A safe collaborative control method for multi-robot system

Abstract

The present invention discloses a safe cooperative control method for a multi-robot system, and relates to the field of robot control technology. The method comprises: constructing a multi-robot system model of a multi-robot manipulator; setting the end effector of the follower robot in the Cartesian space, and determining the dynamic model of the multi-robot system of a multi-robot manipulator; obtaining a distributed fuzzy observer error according to the input-driven fuzzy state observer and the dynamic model of the multi-robot system of a multi-robot manipulator; constructing a two-way grouping cooperative error, a two-way grouping tracking error, and a fuzzy estimation error according to the symbolic graph network topology; applying the backstepping method, obtaining a time-varying Tan-type Lyapunov obstacle function; and then determining a distributed formation controller and an adaptive law, and determining a distributed two-way cooperative controller of a multi-robot system of a multi-robot manipulator. The present invention improves the safety of a multi-robot system of a multi-robot manipulator operating within a specific task space.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a safe collaborative control method for a multi-robot system. Background Art

[0002] In order to meet the actual multi-task coupling constraint requirements, in practical applications, it is necessary to consider the constraint range of the manipulator itself and the unmeasurable states of the sensor constraints. In addition, as a mechanical system, the existence of non-smooth inputs such as unknown dead zones also needs to be considered. Therefore, it is necessary to study the bidirectional cooperative control problem of a multi-link manipulator with state constraints and local unmeasurable states containing dead zones.

[0003] While collaborative control operations should also avoid physical constraints such as collisions; there are unpredictable states in the system, and it is difficult to obtain accurate distributed intelligent state controllers, which affects the control stability of the system. At present, there is little research on such issues, and there are many safety issues. Summary of the invention

[0004] The purpose of the present invention is to provide a safe collaborative control method for a multi-robot system, which can improve the safety of a multi-manipulator multi-robot system operating within a specific task space.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A safe collaborative control method for a multi-robot system, characterized in that the method comprises:

[0007] Constructing a multi-robotic arm multi-robot system model; the multi-robotic arm multi-robot system model includes a follower robot dynamics model and a leader robot dynamics model;

[0008] Setting the end effector of the follower robot in Cartesian space and determining the dynamic model of the multi-manipulator multi-robot system model;

[0009] Obtaining a distributed fuzzy observer error according to an input-driven fuzzy state observer and a dynamics model of the multi-manipulator multi-robot system model;

[0010] Based on the network topology of the signed graph, the two-way group coordination error, two-way group tracking error and fuzzy estimation error are constructed;

[0011] According to the distributed fuzzy observer error, the two-way group coordination error, the two-way group tracking error and the fuzzy estimation error, a backstepping method is applied to obtain a time-varying Tan-type Lyapunov barrier function;

[0012] Determining the distributed formation controller and the adaptive law according to a time-varying Tan-type Lyapunov barrier function;

[0013] According to the distributed formation controller and the adaptive law, a distributed bidirectional collaborative controller of a multi-manipulator multi-robot system is determined.

[0014] Optionally, the follower robot dynamics system model is:

[0015]

[0016] Where i=1,2,…,M is the serial number of the ith follower robot, and there are M follower robots in total; q i ∈R n , and are the generalized angular position, angular velocity and angular acceleration vectors of the ith robot, respectively, and n is the number of links in the link manipulator; is a positive definite inertia matrix representing the unknown centripetal force; is the matrix of Coriolis moment; G i (q i )∈R n is the uncertain gravitational vector; d i (t)∈R n is an unknown external force, is the unknown reversible Jacobian matrix; τ i ∈R n is the input joint torque vector with uncertain dead zone;

[0017] The leader robot dynamics system model is:

[0018]

[0019] Among them, l is the leader robot serial number, there is 1 leader robot; q l ∈R n , and are the generalized angular position, angular velocity and angular acceleration vector of the leader robot respectively; M l (q l )∈R n×n Represent the known centripetal force as a positive definite inertia matrix; is the expected matrix of Coriolis moment; G l (q l )∈R n×n is the determined gravitational vector; τ l ∈R n represents the resultant force moment vector.

[0020] Optionally, the dynamic model of the multi-manipulator multi-robot system model is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] ||x ij ||<k cij (t);

[0027] Among them, x i1 =q i ∈R n , are the position and velocity of the end effector of the ith robot in Cartesian space; y i For x i1 The state can be measured output, and x i2 is the unmeasurable state vector; n is the n-link robotic arm; There is an unknown dead zone output controller; b ri , b li and is the unknown coefficient, b ri and b li are the left and right breakpoints of the dead zone input in the ith robot system, is the slope of the uncertain dead zone; Δ i for is the ith follower robot system error, is the inverse of the transposed positive definite inertia matrix of the ith robot, is the unknown reversible Jacobian matrix, d i (t) is the external force on the ith robot; k cij (t) represents a positive time-varying constraint function, j=1,2.

[0028] Optionally, the distributed fuzzy observer error is:

[0029]

[0030] e i =[e i1 ,e i2 ] T ;

[0031] Ai =[-k 1i ,1;-k 2i ,0];

[0032]

[0033] Λ i =[0,1] T ;

[0034]

[0035]

[0036] Among them, e i =[e i1 ,e i2 ] T is the fuzzy observer error of the ith robot, e i1 and e i2 are the observer errors of position state and velocity state respectively; A i =[-k 1i ,1;-k 2i ,0] is a strict Hurwitz matrix, where k 1i and k 2i is the fuzzy observer gain, which needs to satisfy P i and Q i is a positive definite symmetric matrix; I n is an n-dimensional unit vector, and n is an n-link robotic arm; is the Kronecker product; is the estimation error of the fuzzy logic system; f i (·) is the unknown vector equation, and the fuzzy logic system is used to in is the optimal weight, is the fuzzy membership function vector, ε i (·) is the minimum estimated error; The unknown equation f i (·) estimates; for where x i1 and x i2 are the position state and velocity state of the end effector of the ith robot in Cartesian space respectively; for estimates; is the optimal fuzzy weight Estimate of ; i =[0,1] T ; Δ i for is the ith follower robot system error, where is the inverse of the transposed positive definite inertia matrix of the ith robot; is the unknown reversible Jacobian matrix; d i (t) is the external force on the ith robot; is the perturbation term, satisfying

