A distributed guaranteed cost containment control method for networked multiple mobile robots

Abstract

The present invention relates to a distributed guaranteed cost containment control method for networked multiple mobile robots. First, a dynamic model of mobile robots subjected to uncertain environmental interference is established, and a tracking differentiator is used to estimate the speed states of multiple leader robots. Secondly, a distributed inclusive control protocol for multiple mobile robots is constructed based on the dynamic model of the multiple mobile robots and in combination with the speed state estimation information of the multiple leader robots. Then, a fixed-time interference observer is designed to estimate and compensate for external disturbances in real time. Finally, a performance function is combined with an error conversion function to perform performance conversion on the distributed inclusive control protocol for multiple mobile robots. In view of the situation in which the speed state of the leader robot cannot be accurately obtained and the dynamic performance such as the transient value of the synchronization error and the overshoot cannot be guaranteed in the inclusive control system of multiple mobile robots, the follower robots can be effectively controlled to be driven into the convex hull formed by the leader robot.

Description

Technical Field

[0001] The present invention relates to a distributed guaranteed cost inclusion control method for networked multiple mobile robots, belonging to the technical field of mobile robot cooperative formation control. Background Art

[0002] In recent years, multi-robot systems have gradually developed towards precise, convenient, efficient, and complex intelligent systems, playing an increasingly important role in life, work, and the military. Inclusion control, as a form of multi-robot collaborative control, holds significant theoretical and practical value because it can meet the needs of many specialized engineering projects. The inclusion control problem for multi-mobile robots involves a leader robot forming a fixed formation, with follower robots able to rapidly move within the convex hull formed by the leader formation to complete specialized tasks. When a multi-robot team needs to reach its destination along a path and encounter various dangerous areas or obstacles along the way, the leader robot can detect the obstacles while simultaneously forming a safe zone. In this case, as long as the follower robots maintain their movement within the convex hull formed by the leader through inclusion control, they can safely reach their destination. During large-scale water search and rescue missions, follower robots can be driven into the search and rescue area covered by the leader formation for detailed exploration, significantly improving mission efficiency.

[0003] Traditional multi-mobile robot control methods still have some technical problems: (1) Under ideal conditions, the speed state of the leader robot in the control system can be directly obtained through sensors. However, in actual engineering, the speed state of the leader robot cannot be accurately measured due to the performance limitations of the sensors, and the expected control effect cannot be achieved; (2) During the operation of the multi-mobile robot system, it is inevitably affected by various uncertain interferences, which may cause the system to fail to operate normally and even cause the entire control system to fail. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a distributed guaranteed cost containment control method for networked multiple mobile robots, which effectively ensures that the follower robot is driven into the convex hull formed by the leader robot in the presence of external interference.

[0005] To solve the above technical problems, the present invention adopts the following technical solutions: The present invention designs a distributed guaranteed cost containment control method for networked multi-mobile robots. For an n-dimensional space multi-mobile robot system comprising M leader robots and N follower robots, the following steps are followed to achieve coordinated control of the follower robots in the n-dimensional space multi-mobile robot system.

[0006] Step A. Establish dynamic models corresponding to the multiple navigator robots and the multiple follower robots in the inertial coordinate system, and use tracking differentiators to estimate the velocity states in the dynamic models corresponding to the multiple navigator robots to obtain velocity state estimation information corresponding to the multiple navigator robots, and then proceed to Step B.

[0007] Step B. Construct a distributed inclusive control protocol for multiple mobile robots based on the dynamic models corresponding to the multiple leader robots and the multiple follower robots in the inertial coordinate system and the velocity state estimation information corresponding to the multiple leader robots, and then proceed to Step C.

[0008] Step C. Design a fixed-time disturbance observer for the follower robot dynamics model subject to uncertain environmental disturbances to estimate and compensate for external disturbances in real time, and then proceed to step D.

[0009] Step D. Using the performance function and combining it with the error conversion function, the performance conversion is performed on the distributed inclusive control protocol of the multi-mobile robots, the distributed inclusive control protocol of the multi-mobile robots is updated, and then the process proceeds to step E;

[0010] Step E. Based on the updated multi-mobile robot distributed inclusive control protocol and the observation information of the fixed-time interference observer, a multi-mobile robot distributed inclusive controller is designed to realize collaborative control of each follower robot in the n-dimensional space multi-mobile robot system.

[0011] As a preferred technical solution of the present invention: in step A, the following operations are performed to establish dynamic models corresponding to the multiple leader robots and the multiple follower robots in an inertial coordinate system;

[0012] First, the dynamic model corresponding to the multi-navigator robot in the inertial coordinate system is established as follows:

[0013]

[0014] l=1、...、M,x l =(x l,1 ,…,x l,n ), x l represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system, x l,n represents the position state of the lth leader robot corresponding to the nth dimension; v l represents the velocity state of the lth leader robot in the n-dimensional space multi-mobile robot system; u l represents the control input of the lth leader robot in the n-dimensional space multi-mobile robot system;

[0015] Then the dynamic model corresponding to the multi-follower robot in the inertial coordinate system is established as follows:

[0016]

[0017] k=1,...,N,x k =(x k,1 ,…,x k,n ), x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system, x k,n represents the position state of the kth follower robot corresponding to the nth dimension; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input of the kth follower robot in the n-dimensional space multi-mobile robot system, ω k Represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system.

