preferably, M(q) and The following relation exists: for any matrix

[0014] Where M(q) is the mass inertia matrix of the robotic arm, It is the Coriolis force matrix of the robotic arm. It is the derivative of the mass-inertia matrix of the robotic arm. Represents a real number vector.

[0015] Preferably, the specific steps of step 2, which designs a robust decoupling controller for a multi-sided teleoperated robotic arm system based on fuzzy control theory, are as follows:

[0016] Step 2-1: Design the sliding mode controller for the multi-sided telescopic robotic arm system

[0017] To ensure the asymptotic stability of the multi-sided teleoperated robotic arm system, the master-slave sliding mode controller is designed as follows:

[0018]

[0019]

[0020] in,

[0021] in, These represent the control inputs of the master and slave terminals, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. These represent the gravity matrices of the master and slave robotic arms, respectively; n represents the matrix dimension; s m ,s s,i These represent the sliding surfaces of the master and slave ends, respectively. These represent the ideal speeds of the master and slave ends, respectively. These represent the ideal accelerations of the master and slave ends, respectively; e m ,e s,i These represent the position errors of the master and slave ends, respectively. These represent the speed errors of the master and slave ends, Λ m ,Λ s,i All are positive definite matrices; These are all variables introduced to simplify the system; i represents the sequence number from the robotic arm;

[0022] Step 2-2: Design an adaptive sliding mode controller for a multi-sided teleoperated robotic arm system based on fuzzy theory.

[0023] Fuzzy If-then rules are established using multiple-input multiple-output rules. The form of a fuzzy If-then rule is as follows:

[0024]

[0025] Where R is the union of all fuzzy rules, R l Let R represent the l-th fuzzy rule, where l = 1, 2, ..., M, and each rule R l The form is:

[0026]

[0027]

[0028] U = U1 × U2 × … × U n U i ∈R

[0029] V = V1 × V2 × … × V m V j ∈R

[0030] Where M is the total number of rules, x = (x1, ..., x2) n ) T and y = (y1, ... y m ) T U is the input and output vector of the fuzzy system. i and V j It is a fuzzy set in a subspace. and These are variables within a subspace fuzzy set, accessed through membership functions. and Describe it;

[0031] The output of MIMO-FLS with a center-averaged defuzzifier, product inference engine, and single-valued fuzzifier is shown below:

[0032]

[0033] choose As a free parameter, the above equation can be rewritten as:

[0034]

[0035]

[0036] Among them, y j y represents the system output. j Let ξ(x) represent the mean of the l-th output, where ξ(x) = (ξ1(x), ..., ξ2(x)). M (x)) T This is called the fuzzy basis function vector. This is called the parameter vector;

[0037] MIMO-FLS rewritten as:

[0038] y = Θ T ξ(x)

[0039] Where Θ is an M×m matrix, Θ j It represents the j-th column of matrix Θ.

[0040] Coupling terms Abstracted as an unknown nonlinear term Using fuzzy systems To approximate the coupling terms and eliminate the mutual coupling between the robotic arms, an adaptive control law based on fuzzy compensation is designed as follows:

[0041]

[0042] Where c is a constant, g ij q is the coupling coefficient, where 1 represents coupling and 0 represents no coupling; s , H represents the position vector, velocity vector, and acceleration vector of the robotic arm; H represents the nonlinear term. Representing a fuzzy system;

[0043] τ s,i M represents the control input from the slave end. s,i (q s,i ) represents the mass inertia matrix of the robotic arm. G represents the Coriolis force matrix from the robotic arm. s,i (q s,i ) represents the gravity matrix from the robotic arm; K D =diag(K) i ), K i It is a positive constant, s s,i This represents the sliding surface at the slave end, where i is the serial number of the slave robot arm;

[0044]

[0045] The fuzzy approximation error w is:

[0046] Where, Θ * The parameter matrix represents the ideal state.

[0047] The adaptive law is designed as follows:

[0048] Where Γ is a positive definite matrix and i is the robotic arm index.