[0037] Optionally, the distributed formation controller and the adaptive law are:

[0038]

[0039]

[0040] in, for m is the number of fuzzy membership functions in the fuzzy dead zone; The time-varying gain is expressed as k bi2 =k ci2 -q i , k ci2 represents the time-varying constraint function of the velocity state of the ith robot, β i2 A parameter > 0; k 2i Fuzzy observer gain; z i2 is the second-order bidirectional cooperative dynamic surface error; e i1 is the fuzzy observer error of the position state of the ith robot; is the optimal fuzzy weight matrix Transpose of the estimate; Right now is the fuzzy membership function vector; is the derivative of the command filter; k bi2 The square of is the absolute value of the information interaction between the ith robot and the jth robot, b li The ith robot has information exchange with the leader robot; in is the bipartite consistency synchronization error, j i is the ith item in the normalized matrix J, used for grouping; μ i2 is a non-negative parameter greater than zero; w i2 for r i and is a parameter, is the optimal fuzzy weight matrix The estimate, is the fuzzy membership function vector.

[0041] Optionally, the distributed bidirectional collaborative controller is:

[0042]

[0043] in, is the transpose of the positive definite inertia matrix of the ith robot; For The defuzzification is expressed as and The exact output, μ, can be solved ij is the fuzzy membership function; m is the number of fuzzy membership functions in the fuzzy dead zone; The time-varying gain is expressed as k bi2 =k ci2 -q i , k ci2 represents the time-varying constraint function of the velocity state of the ith robot, β i2 A parameter > 0; z i2 is the second-order bidirectional cooperative dynamic surface error; e i1 is the position state observer error of the ith robot; is the transpose of the optimal fuzzy weight estimate; Right now is the fuzzy membership function vector; k bi2 The square of is the absolute value of the information interaction between the ith robot and the jth robot, b li The ith robot has information exchange with the leader robot; is the bisection consistency synchronization error.

[0044] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] The present application provides a safe collaborative control method for a multi-robot system. Through a design based on a symbolic graph topology, the unknown dead zone is reasonably suppressed or compensated, the state capability boundary of the double-link manipulator is guaranteed, the group consistency collaborative control of the multi-robot robot is realized, and the problems of group consistency and coordinated group tasks are solved. In order to achieve the control goal, the unknown functions and parameters existing in the design process are identified by using fuzzy logic systems (FLSs), and a distributed intelligent state observer is constructed to estimate the unknown state and estimate the unmeasurable state through output feedback. At the same time, the Tan-BLFs function is used to ensure that the state does not violate the time-varying state constraint boundary, and an adaptive fuzzy leader-follower manipulator robot system bidirectional group collaborative control strategy is designed. The implementation of the algorithm design can make the multi-robot system of multi-robot safe, stable and reliable within a specific task space, whether it is transient or steady state. The effective control of the multi-robot collaboration by the control strategy will effectively reduce the tedious and repetitive labor, improve the work efficiency, and bring substantial benefits to production. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 Schematic diagram for simulating the application of bidirectional cooperative control algorithm in robots;

[0048] Figure 2 It is a schematic diagram of the traditional linear dead zone model;

[0049] Figure 3 It is a schematic diagram of the traditional nonlinear dead zone model;

[0050] Figure 4 To propose a schematic diagram of the fuzzy dead zone model;

[0051] Figure 5 A schematic diagram of directed symbolic topology based on group cooperative control;

[0052] Figure 6 Schematic diagram of the trajectory with time-varying constraints;

[0053] Figure 7 Schematic diagram of the trajectory with time-varying constraints;

[0054] Figure 8 It is a schematic diagram of the trajectory of joint 1 with time-varying constraints;

[0055] Fig. 9It is a schematic diagram of the trajectory of joint 2 with time-varying constraints;

[0056] Fig.10 It is a schematic diagram of the phase of the bidirectional cooperative control angular displacement trajectory;

[0057] Fig.11 It is a schematic diagram of the phase of the angular velocity trajectory of the two-way coordinated control;

[0058] Fig.12 It is a schematic diagram of the angular displacement error of joint 1 under bidirectional collaborative control;

[0059] Fig.13 It is a schematic diagram of the angular displacement error of joint 2 under bidirectional collaborative control;

[0060] Fig.14 It is a schematic diagram of the angular velocity error of joint 1 under bidirectional collaborative control;

[0061] Fig.15 It is a schematic diagram of the angular velocity error of joint 2 under bidirectional collaborative control;

[0062] Fig.16 This is a schematic diagram of the bidirectional controller for joint 1;

[0063] Fig.17 It is the schematic diagram of the bidirectional fuzzy controller for joint 1;

[0064] Fig.18 This is a schematic diagram of the bidirectional control controller for joint 2;

[0065] Fig.19 It is the schematic diagram of the fuzzy controller for the bidirectional cooperative control of joint 2;

[0066] Fig. 20 Flow chart of the safe collaborative control method for a multi-robot system. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] The purpose of the present invention is to provide a safe collaborative control method for a multi-robot system, aiming to improve the safety of a multi-manipulator multi-robot system operating within a specific task space.

[0069] This application aims at complex unstructured group operation scenarios, and solves the group cooperative control strategy problem of multi-arm and multi-robot systems with full-state constraints and nonlinear unknown dead zone inputs based on directed signed graph networks. Specifically, this application will consider a dual-link flexible manipulator robot system, such as a common agricultural picking robot, etc. Figure 1 As shown in the figure, the application of the simulated bidirectional cooperative control algorithm in the robot is realized to realize the cooperative control operation of group tasks. This design can effectively save labor and reduce excessive dependence on technicians.