[0018] As a preferred technical solution of the present invention: in step A, the following operations are performed to estimate the velocity state in the dynamic model corresponding to the multi-navigator robot using a tracking differentiator to obtain velocity state estimation information corresponding to the multi-navigator robot;

[0019] For multiple navigator robots in the n-dimensional space multi-mobile robot system, a second-order tracking differentiator is established as follows:

[0020]

[0021] Where z1 and z2 represent the state variables of the second-order tracking differentiator, and the nonlinear function F(z1,z2)=ξ(z1)+ξ(z2) τ l is the preset constant parameter greater than 0 in the second-order tracking differentiator corresponding to the l-th leader robot. According to the solution of the nonlinear function F(·), z1(t)→0 and z2(t)→0(t→∞), for any integrable and bounded signal Q satisfying T>0, l , update the second-order tracking differentiator as follows, t represents the time variable, z1(t) represents the value of the first-order state component in the second-order tracking differentiator corresponding to time t, z2(t) represents the value of the second-order state component in the second-order tracking differentiator corresponding to time t, T represents a time greater than zero, Q l represents any integrable and bounded signal satisfying T>0, which is the input signal of the tracking differentiator;

[0022]

[0023] That is, to ensure |X1-Q within a limited time l | and Bounded, then the second-order tracking differentiator is applied to obtain the velocity state v in the dynamic model corresponding to the multi-navigator robot l Estimated value of That is, obtain the velocity state estimation information corresponding to the lth leader robot in the multi-leader robot l=1, ..., M, X1 and X2 represent the input signal Q l The state variable of the constructed second-order tracking differentiator, R l Indicates a preset positive adjustable parameter, "." indicates differential, Indicates the input signal Q l The estimated value of the differential signal.

[0024] As a preferred technical solution of the present invention: Step B includes the following:

[0025] First, each mobile robot in the n-dimensional space multi-mobile robot system is regarded as a node, and edges are established between the nodes corresponding to each two mobile robots to define the communication topology of the n-dimensional space multi-mobile robot system. Where, i=1, ..., M+N, j=1, ..., M+N, represents the set of all nodes in the n-dimensional space multi-mobile robot system, υ i Represents the node corresponding to the i-th robot in the n-dimensional space multi-mobile robot system; represents the set of all edges in the n-dimensional multi-mobile robot system, e ji Represents the edge between the node corresponding to the jth robot and the node corresponding to the ith robot in the n-dimensional space multi-mobile robot system, Represents the adjacency matrix of the n-dimensional space multi-mobile robot system, a ij Represents the weight coefficient of each edge in the n-dimensional space multi-mobile robot system. When there is a communication channel between the j-th robot and the i-th robot, then a ij =1, otherwise a ij =0, and a ii =0, a jj = 0, and for each node corresponding to the mobile robot, define the sum of the weight coefficients of the edges directly connected to the node corresponding to the mobile robot as the in-degree of the node corresponding to the mobile robot, that is, d i (υ i )=∑a ij ;

[0026] Then, for the communication topology of the n-dimensional space multi-mobile robot system, according to l = 1, ..., M, k = 1, ..., N, define the weight coefficient b of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot kl , that is, if there is a communication channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0;

[0027] Finally, based on the dynamic models corresponding to multiple navigator robots and multiple follower robots in the inertial coordinate system, combined with the velocity state estimation information corresponding to the multiple navigator robots, the multi-mobile robot consistency inclusion control error surface is constructed as follows: Multi-mobile robot distributed inclusion control protocol;

[0028]

[0029] s kx =[s kx,1 ,…,s kx,n ] T , s kx represents the position loop distributed inclusion control protocol of the kth follower robot in an n-dimensional multi-mobile robot system, s kx,n represents the position loop distributed inclusion control protocol of the kth follower robot corresponding to the nth dimension, s kv =[s kv,1 ,…,s kv,n ] T , s kv represents the distributed inclusive control protocol for the velocity loop of the kth follower robot in an n-dimensional multi-mobile robot system, s kv,n represents the distributed inclusive control protocol for the speed loop of the kth follower robot corresponding to the nth dimension; x j' represents the position state of the j'th follower robot in the n-dimensional space multi-mobile robot system; x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; x l Represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system; Indicates the velocity state estimation information corresponding to the lth leader robot in multiple leader robots.