[0049] Steps 2-3: Add robust functions to the sliding mode controller to obtain an adaptive sliding mode controller for the multilateral teleoperated robotic arm system based on fuzzy theory.

[0050]

[0051]

[0052] in,

[0053] in, These represent the control inputs of the master and slave terminals, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. represents the gravity matrix of the master and slave robotic arms respectively; n represents the dimension of the matrix.

[0054] s m ,s s,i These represent the sliding surfaces of the master and slave ends, respectively. These represent the ideal speeds of the master and slave ends, respectively. These represent the ideal accelerations of the master and slave ends, respectively; e m ,e s,i These represent the position errors of the master and slave ends, respectively. These represent the speed errors of the master and slave ends, Λ m ,Λ s,i All are positive definite matrices; All of these are variables introduced to simplify the system; i represents the sequence number from the robotic arm.

[0055] Describe a fuzzy system, α,β i All are positive numbers, sat(s) m ),sat(s s,i ) represent the saturation functions of the master and slave controllers, respectively.

[0056] Compared with the prior art, the present invention has the following significant advantages: the present invention solves the problem of system instability caused by mutual coupling between manipulators in a multi-sided teleoperated manipulator system. Compared with the traditional control methods, the present invention ensures the stability of the system, enhances the robustness of the system, and maintains the synchronization of the multi-sided teleoperated system.

[0057] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0058] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0059] Figure 1 This invention relates to a multi-sided teleoperated robotic arm system.

[0060] Figure 2 This refers to the latency element in the multi-sided remote operating system proposed in this invention. (Transmission latency)

[0061] Figure 3 This is the engineering drawing of the two-degree-of-freedom robotic arm proposed in this invention.

[0062] Figure 4 The non-decoupling control proposed in this invention tracks the curve from robotic arm 1.

[0063] Figure 5 The non-decoupling control proposed in this invention tracks the curve from the robotic arm 2.

[0064] Figure 6 The error curve of the undecoupled control from the robotic arm 1 is proposed in this invention.

[0065] Figure 7 The error curve of the undecoupled control from the robotic arm 2 is proposed in this invention.

[0066] Figure 8 The present invention proposes a decoupled control method for tracking curves from robotic arm 1.

[0067] Figure 9 The present invention proposes a decoupled control method for tracking curves from robotic arm 2.

[0068] Figure 10 The present invention provides a decoupled control error curve for robotic arm 1.

[0069] Figure 11 The present invention provides a decoupled control error curve for robotic arm 2.

[0070] Figure 12 This is the output curve of the coupling and fuzzy system approximation proposed in this invention.

[0071] Figure 13 This is the fuzzy approximation error curve proposed in this invention. Detailed Implementation

[0072] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0073] As shown in the figure, this invention relates to a multi-arm teleoperated system with unknown nonlinear coupling under robust sliding mode control based on fuzzy control. Under external force, the robotic arms decouple and achieve stable tracking between the master and slave arms. The specific operation steps are as follows:

[0074] Step 1: Establish the dynamic equations of the multi-side teleoperated robotic arm system. In the numerical simulation, a robotic arm system with 1 master and 2 slaves is selected, with the two slave systems coupled together.

[0075] Main client:

[0076] From end 1:

[0077]

[0078] From end 2:

[0079]

[0080] Wherein, the inertia matrix M m M s,1 and M s,2 Coriolis force matrix C m C s,1 and C s,2 Gravity matrix G m G s,1 and G s,2 and human operating torque F h The expression is as follows:

[0081]

[0082]

[0083]

[0084] F h =J m T *[0 1] T *f h

[0085]

[0086] In the simulation, the parameters are selected as follows:

[0087] m1=1kg, m2=1.5kg, l1=1m, l2=0.8m, g=9.81m / s 2 c = 5, g 12 =g 21 =1,f h =1N.