[0070] This application introduces Tan-BLFs into a multi-manipulator multi-robot system under a group interaction network, and all joint link states satisfy the full-state constraint boundary, providing theoretical support for subsequent research on constraint coupling collaborative control of more types of robot systems. The proposed distributed fuzzy output feedback bidirectional group consistency control can effectively estimate and compensate for unmeasurable states through distributed fuzzy state observers, and realize group collaborative integrated control.

[0071] This application considers the impact of unknown dead zones on system performance in an actual robot system with full state constraints, uses FLSs to effectively estimate and identify the unknown of dead zones, breaks through the limitations of the deterministic requirements for dead zone boundaries, and provides a solution for the dead zone input problem of actual robots. This application proposes an adaptive fuzzy output feedback group consistency controller that can effectively solve the group collaborative consistency constraint control of nonlinear multi-double-link robot systems with unmeasurable state unknown dead zones.

[0072] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] Example 1

[0074] like Fig. 20 As shown, the safe collaborative control method of the multi-robot system in this embodiment includes:

[0075] Step S1: construct a multi-robotic arm multi-robot system model; the multi-robotic arm multi-robot system model includes a follower robot dynamics model and a leader robot dynamics model.

[0076] In practical applications, a leader-follower multi-link manipulator multi-robot system with full-state constraints and unknown dead zone input is considered. The purpose of studying the collaborative control mode of the leader-follower robot system is to minimize the interference of the unstructured environment on the system input signal and planning path.

[0077] The follower robot dynamics system model is as follows:

[0078]

[0079] Where i = 1, 2, ..., M is the serial number of the ith follower robot, and there are M follower robots in total; q i ∈R n , and are the generalized angular position, angular velocity and angular acceleration vectors of the ith robot, n is the number of links in the link manipulator; is a positive definite inertia matrix representing the unknown centripetal force; is the matrix of Coriolis moment; G i (q i )∈R n is the uncertain gravitational vector; d i (t)∈R n is an unknown external force, is the unknown reversible Jacobian matrix. τ i ∈R n is the input joint torque vector with uncertain dead zone.

[0080] The leader robot dynamics system model is as follows:

[0081]

[0082] Where l is the leader robot number, there is 1 leader robot; M l (q l )∈R n×n Represent the known centripetal force as a positive definite inertia matrix; G represents the expected matrix of Coriolis torque; l (q l )∈R n×n is the determined gravitational vector; τ l ∈R n represents the resultant force moment vector.

[0083] Step S2: setting the end effector of the follower robot in Cartesian space and determining the dynamic model of the multi-arm multi-robot system.

[0084] In practical applications, for Matrix M i (q i )and satisfy .

[0085] Define x i1 =q i ∈R n , are the position state and velocity state of the end effector of the ith robot in Cartesian space, respectively. The transformed robot dynamic system is:

[0086]

[0087] In the formula x i2 is the unmeasurable state vector, n is the n-link robotic arm; is the inverse of the transposed positive definite inertia matrix of the ith robot, is the matrix of Coriolis moment; G i (x i1 ) is the uncertain gravitational vector. represents the system error of the ith follower robot, satisfying the condition have Established; is the unknown reversible Jacobian matrix, d i (t) is the external force on the ith robot, It means that there is an unknown dead zone output controller, which can be expressed as:

[0088]

[0089] Where b ri , b li and is the unknown coefficient to be determined; b ri and b li Represents the left and right breakpoints of the dead zone input in the ith robot system; Represents the slope of the uncertainty dead zone. Only output y i For x i1 The state is a measurable state, the other state vectors are unmeasurable and all states should satisfy the time-varying state constraint boundary function corresponding to their physical characteristics, satisfying:

[0090] ||x ij ||<k cij (t) (5)

[0091] Where j = 1, 2, k cij (t) represents a positive time-varying state constraint function.

[0092] In actual multi-robot system applications, the main traditional linear and nonlinear dead zone control algorithm methods are difficult to handle Figure 2 and Figure 3There are inaccurate, uncertain or even unmeasurable dead zone outputs in the system. A few fuzzy methods target uncertain or unmeasurable dead zones, such as Figure 4 As shown, its fuzzy form Can compensate for fuzzy, symmetrical or asymmetrical uncertain dead zones, fuzzy dead zones Make the slope more accurate. When μ ij =1 or μ ij = 0, the proposed fuzzy dead zone becomes a conventional model, and

[0093] Using fuzzy algorithm j=1,2,…,p i , p i is the number of fuzzy membership functions; represents all possible fuzzy memberships of the membership function, k ij ∈[0,1].

[0094] Need to defuzzify into:

[0095]

[0096] In the formula It is defuzzification The output generated,

[0097] Then, the fuzzy dead zone is expanded to include linear terms and perturbation terms as follows:

[0098]

[0099] In the formula is a piecewise function,

[0100] Given the leader robot system’s end effector y in Cartesian space l ∈R n , whose system dynamics:

[0101]

[0102] Where y l ∈R n and v l ∈R n are the position state vector and velocity state vector of the leader robot, and Respectively represent the rate of change of its position state and velocity state; It is the reference signal provided by the leader robot after transformation in Cartesian space according to the actual task requirements. It is a bounded piecewise smooth vector function that satisfies the existence of a positive constant Y 2 , there is ||f l (·)||<Y 2 .in is the positive definite inertia matrix centripetal torque of the leader robot The inverse matrix of .

