Multi-robot distributed cooperative formation control method under a specified time

Abstract

The present application belongs to the technical field of intelligent agent cooperative work control, and particularly relates to a multi-robot distributed cooperative formation control method under a specified time; the method comprises: constructing a multi-robot dynamics model; constructing a communication topology structure of the multi-robot formation and determining a desired formation mode; introducing a virtual spring between the robots to construct a potential energy function and defining a formation error of the robot system; designing a gradient descent distributed controller based on time-varying gain at a task level and a controller under a specified time at a joint level; real-time estimating and compensating unknown parameters of the robot dynamics model to obtain an online estimated parameter adaptive law based on time-varying gain; obtaining a total formation controller according to all the controllers and the online estimated parameter adaptive law, and using the total formation controller to realize the multi-robot distributed cooperative formation control; the present application effectively solves the problem of rapid reconstruction of the formation mode under complex dynamic environments such as dynamic obstacle avoidance of a UAV cluster and cooperative work of multiple mechanical arms.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent agent cooperative work control, and particularly relates to a multi-robot distributed cooperative formation control method under a specified time. BACKGROUND

[0002] Multi-robot cooperative formation control is a core problem in the field of distributed intelligent system control, and is widely used in ship formation navigation, underwater robot cooperative exploration, mobile robot, multi-robot arm precision assembly, unmanned aerial vehicle cluster reconnaissance and other fields of national defense, intelligent manufacturing and automation. Current typical control methods mainly include the following three types of theoretical frameworks: consistency control through local interaction protocol to achieve state convergence, but the convergence rate is limited by the algebraic connectivity of the network topology; leader-following architecture that depends on the preset trajectory to achieve formation tracking, but has single-point vulnerability and insufficient dynamic environment adaptability; and methods based on fusion obstacle avoidance and aggregation behavior rules, which have strong flexibility and can solve the multi-agent system in the nonlinear dynamic Euler-Lagrange framework that exists universally in engineering practice, but cannot guarantee the system convergence time. The existing general methods face the following two key challenges: first, the traditional gradual convergence mechanism cannot accurately achieve the formation target in a limited time, especially in sudden task scenarios, which may cause system response lag; second, the centralized control architecture requires global communication, high computing power support and strong hardware resources, and in large-scale systems, it faces problems such as limited communication bandwidth and exponentially increasing computational complexity. For example, the classic cooperative algorithm based on Lyapunov function can guarantee asymptotic stability, but the convergence time is strongly related to the initial state and design parameters, making it difficult to meet the strict demand of ±0.5mm synchronization accuracy for industrial applications and flexible assembly.

[0003] In summary, there is an urgent need for a new multi-robot distributed cooperative formation control method to effectively solve the problem of rapid reconfiguration of formation patterns in complex dynamic environments such as unmanned aerial vehicle cluster dynamic obstacle avoidance and multi-robot arm cooperative work, and to provide verifiable real-time control guarantee for intelligent manufacturing, national defense reconnaissance and other scenarios. SUMMARY

[0004] In view of the deficiencies in the prior art, the application provides a multi-robot distributed cooperative formation control method under a specified time, which comprises the following steps:

[0005] S1: obtaining a robot system composed of multiple robots and constructing a multi-robot dynamics model;

[0006] S2: constructing a communication topology structure of the multi-robot formation and determining a desired formation pattern;

[0007] S3: introducing a virtual spring between the robots to construct a potential energy function and calculating the formation error of the robot system;

[0008] S4: Design of a time-varying gain-based gradient descent distributed controller for the formation error of a robot system at the task level;

[0009] S5: Design of a controller for joint-level specified time based on the passive characteristics of Euler systems;

[0010] S6: Real-time estimation and compensation of unknown parameters of robot dynamics model to obtain online parameter estimation adaptive law based on time-varying gain;

[0011] S7: Obtain the overall formation controller based on the adaptive law of all controllers and online estimated parameters, and use the overall formation controller to realize distributed cooperative formation control of multiple robots.

[0012] The preferred multi-robot dynamics model is expressed as follows:

[0013]

[0014] Among them, M i (q i ,w i Let ) represent the inertia matrix of the i-th robot. Let G represent the Coriolis force matrix of the i-th robot. i (q i ,w i ) represents the gravitational torque of the i-th robot; N represents the total number of robots in the entire formation system, q i , Let w represent the generalized joint rotation angle, velocity, and acceleration vector of the i-th robot, respectively. i Let u represent the constant system parameter vector of the known bounded compact set of the i-th robot. i Let represent the total control input vector of the i-th robot.

[0015] Preferably, the desired formation of the robot system is represented as follows:

[0016]

[0017] in, Let x represent the set of desired formations, and let I represent the global state vector consisting of N robots stacked in m-dimensional space. N Let x be an N×N identity matrix, R be the rotation matrix of the desired formation transformation, and x be the x-axis. * For reference formation configuration, m is the dimension of the Cartesian coordinate system, b is the translation vector, and 1 N A column vector consisting entirely of 1s; SO(m) is a rotation matrix in a special orthogonal group. Let represent a linear space consisting of all m-dimensional real column vectors.

