Multi-mobile-robot system consistency control method and system considering time delay and medium

Abstract

The invention belongs to the related technical field of system consistency control, and particularly discloses a multi-mobile-robot system consistency control method and system considering time delay and a medium, kinematics and dynamics models of mobile robots are established, and on the basis, a communication topological graph of a multi-mobile-robot system is constructed. By designing a cost function and a constraint condition of model prediction control, multi-robot system consistency control under communication delay is realized; meanwhile, the stability of the designed controller is guaranteed by adopting the idea of designing the auxiliary controller, and the influence of time delay on the control effect is overcome by estimating the system state under the communication delay and broadcasting the system state. According to the invention, the stability and reliability of consistency control of the multi-mobile robot system can be improved, so that safe and stable operation of the mobile robot system is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field related to system consistency control, and more specifically, relates to a method, system and medium for consistency control of a multi-mobile robot system taking time delay into consideration. Background Art

[0002] In recent years, multi-mobile robot systems (multi-agent systems) have become a research hotspot due to their advantages in efficiency, flexibility, scalability and reliability. Compared with single robot systems, multi-mobile robot systems can perform complex tasks in a larger range and collaborate effectively in the task environment. Among the control problems of these systems, consistency control is particularly important. It refers to how multiple robots coordinate when performing tasks or making decisions to achieve consistency in the overall goal or behavior of the system. This includes ensuring that all robots maintain consistency in information sharing, decision making and behavior execution to avoid conflicts and confusion. Due to its important role in distributed control, collaborative robots and intelligent transportation systems, consistency control is regarded as a fundamental problem in multi-robot control.

[0003] However, in the current research on consistency control of multi-robot systems, there are still the following two problems and areas that need to be improved:

[0004] 1) How to ensure control performance in the presence of communication time delay;

[0005] 2) How to optimize control performance and ensure controller stability while solving system constraints.

[0006] Therefore, from the perspective of theory and practical application, an optimization method that can comprehensively consider system constraints and communication time delay is urgently needed for the consistency problem of multi-mobile robot systems. Such an optimization method not only needs to ensure the effectiveness of consistency control when dealing with uncertainties such as delay, but also needs to ensure that the multi-mobile robot system can still achieve coordination and consistency when facing various task requirements. This has far-reaching significance for ensuring the safe operation of the multi-mobile robot system and improving the overall control performance of the system. Summary of the invention

[0007] In view of the above defects or improvement needs of the prior art, the present invention provides a method, system and medium for consistency control of a multi-mobile robot system taking into account time delay, the purpose of which is to ensure the consistency control performance of the multi-mobile robot system in the case of communication delay.

[0008] To achieve the above object, according to a first aspect of the present invention, a method for coherence control of a multi-mobile robot system considering time delay is proposed, comprising the following steps:

[0009] For a single robot in a multi-mobile robot system, a cost function is constructed based on its consistent state error, and the optimal control input of the robot is obtained by minimizing the cost function; the above steps are repeated for each robot to obtain the optimal control input of each robot, thereby achieving consistent control of the multi-mobile robot system;

[0010] Among them, robot i in the multi-mobile robot system predicts its consistency state error ξ at time t at time t+k ei The calculation formula for (t+k|t) is:

[0011]

[0012] t+k|t represents the prediction of time t+k at time t, k=0,1,2,…N-1, N is the prediction time domain; ξ i (t+k|t) represents the estimated position state of robot i at time t+k predicted at time t, N i represents the neighbor set of robot i. The robots in this set have information exchange with robot i, i.e., neighbors of robot i; a ij =1 / |N i |,|N i | represents the number of neighbors of robot i; It represents the estimated position state quantity of robot j at time t+k broadcasted to its neighbors at time t, and the calculation formula is:

[0013]

[0014] ξ j (t+kp t ) indicates that in p t The estimated position state of robot j at time t+k predicted at the moment; p t represents the time when the state quantity was most recently broadcast to the neighbors before time t, N′ represents the maximum number of state quantities that robot j can broadcast to its neighbors under communication delay, N′=p t +Nt; A represents the weighted adjacency matrix of the undirected graph of the multi-mobile robot system communication topology, Represents the estimated position state of robot j at time t+k-1 broadcasted to its neighbors at time t.