[0103] The following assumptions should be met:

[0104] (1) i=1,2,…,M,j=1,2,m=1,2. There is a constant and And satisfy

[0105] (2) For i = 1, 2, ..., M, suppose there exists y l (t) and is continuous and bounded, and there exists a positive constant Y 0 and Y m , satisfying ||y l (t)||≤Y 0 <k ci1 (t) and

[0106] (3) For i = 1, 2, ..., M, assume Perturbation Δ i (t) Satisfaction

[0107] Among them, k cij (t) and are the boundary functions k cij (t) and its m-th derivative, less than a constant and y l (t) is the m-order derivative of the position state vector of the leader robot; Y 0 and Y m It is divided into the leader position state vector function and the upper bound constant of its m-th order derivative, which satisfies less than k ci1 (t) This time-varying constraint function is defined in formula (5). i (t) and the modulus of the fuzzy dead zone perturbation term cannot be greater than a given constant

[0108] Directed symbolic communication graph G = (V, E, A G) represents the establishment of a group network interaction model between the follower robot and the leader robot. i ∈V, i = 1,…,M represents the point set consisting of M follower robots; represents the edge set, e ij represents the interaction between the ith robot and the jth robot; N i ={j:(v i ,v j )∈Ε,j≠i} represents the same i All neighbor robots that the robot interacts with v j The node set formed by A G =[a ij ]∈R M×M represents the adjacency weight matrix, if Otherwise ij =0; a ij >0 indicates robot ν j and ν i There is a same group relationship between them; a ij <0 means robot ν j and ν i are different group relations. There is no self-loop, a ii = 0. Laplacian matrix L = [l ij ] M×M for:

[0109] L=D G -A G (9)

[0110] In the formula D G =diag{d 1 ,d 2 ,…,d M} T ∈R M×M is the defined in-degree matrix, where Indicates the in-degree value corresponding to the ith robot. Assume that the leader ν 0 is the root node of a directed signed weighted graph, then the leader-follower signed weighted graph can be expanded to G 0 =(V 0 ,E 0 ), V 0 =V∪{v 0}.

[0111]

[0112] In the formula represents the Laplacian matrix corresponding to the leader-follower robot system, where BL =diag{b l1 ,…,b li …,b lM} represents the follower and leader's interactive pinning matrix, where b li ∈B L indicates that there is interaction between the ith follower robot and the leader robot, then b li =1, otherwise b li = 0. At least one robot interacts with the leader robot

[0113] If the Laplacian matrix of a directed graph exists with ν 0 is the spanning tree of the root node, and is a non-singular matrix, then the directed graph G 0 are connected.

[0114] Definition 1: Directed signed graph G = [V, E, A G ] is a structurally balanced graph. If the follower node set V can be decomposed into two non-intersecting subsets Node ν i and ν j , and the corresponding edge (ν i ,ν j ) belong to the same node set (ν i ,ν j ∈V q or i ,ν j ∈V r ), (q,r=1,2), then a ij ≥0; if node ν i and ν j , and the corresponding edge (ν i ,ν j ) belong to different node sets (ν i ∈V q ,ν j ∈V r ), (q≠r, (q,r=1,2)), then a ij ≤0.

[0115] Definition 2: To achieve the leader-follower bidirectional collaborative consistency control of a multi-robot system, the following conditions are required:

[0116]

[0117] Where y i (t) = x i1 is the output feedback state vector of the ith follower robot. l(t) is the state vector of the leader robot.

[0118] A directed signed graph G is called a structurally balanced graph if and only if there exists a canonical transformation matrix J = diag{j 1 ,…,j N} makes the off-diagonal elements negative in JLJ and negative in JA G J is positive.

[0119] In fact, i ∈J provides a partition, V 1 ={i|j i >0} and V 2 ={i|j i <0} corresponds to the weight a of the edge in the directed signed graph G ij For convenience, define L J JLJ+B L , JJ T =I N .L J is a non-singular M-matrix.

[0120] Control objective: Based on a balanced directed signed graph network, a distributed adaptive fuzzy bidirectional group consensus collaborative control strategy is designed for the leader-follower system with full state constraints, unknown dead zones and unmeasurable states, which is modeled as a multi-robot system with two-link manipulators and unknown nonlinearities. The control strategy can satisfy:

[0121] (1) Ensure that the error of the distributed fuzzy observer converges to a small neighborhood containing the origin.

[0122] (2) For a nonlinear multi-robot system with a time-varying constraint boundary, all the links and their corresponding states must be within the time-varying constraint boundary range: ||q i ||<k ci1 (t), Among them, ||q i || and are the moduli of the position and velocity state vectors of the end effector of the ith robot in Cartesian space; k ci1 (t) and k ci2 (t) are the time-varying constraint functions of position and velocity states respectively.

[0123] (3) An adaptive fuzzy distributed output feedback consistency controller τ is proposed i , can handle unknown dead zones to ensure that the multi-robot system under the signed graph network can achieve output feedback bidirectional group consistency cooperative control, and all signals in the closed-loop system are semi-globally consistent and ultimately bounded (SUUB);

[0124] Step S3: obtaining a distributed fuzzy observer error according to the input-driven fuzzy state observer and the dynamics model of the multi-manipulator multi-robot system model.

[0125] In practical applications, unknown functions can be estimated to any desired accuracy using FLSs as follows:

[0126]

[0127] Where i = 1, 2, ..., M, Represents the optimal fuzzy weight matrix The transpose of express The estimated value of q i represents the number of fuzzy rules; represents the fuzzy membership function vector; ε i (·) is the minimum estimated error, abbreviated as ε i ,satisfy is the unknown vector equation f i Estimation of (·)

[0128] Here only y i is available, status x i2 Is not available. Using the input-driven fuzzy state observer:

[0129]

[0130] Where i = 1, 2, ..., M; k 1i and k 2i Observer gain, parameter selection needs to satisfy the Hurwitz matrix condition. and is x i1 and x i2 The state estimate of . It can be written as follows:

[0131]

[0132] Where K i =[k 1i ,k 2i ] T , A i =[-k 1i ,1;-k 2i ,0] is a strict Hurwitz matrix, where k 1i and k 2i is the fuzzy observer gain, satisfying Here P iand Q i is a positive definite symmetric matrix; I n is an n-dimensional unit vector, and n is an n-link robotic arm; Λ i =[0,1] T ; C i =[1,0] T ; represents the Kronecker product.