[0030] As a preferred technical solution of the present invention: in step C, for the follower robot dynamics model affected by uncertain environmental disturbances, a fixed-time disturbance observer is designed as follows to estimate and compensate for external disturbances in real time;

[0031]

[0032]

[0033]

[0034] x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ω k represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system; They are x k 、v k 、ω k estimated value of; μ k It is v i The error estimate of ρ k ,η k , σ k , κ k is the preset disturbance observer design parameter corresponding to the kth follower robot, sig(μ k )=sign(μ k )|μ k |, sign(·) is the sign function, is the integration variable.

[0035] As a preferred technical solution of the present invention: Step D includes the following operations:

[0036] First, build the performance function as follows:

[0037] ζ(t)=(ζ0-ζ ∞ )e -ct +ζ ∞

[0038] e represents a natural constant, t represents a time variable; c represents a preset adjustable parameter used to adjust the convergence speed; ζ0, ζ ∞ Indicates a preset positive parameter and satisfies ζ0>ζ ∞ >0,

[0039] Then according to the preset requirements of the system error: -δ1ζ(t)<s kx <δ2ζ(t), The error conversion function ψ(·) is used to convert the inclusive control error surface in the distributed inclusive control protocol of multiple mobile robots into a preset performance error. The inclusive control error surface is made to converge to the preset performance boundary, and the distributed inclusive control protocol of multiple mobile robots is updated; wherein, The error variable corresponding to the k-th follower robot in the distributed inclusive control protocol of the multi-mobile robot system in n-dimensional space is converted by the error conversion function ψ(·), that is, the preset performance error. The error conversion function ψ(·): (-δ1, δ2)→(-∞, +∞) is an increasing smooth function, and the function ψ(·) is as follows:

[0040]

[0041] Wherein, λ is a preset adjustable parameter constant, 0<δ1<1, 0<δ2<1 are preset design parameters used to adjust the preset performance boundary.

[0042] As a preferred technical solution of the present invention: Step E includes the following operations:

[0043] First, the backstepping technique is used to adjust the preset performance error Taking the derivative, we get:

[0044]

[0045] k=1、...、N,v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ζ(t) represents the performance function, which is a positive continuously decreasing function; represents the first-order derivative of the performance function ζ(t); d k represents the in-degree of the node corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; a kj' Represents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the j'th follower robot in the communication topology of the n-dimensional space multi-mobile robot system. When there is a communication interaction channel between the kth follower robot and the j'th follower robot, then a kj' =1, otherwise a kj' =0; j'=1, ..., N, v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; l = 1, ..., M, b klrepresents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot, that is, if there is a communication interaction channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0; Indicates the velocity state estimation information corresponding to the lth leader robot in multiple leader robots; s kx Represents a distributed inclusion control protocol for the position loop of the kth follower robot in a multi-mobile robot system in n-dimensional space;

[0046] Then according to Lyapunov stability theory, combined with Building a Virtual Controller α k as follows:

[0047]

[0048] α k It represents the virtual control signal of the position loop of the kth follower robot in the n-dimensional space multi-mobile robot system, and then further constructs the error e k as follows:

[0049]

[0050] Finally get the control protocol u k As follows, u k represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system, that is, a multi-mobile robot distributed inclusive controller is obtained, which is used to realize the coordinated control of each follower robot in the n-dimensional space multi-mobile robot system;

[0051]

[0052] Among them, β k1 , β k2 represents the preset controller design parameters corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system, and β k1 >0,β k2 >0.

[0053] The distributed guaranteed cost containment control method for networked multiple mobile robots described in the present invention has the following technical effects compared with the prior art:

[0054] The present invention designs a distributed guaranteed cost containment control method for networked multiple mobile robots. First, a dynamic model of the mobile robots affected by uncertain environmental interference is established. At the same time, considering the problem that the leader robot's speed information cannot be accurately obtained due to sensor performance constraints, a tracking differentiator is used to estimate the speed state of the multiple leader robots; secondly, based on the dynamic model of the multiple mobile robots and combined with the speed state estimation information of the multiple leader robots, a distributed inclusive control protocol for the multiple mobile robots is constructed; then, in order to eliminate the influence of uncertain dynamic environmental interference in the system, a fixed-time interference observer is designed to estimate and compensate for external disturbances in real time; finally, the performance function is combined with the error conversion function to perform performance conversion on the distributed inclusive control protocol of the multiple mobile robots. In view of the situation that the speed state of the leader robot cannot be accurately obtained and the dynamic performance such as the transient value of the synchronization error and the overshoot cannot be guaranteed in the inclusive control system of the multiple mobile robots, the follower robots can be effectively controlled to be driven into the convex hull formed by the leader robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of the distributed guaranteed cost inclusion control method for networked multiple mobile robots designed by the present invention;

[0056] Figure 2 It is a schematic diagram of the communication topology of a networked multi-mobile robot system;

[0057] Figure 3 This is a schematic diagram of the tracking differentiator's estimated effect on the X and Y axis velocities of the navigator robot;

[0058] Figure 4 This is a schematic diagram of the response of each follower robot to the X-axis direction consistency including control error under the performance constraint;