[0015] As a further preferred embodiment, the cost function J of robot i at time t is i for:

[0016]

[0017] Among them, τ i (t+k|t) represents the control input of robot i at time t+k; Qi , R i Respectively represent the weight coefficients of the error amount and the control input amount in the cost function, Respectively represent the weight coefficients as Q i , R i The Euclidean norm of .

[0018] As a further preferred method, to minimize the cost function J i As the goal, solve the optimal control input of robot i at the current time t The constraints during solution include: system model constraints, system initial state constraints, stability constraints and input saturation constraints.

[0019] As further preferred, the discrete form of the system model constraint is expressed as:

[0020] ξ i (t+1|t)=f(ξ i (t),τ i (t))

[0021] Among them, ξ i (t) represents the state of robot i at the current time t, ξ i (t+1|t) represents the state of robot i at time t predicted by robot i at time t; τ i (t) is the control input at the current time t; f represents the system dynamics model, and its continuous form is:

[0022]

[0023] Among them, M′ i =R(θ i )M i R T (θ i ) F i ′=R(θ i )F i R T (θ i ), B2′=R(θ i )B2;M i is the inertia matrix of the system, which is symmetric and positive definite; C i is the centripetal force and the Coriolis matrix, which is skew-symmetric; R(θ i ) is the state transfer matrix, θ i Indicates the robot's posture, is R(θ i )’s first-order derivative; F i is the damping matrix, B2 is the input matrix; τ i To control the input, For i The first derivative of For i The second derivative of i is the robot's posture state vector.

[0024] As a further preference, the system initial state constraint is expressed as:

[0025] ξ i (t|t)=ξ i (t)

[0026] Among them, ξ i (t) is the initial state of robot i at time t, ξ i (t|t) is the corresponding initial state in the controller.

[0027] As further preferred, the stability constraint is expressed as:

[0028]

[0029] Among them, V i is the Lyapunov function, τ i (t|t) and τ ia (t|t) represent the control variables obtained by the controller and the auxiliary controller based on Lyapunov function, respectively.

[0030] As a further preferred embodiment, the auxiliary controller τ based on the Lyapunov function ia The expression is as follows:

[0031]

[0032] in, is the pose change rate of the desired trajectory, is the posture error, R is the state transfer matrix; K is the rate of change of posture error; i1 is a positive definite and symmetric control gain matrix, K i2 is the control gain matrix, K i2 =R(θ i )M i (ξ i )R T (θ i ).

[0033] As further preferred, the input saturation constraint is expressed as:

[0034]

[0035] in, is the maximum control input of robot i, τ i (t+kt) max is the calculated maximum amplitude of the control input of robot i.

[0036] According to a second aspect of the present invention, there is provided a multi-mobile robot system consistency control system considering time delay, comprising a processor, wherein the processor is used to execute the multi-mobile robot system consistency control method considering time delay.

[0037] According to a third aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for consistent control of a multi-mobile robot system taking into account time delay.

[0038] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0039] 1. The present invention overcomes the influence of time delay on control effect and realizes consistent control of multi-robot system under communication delay by estimating the system state under communication delay and broadcasting it, and constructing a cost function based on the consistent state error accordingly; the present invention can improve the stability and reliability of consistent control of multi-mobile robot system, thereby realizing safe and smooth operation of mobile robot system.

[0040] 2. The present invention takes into account the influence of delay factors such as communication delay on the control effect, and designs the cost function and constraints of the model predictive control; specifically, by using the current optimal state of the system predicted at the last broadcast time, and estimating the NN′ state of the system in the presence of delay, the influence of communication delay on the consistency control effect is compensated.

[0041] 3. The present invention designs an auxiliary controller based on the Lyapunov function and integrates it into the constraints of the model predictive control, thereby ensuring the stability of the system consistency control. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flow chart of consistency control of a multi-mobile robot system taking into account time delay according to an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of a multi-mobile robot system model according to an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the consistency control principle of a multi-mobile robot system taking time delay into account according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] The embodiment of the present invention provides a method for coherence control of a multi-mobile robot system taking into account time delay, such as Figure 1 As shown, the following steps are included:

[0047] (1) For a single mobile robot, a kinematic and dynamic model is established; and based on graph theory, a communication topology diagram of a multi-mobile robot system is constructed.