[0133] Step S4: construct bidirectional group coordination error, bidirectional group tracking error and fuzzy estimation error according to the symbolic graph network topology.

[0134] In practical applications, the unknown and uncertain equation f i (·) can be estimated as Here you can satisfy yes The estimated value of FLSs; the estimated error δ i (·) is defined as follows:

[0135]

[0136] Define observer error j = 1, 2. From the multi-robot system equations (3) and (13), the dynamics of the distributed fuzzy observer error can be obtained as follows:

[0137]

[0138] Where e i =[e i1 ,e i2 ] T ; Δ i is the system error of the ith follower robot; is the perturbation term of the fuzzy dead zone in the controller; the observable bidirectional cooperative error of the output is:

[0139]

[0140] Where j i ∈J is the ith item in the normative matrix J, which is used to divide the area into groups, V 1 ={i|j i >0} and V 2 ={i|j i <0} corresponds to the weight a of the edge in the directed signed graph G ij The symbol z i1 Corresponding to the two-way group coordination error, its derivative can be calculated for:

[0141]

[0142] Where y l ∈R n and v l ∈R n are the position state vector and velocity state vector of the leader robot respectively.

[0143] The bidirectional group consistency coordination synchronization error is defined as:

[0144]

[0145] Where N i v i All neighbor robots that the robot interacts with v j The node set formed by ij ∈A G =[a ij ]∈R M ×M represents the weight corresponding to the interaction between the ith robot and the jth robot; |a ij | and sgn(a ij ) are based on a ij The weight of the positive and negative takes the absolute value and the sign function value. When a ij >0,sgn(a ij )=1, when a ij <0,sgn(a ij )=-1; is the position state x corresponding to the jth robot j1 Estimated value b li Indicates that there is an interaction between the ith follower robot and the leader robot.

[0146] From formula (18), we can get

[0147]

[0148] In the formula and The speed states x of the ith and jth robots are i2 and x j2 Estimated value. 1i and e i1 is the observer gain of the corresponding position state of the ith robot; k 1j and e j1 is the observer gain of the jth robot corresponding to the position state; v l is the velocity state vector of the leader robot.

[0149] In order to reduce the complexity, the following dynamic surface first-order filter is designed:

[0150]

[0151] Where z i2 Corresponding to the second-order two-way group coordination error dynamic surface; α i1 Represents a distributed bidirectional virtual controller; is the filter output. i represents the error generated by the control filter and the bidirectional virtual controller. Then, You can get:

[0152]

[0153] In the formula It is defuzzification The output generated, u i A distributed formation controller for multi-link robots; The unknown equation estimates; The filter output The derivative of k 2i is the observer gain of the velocity state corresponding to the ith robot; a distributed adaptive fuzzy group consensus collaborative control method is designed for the dual-link robot system equations (15)-(16). Before the design process, the fuzzy estimation error is set: yes The estimated value of will be given in detail later, j=0,1.

[0154] Step S5: According to the distributed fuzzy observer error, the two-way group coordination error, the two-way group tracking error and the fuzzy estimation error, a backstepping method is applied to obtain a time-varying Tan-type Lyapunov barrier function.

[0155] In practical applications, the backstepping recursion design framework considers the following time-varying Tan-type barrier Lyapunov function:

[0156]

[0157] Where M represents a total of M connecting rod manipulators; η i1 is the bidirectional group consistency collaborative synchronization error of the ith robot position state, Its square satisfies ||η i1 ||≤k bi1 , and k bi1 =k ci1 -qi1 , is the time-varying state constraint function k after conversion bi1 The square of represents the observer error vector e i =[e i1 ,e i2 ] T The transpose of i is a positive definite symmetric matrix to ensure the existence of a fuzzy observer gain A i is a strict Hurwitz matrix, which must satisfy A i Transpose of a matrix; I n Represents the n-dimensional identity matrix.

[0158] According to the design requirements of the physical boundary of the actual multi-robot system, all system states need to meet a certain constraint range. The design of time-varying constraint boundaries can ensure the transient and steady-state performance in real time as the system runs, prevent the state from exceeding the boundary range, and avoid the overall performance degradation caused by the change of the constraint range required by different control processes. Among them, j=1,2 can solve the problem of limited state constraints of the system. When the control time grows infinitely, it can still ensure that the state does not violate the barrier function. There is a finite limit value, which can ensure the boundedness of the closed-loop system.

[0159] Solve V for formula (23) 1 Derivative, we can get:

[0160]

[0161]

[0162] In the formula Represents the matrix A i The transpose of i =[0,1] T ; δ i (·) is the estimation error of FLSs, which represents the unknown and uncertain equation f i (·) and its estimation The error between i is the system error of the ith follower robot; is the perturbation term of the fuzzy dead zone in the controller; where sec 2 (·) indicates the correctness of (23) It is obtained by taking its derivative; and Respectively represent the constraint function k bi1 Derivatives and squares. is the bidirectional group consistency collaborative synchronization error η of the ith robot position state i1 The derivative of .

[0163] Through Yang's inequality, we can get:

[0164]

[0165] in and Represent the optimal fuzzy weight matrix The transpose and square of and denote the transposed and square of the fuzzy error respectively; ε i and is the square of the fuzzy estimation error and its upper bound; and Respectively represent the status and its estimation Take the fuzzy membership function; ||e i || 2 is the observation error vector e i =[e i1 ,e i2 ] T Take the square of the modulus; for Take the square of the modulus.

[0166] The time-varying control gain can be written as:

[0167]

[0168] In the formula is a time-varying gain equation, where sup(·) represents the upper bound of the function in (·) and Represents a non-negative parameter, which can be scaled to get

[0169] In the formula a ij ∈A G =[a ij ]∈R M×M represents the weight corresponding to the interaction between the ith robot and the jth robot; b li Indicates that there is interaction between the ith follower robot and the leader robot. i ∈J is the ith item in the standard matrix J, which is used to divide the area into groups; v l is the velocity state vector of the leader robot; z i2 Corresponding to the second-order two-way grouping coordination error dynamic surface; is the filter output. The speed state x corresponding to the jth robot j2 Estimated value; k 1i and e i1 is the observer gain of the corresponding position state of the ith robot; k 1j and e j1 is the observer gain of the jth robot corresponding to the position state.