[0059] Figure 5 This is a schematic diagram of the Y-axis consistency of each follower robot under the performance constraint, including the control error response;

[0060] Figure 6 This is a schematic diagram of the consistency of the speed state output of each mobile robot in the X-axis direction;

[0061] Figure 7 This is a schematic diagram of the consistency of the speed state output of each mobile robot in the Y-axis direction;

[0062] Figure 8 It is a schematic diagram of the XY plane motion trajectory of networked multiple mobile robots in the inertial coordinate system. DETAILED DESCRIPTION

[0063] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0064] Aiming at the problem that the speed state of the leader robot cannot be accurately obtained and the dynamic performance such as the transient value of the synchronization error and the overshoot cannot be guaranteed in the multi-mobile robot inclusion control system, the present invention designs a distributed guaranteed cost inclusion control method for networked multi-mobile robots. For an n-dimensional space multi-mobile robot system including M leader robots and N follower robots, such as Figure 1 As shown, the following steps are taken to realize the coordinated control of each follower robot in the n-dimensional space multi-mobile robot system.

[0065] Step A. Establish the dynamic models corresponding to the multiple navigator robots and the multiple follower robots in the inertial coordinate system, and use the tracking differentiator to estimate the velocity state in the dynamic model corresponding to the multiple navigator robots, obtain the velocity state estimation information corresponding to the multiple navigator robots, and then enter step B.

[0066] In the specific design implementation, the following operations are performed in the above step A to establish the dynamic models corresponding to the multiple leader robots and the multiple follower robots in the inertial coordinate system.

[0067] First, the dynamic model corresponding to the multi-navigator robot in the inertial coordinate system is established as follows:

[0068]

[0069] l=1、...、M,x l =(x l,1 ,…,x l,n ), x l represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system, x l,n represents the position state of the lth leader robot corresponding to the nth dimension; v l represents the velocity state of the lth leader robot in the n-dimensional space multi-mobile robot system; u l Represents the control input of the lth leader robot in the n-dimensional space multi-mobile robot system.

[0070] Then the dynamic model corresponding to the multi-follower robot in the inertial coordinate system is established as follows:

[0071]

[0072] k=1,...,N,x k =(x k,1 ,…,x k,n ), x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system, x k,n represents the position state of the kth follower robot corresponding to the nth dimension; vk represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input of the kth follower robot in the n-dimensional space multi-mobile robot system, ω k Represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system.

[0073] A tracking differentiator is further used to estimate the velocity state in the dynamic model corresponding to the multi-navigator robot, and the velocity state estimation information corresponding to the multi-navigator robot is obtained.

[0074] For multiple navigator robots in the n-dimensional space multi-mobile robot system, a second-order tracking differentiator is established as follows:

[0075]

[0076] Where z1 and z2 represent the state variables of the second-order tracking differentiator, and the nonlinear function F(z1,z2)=ξ(z1)+ξ(z2) τ l is the preset constant parameter greater than 0 in the second-order tracking differentiator corresponding to the l-th leader robot. According to the solution of the nonlinear function F(·), z1(t)→0 and z2(t)→0(t→∞), for any integrable and bounded signal Q satisfying T>0, l , update the second-order tracking differentiator as follows, t represents the time variable, z1(t) represents the value of the first-order state component in the second-order tracking differentiator corresponding to time t, z2(t) represents the value of the second-order state component in the second-order tracking differentiator corresponding to time t, T represents a time greater than zero, Q l It represents any integrable and bounded signal satisfying T>0, and is the input signal of the tracking differentiator.

[0077]

[0078] That is, to ensure |X1-Q within a limited time l | and The second-order tracking differentiator is then applied to obtain the velocity state v in the dynamic model corresponding to the multi-navigator robot. l Estimated value of That is, obtain the velocity state estimation information corresponding to the lth leader robot in the multi-leader robot l=1, ..., M, X1 and X2 represent the input signal Q l The state variable of the constructed second-order tracking differentiator, R l Indicates a preset positive adjustable parameter, "." indicates differential, Indicates the input signal Ql The estimated value of the differential signal.

[0079] Step B. Based on the dynamic models corresponding to the multiple navigator robots and the multiple follower robots in the inertial coordinate system, combined with the velocity state estimation information corresponding to the multiple navigator robots, a distributed inclusive control protocol for multiple mobile robots is constructed, and then step C is entered.