[0088] Step 2: Establish a sliding mode controller model for the master-slave robotic arm system

[0089] Main client:

[0090] From end 1:

[0091]

[0092] From end 2:

[0093]

[0094] in,

[0095]

[0096] The parameters are selected as follows:

[0097] In robust control laws, select In the fuzzy system weights, each initial system value is set to 1; the ideal input signal at the master end is: q m1 =q m2 =0.3sint, The initial value of each joint is q m (0) = [0 0], q s,1 (0) = [0 0], q s,2 (0) = [0.5 0.5]. The membership function is defined as:

[0098]

[0099] This invention uses Lyapunov functions to prove the stability of the control system.

[0100] Choose the Lyapunov function as V

[0101] V = V1 + V2 + V3

[0102] V1 is used to prove the stability of the master robotic arm controller; V2 and V3 are used to prove the stability of the slave robotic arm controller.

[0103] Proof that the master-end robotic arm controller is stable:

[0104] The Lyapunov function for the master-end robotic arm sliding mode controller is designed as V1, and its specific expression is as follows:

[0105]

[0106] Calculate the derivative of the Lyapunov function of the master-end robotic arm sliding mode controller:

[0107] Take α≥||F h ||, yields the following expression:

[0108]

[0109] Since V1≥0, the sliding mode controller of the main end robotic arm is stable.

[0110] Prove that the end-effector observer is stable:

[0111]

[0112] Calculate the derivative of the Lyapunov function of the sliding mode controller for the slave robot arm:

[0113] Take β≥||F e ||, yields the following expression:

[0114]

[0115] As long as K D The design is large enough to ensure when At that time, s s ≡0, according to the LaSalle invariance principle, as t→∞, s→0. The convergence rate of the system depends on K. D Because V2 + V3 ≥ 0, Therefore, the sliding mode controller of the end robotic arm is stable.

[0116] Finally, the simulation results are summarized as follows: In the control system of a multi-sided teleoperated robotic arm based on fuzzy control and sliding mode control, from Figures 4-7 It can be seen that without a decoupling controller, the slave robotic arm, due to the coupling between itself and the master arm, is unable to stably track the position and velocity information of the master arm; Figures 8-11 It can be seen that, with the addition of a decoupling controller, the decoupling controller compensates for the coupling relationship between the slave robotic arms, enabling multiple slave robotic arms to stably track the position and velocity information of the master robotic arm; Figure 12 and Figure 13 It can be seen that the fuzzy controller can approximate and compensate for the nonlinear coupling of the system.