[0170] Through Yang's inequality, we can get:

[0171]

[0172]

[0173] Substituting formula (21), formula (28)-formula (29) into formula (27) yields:

[0174]

[0175] Where Υ i represents the error generated by the control filter and the bidirectional virtual controller. By Yang's inequality:

[0176]

[0177] In the formula It is the square of the error caused by the control filter and the bidirectional virtual controller. You can get:

[0178]

[0179] Where Q i is a positive definite symmetric matrix that satisfies the Hurwitz matrix of the observer gain, λ min (Q i ) represents the matrix Q i The minimum value of the root in i1 is a constant Used to simplify the length of the formula. i1 Distributed bidirectional virtual controllers can be designed as:

[0180]

[0181] Where μ i1 is a design parameter.

[0182] When η ij →0, applying equivalent infinitesimal substitution, we can get the following form:

[0183]

[0184] Although the denominator limit approaches zero, eliminating the zero factors that can be eliminated will not produce singular points. From formula (33), You can get:

[0185]

[0186] μ i1 is a design parameter, and Substituting into formula (34), consider the following time-varying Tan-type barrier Lyapunov function:

[0187]

[0188] Where r i > 0 is a design parameter. tr[·] means finding the trace of the matrix in [·]. Represents an R n×n dimensional reversible matrix.

[0189] You can get:

[0190]

[0191] definition here And β i2 >0, the same design as in formula (26), For parameters The adaptive law of

[0192] α i1 satisfy:

[0193]

[0194] In the formula represents the end effector y of the leader robot in Cartesian space l ∈R n The j-order derivative function; note here that when Can guarantee A bounded vector equation. From formula (37) You can get:

[0195]

[0196]

[0197] There exists a positive constant H i1 >0Satisfied From formula (23) and formula (38), we can get:

[0198]

[0199] Where λ i2 =λ i1 +1 / 2.

[0200] Step S6: Determine the distributed collaborative controller and the adaptive law according to the time-varying Tan-type Lyapunov barrier function.

[0201] Design the distributed cooperative controller and the adaptive law as follows:

[0202]

[0203]

[0204] Step S7: Determine a distributed bidirectional collaborative controller for a multi-manipulator multi-robot system based on the distributed collaborative controller and the adaptive law.

[0205] Design of distributed bidirectional cooperative controller for multi-machine systems:

[0206]

[0207] If the following inequality is satisfied, then, Finally, we can get:

[0208]

[0209]

[0210] In the formula

[0211] In the design of the adaptive distributed bidirectional cooperative controller, the following requirements are guaranteed:

[0212] For the uncertain nonlinear multi-robot system equations (1) and (3), the bidirectional topology definition 1 and bidirectional collaborative consistency definition 2 satisfying assumptions (1) to (3) are obtained. By using the distributed state fuzzy observer formula (13), the fuzzy adaptive law formula (42), the adaptive fuzzy virtual controller formula (33) and the adaptive fuzzy bidirectional collaborative controller (43), appropriate design parameters are selected as Theorem 1, which can ensure that:

[0213] (1) The bidirectional collaborative synchronization error and the observer error can be guaranteed to be within the neighborhood near the origin.

[0214] (2) All states do not violate the time-varying capacity boundary of their corresponding states, and the unknown dead zone input problem can be solved by constructing FLSs:

[0215] ① Defuzzification All signals are guaranteed to achieve SUUB in a closed-loop constrained multi-robot system.

[0216] ②Fuzzy numerical value satisfy And γ i is a perturbation, 0≤γ i ≤k i / 2, all signals can ensure the realization of SUUB in the closed-loop constrained multi-robot system.

[0217] The correctness of the distributed bidirectional collaborative controller for the multi-machine system provided by the present invention is discussed below.

[0218] From formula (24) and formula (38), from the virtual fuzzy controller formula (33) and the distributed fuzzy bidirectional consistency controller formula (43), we can get satisfy:

[0219]

[0220] Where: Then, formula (46) can be scaled to obtain:

[0221]

[0222] In the formula Taking the indefinite integral of formula (47) on [0, t], we can obtain:

[0223]

[0224] Where 0<e -ρt <1, Bidirectional group coordination error η i1 , bidirectional group tracking error z i2 , Adaptive Law and the distributed fuzzy observer error e i satisfy:

[0225]

[0226]

[0227]

[0228]

[0229] If ||x l (t)||≤Y 0 , then there is a state that satisfies the boundary ||x i1 ||≤||η i1 ||+||x l (t)||≤k bi1 (t)+Y 0 If ||x i1 ||≤k ci1 (t), then the following boundary conditions hold: k ci1 (t) = k bi1 (t)+Y 0 . Further, the system output state satisfies the bounded condition: ||y i ||=||x i1 ||≤k ci1 (t). Next, the virtual controller is bounded in Equation (31) by introducing the constant And satisfy Then the state estimation satisfies: Right now in Here the state x i1 , estimated state Adaptive Law u i and τ i are all bounded, i = 1, 2, ..., M. In particular, the fuzzy membership here satisfy If the dead zone is a fixed value, in the Backstepping feedback control process, the second step is used replace And satisfy Sort in ascending order 0<γ i ≤k i1 / 2, The analysis here proves that it is similar to the previous analysis, and the numerical Fuzzy Value And other signals in the closed-loop full-state constraint multi-robot system group consistency cooperative control satisfy semi-global consistent bounded SUUB. By adjusting appropriate parameters, the full state satisfies the time-varying constraint boundary, compensates for the dead zone input, and realizes two-way group consistency cooperative control. Its two-way group cooperation error can converge to a small neighborhood around the origin.