[0080] In actual implementation, the above step B is specifically designed and executed as follows:

[0081] First, each mobile robot in the n-dimensional space multi-mobile robot system is regarded as a node, and edges are established between the nodes corresponding to each two mobile robots to define the communication topology of the n-dimensional space multi-mobile robot system. Where, i=1, ..., M+N, j=1, ..., M+N, represents the set of all nodes in the n-dimensional space multi-mobile robot system, υ i Represents the node corresponding to the i-th robot in the n-dimensional space multi-mobile robot system; represents the set of all edges in the n-dimensional multi-mobile robot system, e ji Represents the edge between the node corresponding to the jth robot and the node corresponding to the ith robot in the n-dimensional space multi-mobile robot system, Represents the adjacency matrix of the n-dimensional space multi-mobile robot system, a ij Represents the weight coefficient of each edge in the n-dimensional space multi-mobile robot system. When there is a communication channel between the j-th robot and the i-th robot, then a ij =1, otherwise a ij =0, and a ii =0, a jj = 0. Since each node in the system has stored its own information, it does not need to communicate with itself. For each node corresponding to the mobile robot, the sum of the weight coefficients of the edges directly connected to the node corresponding to the mobile robot is defined as the in-degree of the node corresponding to the mobile robot, that is, d i (υ i )=∑a ij .

[0082] Then, for the communication topology of the n-dimensional space multi-mobile robot system, according to l = 1, ..., M, k = 1, ..., N, define the weight coefficient b of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot kl , that is, if there is a communication channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0.

[0083] Finally, based on the dynamic models corresponding to multiple navigator robots and multiple follower robots in the inertial coordinate system, combined with the velocity state estimation information corresponding to the multiple navigator robots, the multi-mobile robot consistency inclusion control error surface is constructed as follows: Multi-mobile robot distributed inclusion control protocol;

[0084]

[0085] s kx =[s kx,1 ,…,s kx,n ] T , s kx represents the position loop distributed inclusion control protocol of the kth follower robot in an n-dimensional multi-mobile robot system, s kx,n represents the position loop distributed inclusion control protocol of the kth follower robot corresponding to the nth dimension, s kv =[s kv,1 ,…,s kv,n ] T , s kv represents the distributed inclusive control protocol for the velocity loop of the kth follower robot in an n-dimensional multi-mobile robot system, s kv,n represents the distributed inclusive control protocol for the speed loop of the kth follower robot corresponding to the nth dimension; x j' represents the position state of the j'th follower robot in the n-dimensional space multi-mobile robot system; x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; x l Represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system; It represents the velocity state estimation information corresponding to the lth leader robot in a multi-robot system. During the operation of the multi-robot system, when the inclusion error surface of the follower robot approaches zero, it means that the follower robot has been driven into the convex hull formed by the leader robot.

[0086] Step C. For the follower robot dynamics model affected by uncertain environmental disturbances, a fixed-time disturbance observer is designed as follows to estimate and compensate for external disturbances in real time, and then proceed to step D.

[0087]

[0088]

[0089]

[0090] x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ω k represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system; They are x k 、v k 、ω k estimated value of; μ k It is v i The error estimate of ρ k ,η k , σ k , κ k is the preset disturbance observer design parameter corresponding to the kth follower robot, sig(μ k )=sign(μ k )|μ k |, sign(·) is the sign function, is the integration variable.

[0091] Step D. Using the performance function and combining it with the error conversion function, perform the following operations to perform performance conversion on the multi-mobile robot distributed inclusive control protocol, update the multi-mobile robot distributed inclusive control protocol, and then proceed to step E.

[0092] First, build the performance function as follows:

[0093] ζ(t)=(ζ0-ζ ∞ )e -ct +ζ ∞

[0094] e represents a natural constant, t represents a time variable; c represents a preset adjustable parameter used to adjust the convergence speed; ζ0, ζ ∞ Represents a preset positive parameter and satisfies ζ0>ζ ∞ >0,

[0095] Then according to the preset requirements of the system error: -δ1ζ(t)<s kx <δ2ζ(t), In order to make the inclusive control error surface converge to the preset performance boundary, the inclusive control error surface in the distributed inclusive control protocol of multiple mobile robots is converted into a preset performance error through the error conversion function ψ(·) The inclusive control error surface is made to converge to the preset performance boundary, and the distributed inclusive control protocol of multiple mobile robots is updated; wherein, The error variable corresponding to the k-th follower robot in the distributed inclusive control protocol of the multi-mobile robot system in n-dimensional space is converted by the error conversion function ψ(·), that is, the preset performance error. The error conversion function ψ(·): (-δ1, δ2)→(-∞, +∞) is an increasing smooth function, and the function ψ(·) is as follows:

[0096]

[0097] Wherein, λ is a preset adjustable parameter constant, 0<δ1<1, 0<δ2<1 are preset design parameters used to adjust the preset performance boundary.

[0098] Step E. Based on the updated multi-mobile robot distributed inclusive control protocol and the observation information of the fixed-time interference observer, perform the following operations to design a multi-mobile robot distributed inclusive controller for realizing collaborative control of each follower robot in the n-dimensional space multi-mobile robot system.