[0117] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

[0118] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

[0119] It should be understood that the modules, units, components, etc., included in the device of one embodiment of the present invention can be adaptively changed to be placed in a device different from that embodiment. Different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A robust decoupling control method for a multilateral teleoperation system based on fuzzy control, characterized in that, Includes the following steps: Step 1: Establish the dynamic equations of the multi-sided teleoperated robotic arm system. The specific method is as follows: Based on the Euler-Lagrange equations, the dynamic equations of a multilateral teleoperated manipulator system are established. The structure of the multilateral teleoperated manipulator system is a master-slave teleoperation system. The dynamic equations of the multilateral teleoperated manipulator system are as follows: Where m and s represent the master and slave robotic arm systems, respectively; These represent the position vectors of the master and slave robotic arms, respectively. These represent the velocity vectors of the master and slave robotic arms, respectively. These represent the acceleration vectors of the master and slave robotic arms, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. These represent the gravity matrices of the master and slave robotic arms, respectively. These represent the external force acting on the main end and the force exerted by the secondary end on the environment, respectively. These represent the control inputs from the master and slave ends, respectively; i, j represent the slave robot arm serial numbers, c is a constant, and g... ij This represents the coupling coefficient between robotic arms, with 1 for mutual coupling and 0 for no coupling, and n represents the matrix dimension. Step 2: Design robust decoupling for a multi-sided teleoperated robotic arm system based on fuzzy control theory. The specific steps are as follows: Step 2-1: Design the controller for the multi-sided telescopic robotic arm system To ensure the asymptotic stability of the multi-sided teleoperated robotic arm system, the master-slave controller is designed as follows: in, in, These represent the control inputs of the master and slave terminals, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. represents the gravity matrix of the master and slave robotic arms respectively; n represents the dimension of the matrix; These represent the ideal speeds of the master and slave ends, respectively. These represent the ideal accelerations of the master and slave ends, respectively; e m ,e s,i These represent the position errors of the master and slave ends, respectively. These represent the speed errors of the master and slave ends, Λ m ,Λ s,i All are positive definite matrices; These are all variables introduced to simplify the system; i represents the sequence number from the robotic arm; Step 2-2: Design an adaptive sliding mode controller for a multi-sided teleoperated robotic arm system based on fuzzy theory. Fuzzy If-then rules are established using multiple-input multiple-output rules. The form of a fuzzy If-then rule is as follows: Where R is the union of all fuzzy rules, R l Let R represent the l-th fuzzy rule, where l = 1, 2, ..., M, and each rule R l The form is: U=U1×U2×…×U n ,IN i ∈R V=V1×V2×…×V m ,V j ∈R Where M is the total number of rules, x = (x1, ..., x2) n ) T and y = (y1, ... y m ) T U is the input and output vector of the fuzzy system. i and V j It is a fuzzy set in a subspace. and These are variables within a subspace fuzzy set, accessed through membership functions. and Describe it; The output of MIMO-FLS with a center-averaged defuzzifier, product inference engine, and single-valued fuzzifier is shown below: choose As a free parameter, the above equation can be rewritten as: Among them, y j y represents the system output. j Let ξ(x) represent the mean of the l-th output, where ξ(x) = (ξ1(x), ..., ξ2(x)). M (x)) T This is called the fuzzy basis function vector. This is called the parameter vector; MIMO-FLS rewritten as: y=Θ T ξ(x) Where Θ is an M×m matrix, Θ j Represents the j-th column of matrix Θ; Coupling terms Abstracted as an unknown nonlinear term Using fuzzy systems To approximate the coupling terms and eliminate the mutual coupling between the robotic arms, an adaptive control law based on fuzzy compensation is designed as follows: Where c is a constant, g ij The coupling coefficient is 1 for coupling and 0 for no coupling. H represents the position vector, velocity vector, and acceleration vector of the robotic arm; H represents the nonlinear term. Representing a fuzzy system; τ s,i M represents the control input from the slave end. s,i (q s,i ) represents the mass inertia matrix of the robotic arm. G represents the Coriolis force matrix from the robotic arm. s,i (q s,i ) represents the gravity matrix from the robotic arm; K D =diag(K) i ), K i It is a positive constant, s s,i This represents the sliding surface at the slave end, where i is the serial number of the slave robot arm; The fuzzy approximation error w is: Where, Θ * The parameter matrix represents the ideal state. The adaptive law is designed as follows: Where Γ is a positive definite matrix, and i is the index of the robotic arm; Steps 2-3: Add robust functions to the sliding mode controller to obtain an adaptive sliding mode controller for the multilateral teleoperated robotic arm system based on fuzzy theory. in, in, These represent the control inputs of the master and slave terminals, respectively. These represent the mass inertia matrices of the master and slave robotic arms, respectively. These represent the Coriolis force matrices of the master and slave robotic arms, respectively. represents the gravity matrix of the master and slave robotic arms respectively; n represents the dimension of the matrix; s m ,s s,i These represent the sliding surfaces of the master and slave ends, respectively. These represent the ideal speeds of the master and slave ends, respectively. These represent the ideal accelerations of the master and slave ends, respectively; e m ,e s,i These represent the position errors of the master and slave ends, respectively. These represent the speed errors of the master and slave ends, Λ m ,Λ s,i All are positive definite matrices; These are all variables introduced to simplify the system; i represents the sequence number from the robotic arm; Describe a fuzzy system, α,β i All are positive numbers, sat(s) m ),sat(s s,i ) represent the saturation functions of the master and slave controllers, respectively.

2. The robust decoupling control method for a multi-sided teleoperation system based on fuzzy control according to claim 1, characterized in that, M(q) and The following relation exists: for any matrix Where M(q) is the mass inertia matrix of the robotic arm, It is the Coriolis force matrix of the robotic arm. It is the derivative of the mass-inertia matrix of the robotic arm. Represents a real number vector.

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