[0230] The following is a simulation of this application, as follows:

[0231] Consider the following multi-robot system, a nonlinear second-order two-link flexible manipulator robot system with full state constraints and unknown dead zone input, which consists of 4 follower robots and 1 leader robot. The dynamic transformation model of the ith follower robot system is as follows:

[0232]

[0233] Where i = 1…4, q i1 ∈R 2 and q i2 ∈R 2 Represent the position state and speed state respectively. i (q i1 ) is the symmetric positive definite inertia matrix, M i (q i1 )=[M i11 M i12 ;M i21 M i22 ] T , according to the double-link flexible robot system, it can be expressed as: The parameters here are as follows: i1 =1kg,m i2 =0.85kg, l ic1 =1.6m,l ic2 =1m, g=9.8m / s; C i (q i1 ,q i2 )=[C i11 C i12 ; C i21 C i22 ] and C i12 =-m i2 l ic1 l ic2 q i21 sin(q i12 );C i22 =0, C i11 =-m i2 l ic1 l ic2 sin(q i12 )q i22 ; C i21 =m i2 l ic1 l ic2 sin(q i12 )q i22 . G i =[G i1 ,G i2 ] T ,G i1 =(mi1 +m i2 )gl ic1 sin(q i11 )+m i2 gl ic2 sin(q i11 +q i12 );G i2 =m i2 gl ic2 sin(q i11 +q i12 ). i (q i1 )=[J i11 J i12 ; J i21 J i22 ] T , J i11 =-l ic1 sin(q i1 )-l ic2 sin(q i1 +q i2 );J i12 =-l ic2 sin(q i1 +q i2 );J i21 = l ic1 cos(q i1 )+l ic2 cos(q i1 +q i2 );J i22 = l ic2 cos(q i1 +q i2 ). i (t) is defined as the external disturbance to which the ith two-link robot is subjected: d i (t)=[sin(t)+0.2,2sin(t)+0.5,sin(t)+0.4,0,0].

[0234] Here the leader robot system conversion equation can be written as:

[0235] In the formula like Figure 5 As shown in the figure, the interaction topology of the leader-follower dual-link manipulator system is given. Figure 5 It can be seen that the communication interaction is based on a group-balanced directed signed graph. The robot system can be divided into two groups V 1 = {ν 1 ,ν 2 ,ν 3} and V2 = { 4 ,ν 5}.

[0236] Considering that the robot needs to meet different physical constraints in the working scene, the following time-varying state constraints are set here: k b1 (t) = 11.1 + 0.03 sin (2t), k b2 (t) = 10.75 + 0.35 cos (t), which corresponds to an isomorphic robot whose first link arm satisfies [-k b1 (t),k b1 (t)], the second link robot arm satisfies [-k b2 (t),k b2 (t)]; k c1 (t) = 0.75 + 0.15 sin (t), k c2 (t) = 0.3 + 0.1 sin (1.5 t).

[0237] The virtual controller, adaptive law and actual controller parameters constructed by Theorem 1. Through the above two-way group collaborative control parameter selection, the simulation results are as follows:

[0238] pass Figure 6 It can be seen that the angular displacement of joint 1 of the two-link manipulator robot satisfies the time-varying constraint boundary k c11 Group collaborative consistency control can be well implemented. Figure 7 The angular displacement of the joint 2 of the two-link manipulator robot satisfies the time-varying constraint bound k c12 , which can well realize group coordination consistency control. Figure 8 It can be seen that the angular velocity of joint 1 of the two-link manipulator robot satisfies the time-varying constraint boundary k c21 ;like Fig. 9 As shown, the angular velocity of joint 2 satisfies the time-varying constraint bound k c22 . Fig.10 and Fig.11 The phase diagram of the two-link manipulator is given.

[0239] Fig.12 and Fig.13 The bidirectional coordination error η of the first joint angular distance of the double-link manipulator robot is given respectively. i11 And its error satisfies the time-varying constraint bound η i11 |<k b11 ; The bidirectional coordination error η of the angular distance of the second joint of the two-link manipulator is given i12 And satisfy the time-varying constraint boundary η i12 |<k b12 . Fig.14 and Fig.15The bidirectional coordination error η of the angular velocity of the first joint of the double-link manipulator is given respectively. i21 And its error satisfies the time-varying constraint bound η i21 |<k b21 ; The bidirectional coordination error η of the angular velocity of the second joint of the two-link manipulator is given i22 And satisfy the time-varying constraint boundary η i22 |<k b22 .

[0240] Fig.16 and Fig.17 The bidirectional cooperative controller u of the first joint of the two-link robot arm is given respectively i1 And the bidirectional cooperative fuzzy controller Γu i1 ; Fig.18 and Fig.19 The bidirectional cooperative controller u of the second joint of the two-link robot arm is given respectively. i2 And the bidirectional cooperative fuzzy controller Γu i2 The simulation results show that the designed distributed fuzzy adaptive bidirectional group consistency cooperative controller is effective.

[0241] Aiming at the actual multi-task requirements faced by multi-arm and multi-robot systems in collaborative operations, this application constructs a grouped symbolic graph network topology and studies a class of uncertain nonlinear dual-link robotic arm robot systems. A distributed adaptive fuzzy output feedback time-varying bidirectional collaborative constraint control strategy is proposed. By using the Tan-BLFs function, the requirement that different links need to meet the time-varying constraint boundary during operation is solved; a distributed fuzzy state observer and FLSs are constructed to estimate the unmeasurable state and the unknown dead zone input of the mechanical system, respectively, which can realize the grouped collaborative consistency control of the dual-link robotic arm robot system. The stability of the proposed algorithm and design is proved by the Lyapunov theorem, and its effectiveness is verified by simulation. This lays a theoretical foundation for studying the multi-target grouped formation control of actual multi-robot systems under complex network interactions. This grouped collaborative intelligent control has changed the traditional production model and provided a reference for other practical application research.

[0242] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be deemed to be within the scope of this specification.