[0048] Further, such as Figure 2 As shown, for a multi-agent system including K mobile robots, the kinematic model of the i-th (i=1, 2, ..., K) mobile robot is carried out according to the following relationship:

[0049]

[0050] Its discrete form can be expressed as Where A and B are the state matrix and control input matrix respectively. i and are the robot’s position and velocity state vectors, ξ i =[x i y i θ i ] T ,(x i ,y i ) and θ i Respectively represent the position and posture of the robot; R(θ i ) is the state transfer matrix and has the following form:

[0051]

[0052] For the dynamic model of robot i, the following relationship is used:

[0053]

[0054] Among them, M i ∈R 3×3 is the inertia matrix of the system and is symmetric and positive definite; C i ∈R 3×3 is the centripetal force and the Coriolis matrix, and is skew-symmetric, that is G i ∈R3×1 represents the gravity vector; F i ∈R 3×3 is the damping matrix; B2∈R 3×2 is the input matrix; τ i ∈R 2×1 is the control input vector. In the present invention, the mobile robot system considered is running on a two-dimensional plane, so the gravity vector G i =0.

[0055] Combined with the kinematic model, the above dynamic model can be rewritten as:

[0056]

[0057] Among them, M′ i =R(θ i )XR T (θ i ) F i ′=R(θ i )F i R T (θ i ), B2′=R(θ i )B2.

[0058] Furthermore, for a multi-agent system, its communication topology undirected graph G is composed of nodes V = {v1,v2,...,v K} and edge E, that is, G = (V, E). Among them, each node v i , corresponds to each robot in the multi-robot system. The edge E = {(i, j)|i, j∈V, i≠j} represents the connection relationship between each node. For robot i and robot j, if (i, j)∈E, it means that the two robots can exchange information, that is, they are neighbors. The neighbors of robot i can be represented as N i ={j∈V|(i,j)∈E,i≠j}, the number of its neighbors is denoted by |N i |. For the weighted adjacency matrix of the undirected graph G, A = [a ij ]∈R K*K Indicates that when j∈N i When ij =1 / |N i |, otherwise a ij =0, and a ii = 1. Graph Laplacian matrix L = I K -A, where I K is the K-order identity matrix.

[0059] (2) For a single robot in a multi-robot system, the status information of other robots is obtained through the communication network, and a cost function is constructed with consistency control as the indicator. The optimization problem is constructed and solved by considering the constraints such as the mechanical characteristics and stability of the system to obtain the optimal control quantity.

[0060] Furthermore, for robot i, the cost function J at time t is i as follows:

[0061]

[0062] Where N is the prediction time domain, which means the prediction of the system state quantity at N moments in the future; Q i , R i Respectively represent the weight coefficients of the error amount and the control input amount in the cost function, and Respectively represent the weight coefficients as Q i , R i The Euclidean norm of , for example, The superscript T represents the transpose of the matrix. ei (t+k|t) is the consistency state error, that is ξ i (t+k|t) represents the estimated position state of robot i at time t+k predicted at time t, that is, the position state corresponding to the optimal control input obtained by solving.

[0063] The optimization problem is carried out according to the following relationship:

[0064]

[0065] stξ i (t+1t)=f(ξ i (t),τ i (t))

[0066] ξ i (tt) = ξ i (t)

[0067]

[0068]

[0069] Solving the above optimization problem, we can obtain the optimal control quantity at the current time t To achieve consistency control. Among them, constraint 1 is the system model constraint, f:R 3×1 ×R 2×1 →R 3×1is the system dynamics equation described in step (1), which ensures that the prediction of the system state conforms to the system model; constraint 2 is the system initial state constraint, ξ i (t) is the initial state of the system at time t; constraint 3 is the input saturation constraint, is the maximum control input of robot i, so that the amplitude of the calculated control quantity is within the allowable range of the actuator; constraint 4 is the Lyapunov stability constraint, which restricts the Lyapunov function of the system to make the system stable within the solved control quantity remains stable under the action of i (t|t) and τ ia (t|t) respectively represent the control variables obtained by the designed controller and the auxiliary controller based on the Lyapunov function. For the design of the auxiliary controller, please refer to step (4).