[0099] First, the backstepping technique is used to adjust the preset performance error Taking the derivative, we get:

[0100]

[0101] k=1、...、N,v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ζ(t) represents the performance function, which is a positive continuously decreasing function; represents the first-order derivative of the performance function ζ(t); d k represents the in-degree of the node corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; a kj' Represents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the j'th follower robot in the communication topology of the n-dimensional space multi-mobile robot system. When there is a communication interaction channel between the kth follower robot and the j'th follower robot, then a kj' =1, otherwise a kj' =0; j'=1, ..., N, v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; l = 1, ..., M, b klrepresents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot, that is, if there is a communication interaction channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0; Indicates the velocity state estimation information corresponding to the lth leader robot in multiple leader robots; s kx Represents a distributed inclusion control protocol for the position loop of the kth follower robot in a multi-mobile robot system in n-dimensional space.

[0102] In order to make the system stable, according to Lyapunov stability theory, combined with Building a Virtual Controller α k as follows:

[0103]

[0104] α k It represents the virtual control signal of the position loop of the kth follower robot in the n-dimensional space multi-mobile robot system, and then further constructs the error e k as follows:

[0105]

[0106] Finally get the control protocol u k As follows, u k Represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system, that is, a multi-mobile robot distributed inclusive controller is obtained, which is used to realize collaborative control of each follower robot in the n-dimensional space multi-mobile robot system.

[0107]

[0108] Among them, β k1 , β k2 represents the preset controller design parameters corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system, and β k1 >0,β k2 >0.

[0109] The distributed guaranteed cost control method for networked multi-mobile robots designed in this invention is applied in practice. Consider a multi-mobile robot system consisting of three leader robots and four follower robots in a two-dimensional space. Figure 2As shown, the dotted circles numbered 5, 6, and 7 are defined as leader robots, and the solid circles numbered 1, 2, 3, and 4 are defined as follower robots. The entire communication topology is a directed graph, and each follower robot receives at least one message transmitted from the leader robot, thereby completing multi-robot distributed information interaction.

[0110] The communication weight coefficient of the system is set to a kj' =1,b kl =1, since the navigator robot has no neighbors, the Laplacian matrix of the communication topology graph at this time is defined as:

[0111]

[0112] Design the corresponding Laplacian matrix based on the communication topology graph:

[0113]

[0114] Design a two-dimensional motion trajectory generated by three pilot robots. The motion trajectory along the x-axis and y-axis is defined as:

[0115]

[0116] The controller parameters are set as: β 11 =β 21 =β 31 =β 41 =1,β 12 =β 22 =β 32 =β 42 =1, R5=R6=R7=100, τ 51 =τ 61 =τ 71 =1,τ 52 =τ 62 =τ 72 =2, λ=0.5, δ1=0.55, δ2=0.2, ω k1 =-0.2sin((π(t-1)) / 2),ω k2 =cos(π(t-1)),ζ k =10,ρ k =0.5,η k =5,σ k =0.7,κ k =0.5, the distributed guaranteed cost control system of multiple mobile robots can achieve the control effect based on the above parameters.

[0117] In actual implementation, Figures 3 to 8As shown, there are, in sequence, the estimation effect of the tracking differentiator on the X and Y axis velocities of the leader robot, the schematic diagram of the consistency of the X axis direction of each follower robot under the guaranteed performance constraint including the control error response, the schematic diagram of the consistency of the Y axis direction of each follower robot under the guaranteed performance constraint including the control error response, the schematic diagram of the consistency of the X axis velocity state output of each mobile robot, the schematic diagram of the consistency of the Y axis velocity state output of each mobile robot, and the schematic diagram of the XY plane motion trajectory of the networked multi-mobile robots in the inertial coordinate system.

[0118] The distributed guaranteed cost-inclusive control method for networked multi-mobile robots designed by the above technical solution first establishes a dynamic model of mobile robots affected by uncertain environmental interference. At the same time, considering the problem that the leader's speed information cannot be accurately obtained due to sensor performance constraints, a tracking differentiator is used to estimate the speed state of the multi-leader robots; secondly, based on the dynamic model of the multi-mobile robots and combined with the speed state estimation information of the multi-leader robots, a distributed inclusive control protocol for the multi-mobile robots is constructed; then, in order to eliminate the influence of uncertain dynamic environmental interference in the system, a fixed-time interference observer is designed to estimate and compensate for external disturbances in real time; finally, the performance function is combined with the error conversion function to perform performance conversion on the distributed inclusive control protocol of the multi-mobile robots. In the case that the speed state of the leader robot cannot be accurately obtained and the dynamic performance such as the transient value of the synchronization error and the overshoot cannot be guaranteed in the inclusive control system of the multi-mobile robots, the follower robot can be effectively controlled to be driven into the convex hull formed by the leader robot.