[0243] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention; at the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A safe collaborative control method for a multi-robot system, characterized in that: The method comprises: Constructing a multi-robotic arm multi-robot system model; the multi-robotic arm multi-robot system model includes a follower robot dynamics model and a leader robot dynamics model; Setting the end effector of the follower robot in Cartesian space and determining the dynamic model of the multi-manipulator multi-robot system model; Obtaining a distributed fuzzy observer error according to an input-driven fuzzy state observer and a dynamics model of the multi-manipulator multi-robot system model; Based on the network topology of the signed graph, the two-way group coordination error, two-way group tracking error and fuzzy estimation error are constructed; According to the distributed fuzzy observer error, the two-way group coordination error, the two-way group tracking error and the fuzzy estimation error, a backstepping method is applied to obtain a time-varying Tan-type Lyapunov barrier function; Determining the distributed formation controller and the adaptive law according to a time-varying Tan-type Lyapunov barrier function; Determine a distributed bidirectional collaborative controller for a multi-manipulator multi-robot system according to the distributed formation controller and the adaptive law; The distributed bidirectional collaborative controller is: in, is the transpose of the positive definite inertia matrix of the ith robot; For The defuzzification is expressed as and The exact output, μ, can be solved ij is the fuzzy membership function; m is the number of fuzzy membership functions in the fuzzy dead zone; The time-varying gain is expressed as k bi2 =k ci2 -q i , k ci2 represents the time-varying constraint function of the velocity state of the ith robot, β i2 A parameter > 0; z i2 is the second-order bidirectional cooperative dynamic surface error; e i1 is the position state observer error of the ith robot; is the transpose of the optimal fuzzy weight estimate; Right now is the fuzzy membership function vector; k bi2 The square of for is the absolute value of the information interaction between the ith robot and the jth robot, b li The ith robot has information interaction with the leader robot; w i1 for is the bisection consistency synchronization error.

2. The safe collaborative control method of a multi-robot system according to claim 1, characterized in that: The follower robot dynamics system model is: Where i=1,2,…,M is the serial number of the ith follower robot; M is the number of follower robots; q i ∈R n , and are the generalized angular position, angular velocity and angular acceleration vectors of the ith robot respectively; n is the number of links in the link manipulator; is a positive definite inertia matrix representing the unknown centripetal force; is the matrix of Coriolis moment; G i (q i )∈R n is the uncertain gravitational vector; d i (t)∈R n is an unknown external force, is the unknown reversible Jacobian matrix; τ i ∈R n is the input joint torque vector with uncertain dead zone; The leader robot dynamics system model is: Among them, l is the leader robot number, there is 1 leader robot, q l ∈R n , and are the generalized angular position, angular velocity and angular acceleration vector of the leader robot respectively; M l (q l )∈R n×n Represent the known centripetal force as a positive definite inertia matrix; is the expected matrix of Coriolis moment; G l (q l )∈R n×n is the determined gravitational vector; τ l ∈R n represents the resultant force moment vector.

3. The safe collaborative control method of a multi-robot system according to claim 1, characterized in that: The dynamic model of the multi-manipulator multi-robot system model is: Among them, x i1 =q i ∈R n , are the position and velocity of the end effector of the ith robot in Cartesian space; y i For x i1 The state can be measured output, and x i2 is the unmeasurable state vector; n is the number of links in the link robot; There is an unknown dead zone output controller; b ri , b li and is the unknown coefficient, b ri and b li are the left and right breakpoints of the dead zone input in the ith robot system, is the slope of the uncertain dead zone; Δ i for is the ith follower robot system error, is the inverse of the transposed positive definite inertia matrix of the ith robot; is the unknown reversible Jacobian matrix; d i (t) is the external force on the ith robot; k cij (t) represents a positive time-varying constraint function, j=1,2.

4. The safe collaborative control method of a multi-robot system according to claim 1, characterized in that: The distributed fuzzy observer error is: Among them, e i =[e i1 ,e i2 ] T is the fuzzy observer error of the ith robot, e i1 and e i2 are the observer errors of position state and velocity state respectively; A i =[-k 1i ,1;-k 2i ,0] is a strict Hurwitz matrix, where k 1i and k 2i is the fuzzy observer gain, which needs to satisfy P i and Q i is a positive definite symmetric matrix; I n is an n-dimensional unit vector, and n is an n-link robotic arm; is the Kronecker product; δ i (·)for is the estimation error of the fuzzy logic system; f i (·) is the unknown vector equation, and the fuzzy logic system is used to in is the optimal weight, is the fuzzy membership function vector, ε i (·) is the minimum estimated error; The unknown equation f i (·) estimates; for where x i1 and x i2 are the position state and velocity state of the end effector of the ith robot in Cartesian space respectively; for estimates; is the optimal fuzzy weight Estimate of; Δ i for is the ith follower robot system error, where is the inverse of the transposed positive definite inertia matrix of the ith robot; is the unknown reversible Jacobian matrix; d i (t) is the external force on the ith robot; is the perturbation term, satisfying 5. The safe collaborative control method of a multi-robot system according to claim 1, characterized in that: The distributed formation controller and the adaptive law are: in, for m is the number of fuzzy membership functions in the fuzzy dead zone; The time-varying gain is expressed as k bi2 =k ci2 -q i , k ci2 represents the time-varying constraint function of the velocity state of the ith robot, β i2 A parameter > 0; k 2i Fuzzy observer gain; z i2 is the second-order bidirectional cooperative dynamic surface error; e i1 is the fuzzy observer error of the position state of the ith robot; is the optimal fuzzy weight Transpose of the estimate; Right now is the fuzzy membership function vector; is the derivative of the command filter; k bi2 The square of for |a ij | is the absolute value of the information interaction between the ith robot and the jth robot, b li The ith robot has information interaction with the leader robot; w i1 for in is the bipartite consistency synchronization error, j i is the ith item in the normalized matrix J, used for grouping; μ i2 is a non-negative parameter greater than zero; w i2 for r i and is a parameter.

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