[0070] (3) Due to the existence of communication delay, the consistency state error ξ in (2) is adopted ei (t+k|t) will lead to poor control effect. Therefore, the present invention designs a state broadcast mechanism that takes time delay into consideration, obtains the optimal state information of neighbors at the last broadcast time, and estimates the state of the system under the influence of delay, constructs a new consistency state error, and thus reduces the impact of communication delay.

[0071] Further, such as Figure 3 As shown in the figure, the state broadcast mechanism considering the delay is designed as follows:

[0072] For robot i, at each moment it needs to broadcast its own state to its neighbors and store the state broadcasted to it by its neighbors. At time t, the state broadcasted by robot i to its neighbors is for:

[0073]

[0074] Among them, ξ i (t+k|p t ) indicates p t The optimal control input of robot i at time t+k is obtained by solving The corresponding position state quantity; due to factors such as network delay, it is impossible for the robot to feed back its estimated state to its neighbors in real time, so p is used here t It indicates the time before time t when the system normally broadcasts status information to neighbors, that is, the communication delay of the system can be expressed as ω = tp t Assume that there is an upper limit on communication delay Right now N′ represents the maximum number of optimal state quantities that robot i can broadcast to its neighbors in the presence of communication delay, satisfying N′=p t +Nt.

[0075] Assuming that there is no communication delay between the multi-robot systems at the initial moment (t = 0), the corresponding optimal state can be solved by the method in step (2). At each subsequent moment, the consistency error ξ ei (t+k|t) can be rewritten as By using the current optimal state of the system predicted at the last broadcast time ξ i (t+k|p t ), and estimating the NN′ states of the system in the presence of delays can compensate for the impact of communication delays on the consistency control effect.

[0076] (4) Based on the Lyapunov function, an auxiliary controller is designed and used as a constraint in the optimization problem to ensure the stability of the designed controller.

[0077] Furthermore, the auxiliary controller in constraint 4 is designed as follows:

[0078] For robot i, its expected trajectory is denoted as ξ id , then the pose error can be defined as Define the following variables:

[0079]

[0080]

[0081] According to the kinematic model in (1), the following relationship can be obtained:

[0082]

[0083] in, is the expected speed. According to the above relationship, the rate of change of the posture error can be deduced Satisfies the following formula:

[0084]

[0085] The Lyapunov function V is defined as follows i1 :

[0086]

[0087] Among them, K i1 is a positive definite and symmetric control gain matrix. Based on the definition of the above function, its derivative with respect to time can be expressed as:

[0088]

[0089] Furthermore, the Lyapunov function V is defined as follows: i2 :

[0090]

[0091] The coefficient matrix R(θ i )M i (ξ i )R T (θ i ) is abbreviated as K i2 . Similarly, based on the definition of the above function, its derivative with respect to time can be expressed as:

[0092]

[0093] in, satisfy

[0094] Select the system's Lyapunov function V i =V i2 , therefore, the corresponding auxiliary control quantity τ can be designed ia , to ensure the stability of the designed auxiliary controller. According to Lyapunov's stability principle, when the auxiliary control quantity τ ia When the following equation is satisfied, the multi-agent system is stable with the auxiliary control variable as input:

[0095]

[0096] Among them, K i2 is the control gain matrix. Then when the actual control amount is less than the auxiliary control amount τ ia When , the Lyapunov stability constraint in (2) is satisfied. Therefore, with the actual control quantity that satisfies the constraint as input, the multi-agent system is stable.