[0119] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A distributed guaranteed cost containment control method for networked multiple mobile robots, characterized by: For an n-dimensional space multi-mobile robot system consisting of M leader robots and N follower robots, the following steps are performed to achieve coordinated control of the follower robots in the n-dimensional space multi-mobile robot system: Step A. Establish dynamic models corresponding to the multiple navigator robots and the multiple follower robots in the inertial coordinate system, and use tracking differentiators to estimate the velocity states in the dynamic models corresponding to the multiple navigator robots to obtain velocity state estimation information corresponding to the multiple navigator robots, and then proceed to Step B. Step B. Construct a distributed inclusive control protocol for multiple mobile robots based on the dynamic models corresponding to the multiple leader robots and the multiple follower robots in the inertial coordinate system and the velocity state estimation information corresponding to the multiple leader robots, and then proceed to Step C. Step C. Design a fixed-time disturbance observer for the follower robot dynamics model subject to uncertain environmental disturbances to estimate and compensate for external disturbances in real time, and then proceed to step D. Step D. Using the performance function and combining it with the error conversion function, the performance conversion is performed on the distributed inclusive control protocol of the multi-mobile robots, the distributed inclusive control protocol of the multi-mobile robots is updated, and then the process proceeds to step E; Step E. Based on the updated multi-mobile robot distributed inclusive control protocol and the observation information of the fixed-time interference observer, a multi-mobile robot distributed inclusive controller is designed to realize collaborative control of each follower robot in the n-dimensional space multi-mobile robot system.

2. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: In step A, the following operations are performed to establish dynamic models corresponding to multiple leader robots and multiple follower robots in an inertial coordinate system; First, the dynamic model corresponding to the multi-navigator robot in the inertial coordinate system is established as follows: l=1、...、M,x l =(x l,1 ,…,x l,n ), x l represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system, x l,n represents the position state of the lth leader robot corresponding to the nth dimension; v l represents the velocity state of the lth leader robot in the n-dimensional space multi-mobile robot system; u l represents the control input of the lth leader robot in the n-dimensional space multi-mobile robot system; Then the dynamic model corresponding to the multi-follower robot in the inertial coordinate system is established as follows: k=1,...,N,x k =(x k,1 ,…,x k,n ), x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system, x k,n represents the position state of the kth follower robot corresponding to the nth dimension; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input of the kth follower robot in the n-dimensional space multi-mobile robot system, ω k Represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system.

3. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: In step A, the following operations are performed to estimate the velocity state in the dynamic model corresponding to the multi-navigator robot using a tracking differentiator to obtain velocity state estimation information corresponding to the multi-navigator robot; For multiple navigator robots in an n-dimensional space multi-mobile robot system, a second-order tracking differentiator is established as follows: Where z1 and z2 represent the state variables of the second-order tracking differentiator, and the nonlinear function F(z1,z2)=ξ(z1)+ξ(z2) τ l is the preset constant parameter greater than 0 in the second-order tracking differentiator corresponding to the l-th leader robot. According to the solution of the nonlinear function F(·), z1(t)→0 and z2(t)→0(t→∞), for any integrable and bounded signal Q satisfying T>0, l , update the second-order tracking differentiator as follows, t represents the time variable, z1(t) represents the value of the first-order state component in the second-order tracking differentiator corresponding to time t, z2(t) represents the value of the second-order state component in the second-order tracking differentiator corresponding to time t, T represents a time greater than zero, Q l represents any integrable and bounded signal satisfying T>0, which is the input signal of the tracking differentiator; That is, to ensure |X1-Q within a limited time l | and Bounded, then the second-order tracking differentiator is applied to obtain the velocity state v in the dynamic model corresponding to the multi-navigator robot l Estimated value of That is, obtain the velocity state estimation information corresponding to the lth leader robot in the multi-leader robot l=1, ..., M, X1 and X2 represent the input signal Q l The state variable of the constructed second-order tracking differentiator, R l Indicates a preset positive adjustable parameter, "." indicates a differential, Indicates the input signal Q l The estimated value of the differential signal.

4. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: The step B comprises the following: First, each mobile robot in the n-dimensional space multi-mobile robot system is regarded as a node, and edges are established between the nodes corresponding to each two mobile robots to define the communication topology of the n-dimensional space multi-mobile robot system. Where, i=1, ..., M+N, j=1, ..., M+N, represents the set of all nodes in the n-dimensional space multi-mobile robot system, υ i Represents the node corresponding to the i-th robot in the n-dimensional space multi-mobile robot system; represents the set of all edges in the n-dimensional multi-mobile robot system, e ji Represents the edge between the node corresponding to the jth robot and the node corresponding to the ith robot in the n-dimensional space multi-mobile robot system, Represents the adjacency matrix of the n-dimensional space multi-mobile robot system, a ij Represents the weight coefficient of each edge in the n-dimensional space multi-mobile robot system. When there is a communication channel between the j-th robot and the i-th robot, then a ij =1, otherwise a ij =0, and a ii =0, a jj = 0, and for each node corresponding to the mobile robot, define the sum of the weight coefficients of the edges directly connected to the node corresponding to the mobile robot as the in-degree of the node corresponding to the mobile robot, that is, d i (υ i )=∑a ij ; Then, for the communication topology of the n-dimensional space multi-mobile robot system, according to l = 1, ..., M, k = 1, ..., N, define the weight coefficient b of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot kl , that is, if there is a communication channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0; Finally, based on the dynamic models corresponding to multiple navigator robots and multiple follower robots in the inertial coordinate system, combined with the velocity state estimation information corresponding to the multiple navigator robots, the multi-mobile robot consistency inclusion control error surface is constructed as follows: Multi-mobile robot distributed inclusion control protocol; s kx =[s kx,1 ,…,s kx,n ] T , s kx represents the position loop distributed inclusion control protocol for the kth follower robot in an n-dimensional multi-mobile robot system, s kx,n represents the position loop distributed inclusion control protocol of the kth follower robot corresponding to the nth dimension, s kv =[s kv,1 ,…,s kv,n ] T , s kv represents the distributed inclusive control protocol for the velocity loop of the kth follower robot in an n-dimensional multi-mobile robot system, s kv,n represents the distributed inclusive control protocol for the speed loop of the kth follower robot corresponding to the nth dimension; x j' represents the position state of the j'th follower robot in the n-dimensional space multi-mobile robot system; x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; x l Represents the position state of the lth leader robot in the n-dimensional space multi-mobile robot system; Indicates the velocity state estimation information corresponding to the lth leader robot in multiple leader robots.

5. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: In step C, for the follower robot dynamics model affected by uncertain environmental disturbances, a fixed-time disturbance observer is designed as follows to estimate and compensate for external disturbances in real time; x k represents the position state of the kth follower robot in the n-dimensional space multi-mobile robot system; v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ω k represents the uncertain external interference corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; u k represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system; They are x k 、v k 、ω k estimated value of; μ k It is v i The error estimate of ρ k ,η k , σ k , κ k is the preset disturbance observer design parameter corresponding to the kth follower robot, sig(μ k )=sign(μ k )|μ k |, sign(·) is the sign function, is the integration variable.

6. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: The step D comprises the following operations: First, build the performance function as follows: ζ(t)=(ζ0-ζ ∞ )e -ct +g ∞ e represents a natural constant, t represents a time variable; c represents a preset adjustable parameter used to adjust the convergence speed; ζ0, ζ ∞ Represents a preset positive parameter and satisfies ζ0>ζ ∞ >0, Then according to the preset requirements of the system error: -δ1ζ(t)<s kx <δ2ζ(t), The error conversion function ψ(·) is used to convert the inclusive control error surface in the distributed inclusive control protocol of multiple mobile robots into a preset performance error. The inclusive control error surface is made to converge to the preset performance boundary, and the distributed inclusive control protocol of multiple mobile robots is updated; wherein, The error variable corresponding to the k-th follower robot in the distributed inclusive control protocol of the multi-mobile robot system in n-dimensional space is converted by the error conversion function ψ(·), that is, the preset performance error. The error conversion function ψ(·): (-δ1, δ2)→(-∞, +∞) is an increasing smooth function, and the function ψ(·) is as follows: Wherein, λ is a preset adjustable parameter constant, 0<δ1<1, 0<δ2<1 are preset design parameters used to adjust the preset performance boundary.

7. The distributed guaranteed cost control method for networked multiple mobile robots according to claim 1, characterized in that: The step E comprises the following operations: First, the backstepping technique is used to adjust the preset performance error θ kx (t) Taking the derivative, we get: k=1、...、N,v k represents the velocity state of the kth follower robot in the n-dimensional space multi-mobile robot system; ζ(t) represents the performance function, which is a positive continuously decreasing function; represents the first-order derivative of the performance function ζ(t); d k represents the in-degree of the node corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system; a kj' Represents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the j'th follower robot in the communication topology of the n-dimensional space multi-mobile robot system. When there is a communication interaction channel between the kth follower robot and the j'th follower robot, then a kj' =1, otherwise a kj' =0; j'=1, ..., N, v j' represents the velocity state of the j'th follower robot in the n-dimensional space multi-mobile robot system; l = 1, ..., M, b kl represents the weight coefficient of the edge between the node corresponding to the kth follower robot and the node corresponding to the lth leader robot, that is, if there is a communication interaction channel between the kth follower robot and the lth leader robot, then b kl =1, otherwise b kl =0; Indicates the velocity state estimation information corresponding to the lth leader robot in multiple leader robots; s kx Represents a distributed inclusion control protocol for the position loop of the kth follower robot in a multi-mobile robot system in n-dimensional space; Then according to Lyapunov stability theory, combined with Building a Virtual Controller α k as follows: α k It represents the virtual control signal of the position loop of the kth follower robot in the n-dimensional space multi-mobile robot system, and then further constructs the error e k as follows: Finally get the control protocol u k As follows, u k represents the control input signal of the kth follower robot in the n-dimensional space multi-mobile robot system, that is, a multi-mobile robot distributed inclusive controller is obtained, which is used to realize the coordinated control of each follower robot in the n-dimensional space multi-mobile robot system; Among them, β k1 , β k2 represents the preset controller design parameters corresponding to the kth follower robot in the n-dimensional space multi-mobile robot system, and β k1 >0,β k2 >0.

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