[0097] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for coherence control of a multi-mobile robot system considering time delay, characterized in that: The steps include: For a single robot in a multi-mobile robot system, a cost function is constructed based on its consistent state error, and the optimal control input of the robot is obtained by minimizing the cost function; the above steps are repeated for each robot to obtain the optimal control input of each robot, thereby achieving consistent control of the multi-mobile robot system; Among them, robot i in the multi-mobile robot system predicts its consistency state error ξ at time t at time t+k ei The calculation formula for (t+k|t) is: t+k|t represents the prediction of time t+k at time t, k=0,1,2,…N-1, N is the prediction time domain; ξ i (t+k|t) represents the estimated position state of robot i at time t+k predicted at time t, N i represents the neighbor set of robot i. The robots in this set have information exchange with robot i, i.e., neighbors of robot i; a ij =1 / |N i |,|N i | represents the number of neighbors of robot i; It represents the estimated position state of robot j at time t+k broadcasted to its neighbors at time t, and the calculation formula is: ξ j (t+kp t ) indicates that in p t The estimated position state of robot j at time t+k predicted at the moment; p t represents the time when the state quantity was most recently broadcast to the neighbors before time t, N′ represents the maximum number of state quantities that robot j can broadcast to its neighbors under communication delay, N′=p t +Nt; A represents the weighted adjacency matrix of the undirected graph of the multi-mobile robot system communication topology, Represents the estimated position state of robot j at time t+k-1 broadcasted to its neighbors at time t.

2. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 1, characterized in that: The cost function J of robot i at time t i for: Among them, τ i (t+k|t) represents the control input of robot i at time t+k; Q i , R i Respectively represent the weight coefficients of the error amount and the control input amount in the cost function, Respectively represent the weight coefficients as Q i , R i The Euclidean norm of .

3. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 2, characterized in that: To minimize the cost function J i As the goal, solve the optimal control input of robot i at the current time t The constraints during solution include: system model constraints, system initial state constraints, stability constraints and input saturation constraints.

4. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 3, characterized in that: The discrete form of the system model constraints is expressed as: x i (t+1|t)=f(ξ i (t),τ i (t)) Among them, ξ i (t) represents the state of robot i at the current time t, ξ i (t+1|t) represents the state of robot i at time t predicted by robot i at time t; τ i (t) is the control input at the current time t; f represents the system dynamics model, and its continuous form is: Among them, M′ i =R(θ i )M i R T (θ i ), C′ i =R(θ i )[C i -M i RT(θ i )R(θ i )]RT(θ i ), F i ′=R(θ i )F i R T (θ i ), B2′=R(θ i )B2;M i is the inertia matrix of the system, which is symmetric and positive definite; C i is the centripetal force and the Coriolis matrix, which is skew-symmetric; R(θ i ) is the state transfer matrix, θ i Indicates the robot's posture, is R(θ i )’s first-order derivative; F i is the damping matrix, B2 is the input matrix; τ i To control the input, For i The first derivative of For i The second derivative of i is the robot's posture state vector.

5. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 4, characterized in that: The system initial state constraint is expressed as: x i (t|t)=ξ i (t) Among them, ξ i (t) is the initial state of robot i at time t, ξ i (t|t) is the corresponding initial state in the controller.

6. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 5, characterized in that: The stability constraint is expressed as: Among them, V i is the Lyapunov function, τ i (t|t) and τ ia (t|t) represent the control variables obtained by the controller and the auxiliary controller based on Lyapunov function, respectively.

7. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 6, characterized in that: Auxiliary controller τ based on Lyapunov function ia The expression is as follows: in, is the pose change rate of the desired trajectory, is the posture error, R is the state transfer matrix; K is the rate of change of posture error; i1 is a positive definite and symmetric control gain matrix, K i2 is the control gain matrix, K i2 =R(θ i )M i (ξ i )R T (θ i ).

8. The method for coherence control of a multi-mobile robot system considering time delay as claimed in claim 3, characterized in that: The input saturation constraint is expressed as: in, is the maximum control input of robot i, τ i (t+kt) max is the calculated maximum amplitude of the control input of robot i.

9. A multi-mobile robot system consistency control system considering time delay, characterized in that: It includes a processor, which is used to execute the consistency control method of a multi-mobile robot system considering time delay as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for coherent control of a multi-mobile robot system taking into account delay as described in any one of claims 1 to 8 is implemented.

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