[0018] Preferably, the formation error of the robotic system is obtained by scaling the original formation error in task space by a time-varying gain function, which is denoted as:

[0019]

[0020] where z k denotes the actual Euclidean distance corresponding to the kth edge, denotes the desired distance corresponding to the kth edge, e k (t) is the original error signal in task space corresponding to the kth edge at time t;

[0021] The formation error of the robotic system is denoted as:

[0022] η k (t) = μ(t)e k (t)

[0023] where η k (t) denotes the formation error corresponding to the kth edge at time t, and μ(t) denotes the time-varying gain function.

[0024] Preferably, the control law of the gradient descent distributed controller based on the time-varying gain at the task level is denoted as:

[0025]

[0026] where u i t denotes the control law at the task level for the ith robot, K p > 0 denotes a positive control gain, J i (q i , a i ) is the generalized Jacobian matrix of the ith robot transformed by a linear regression matrix, q i denotes the generalized joint angle vector of the ith robot, a i denotes the actual vector of kinematic parameters, denotes the gradient vector of the potential energy function of the ith robot at time t.

[0027] Preferably, the control law of the controller at the joint level under a specified time is denoted as:

[0028] u i j = -K D ξ i + G i (q i , w i )

[0029] where u i jK D represents the control gain design parameter, ξ i represents the joint velocity vector of the ith robot, G i (q i ,w i ) represents the gravity vector of the ith robot system, q i represents the generalized joint angle vector of the ith robot, w i represents the constant system parameter vector of the ith robot known to be bounded compact set.

[0030] Preferably, the online estimation parameter adaptive law based on time-varying gain is represented as:

[0031]

[0032] wherein, represents the time derivative vector of the parameter estimation value of the ith robot, μ(t) represents the time-varying gain function, represents the linear regression matrix of the ith robot, represents the gradient vector of the potential function of the ith robot, α > 0 represents the positive design gain parameter, q i represents the generalized joint angle vector of the ith robot, represents the kinematic parameter estimation vector of the ith robot, ξ i represents the joint velocity vector of the ith robot.

[0033] Preferably, the formation total controller is represented as:

[0034]

[0035] wherein, u i represents the total control input vector of the ith robot, K p > 0 represents the positive control gain, represents the generalized Jacobian matrix of the ith robot transformed by the linear regression matrix, q i represents the generalized joint angle vector of the ith robot, a i represents the kinematic parameter actual vector of the ith robot, represents the gradient vector of the potential function of the ith robot at time t, K D > 0 represents the design control gain, ξ i represents the joint velocity vector of the ith robot, G i (q i ,w i ) represents the gravity vector of the ith robot system, w ia constant system parameter vector representing a known bounded compact set of the i th robot, a parameter estimation value of the i th robot a time derivative vector of the i th robot, μ(t) represents a time-varying gain function, a kinematics regression matrix of the i th robot, and α > 0 represents a design gain parameter, a kinematics parameter estimation vector of the i th robot.

[0036] The present application has the following beneficial effects:

[0037] The present application aims at the unknown parameter identification problem of the robot dynamics model, and a linear observer architecture based on a regression matrix is constructed. The observer realizes the global convergence of the parameter estimation error within a user-specified time interval by introducing a time-varying gain mechanism. Compared with the prior art, the proposed observer can realize more accurate parameter estimation within a specified time, further improving the convergence speed of the observer;

[0038] Compared with the prior art, the present application proposes a distributed cooperative formation control method under a specified time for the distributed formation control of multi-agent systems. The designed specified time gradient descent controller realizes accurate convergence within a user-specified time. Through the distributed control architecture, cooperative parallel computing reduces the communication load, increases the fault tolerance and scalability of the system, and reduces the hardware requirements of the system. This method improves the feasibility in practical engineering applications and provides a new methodological framework for real-time parameter identification and cooperative control of complex dynamic systems;

[0039] The present application effectively solves the problem of rapid reconstruction of formation in complex dynamic environments such as dynamic obstacle avoidance of UAV clusters and cooperative work of multiple mechanical arms, and provides verifiable real-time control guarantee for intelligent manufacturing, national defense detection and other scenes, showing significant practical engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 A flowchart of the multi-robot distributed cooperative formation control method under a specified time in the present application;

[0041] Figure 2 A schematic diagram of the virtual coupling and topological communication relationship between the multi-robot in the present application;

[0042] Figure 3 A position and speed simulation schematic diagram of the end effector of the multi-robot in the present application;

[0043] Figure 4 A schematic diagram of the cooperative formation control formation and trajectory of the multi-robot under a specified time in the present application;

[0044] Figure 5 This is a comparison chart of errors in the multi-robot collaborative formation under different specified time periods in this invention;

[0045] Figure 6 This is a schematic diagram illustrating the changes in the estimated values ​​of kinematic parameters estimated by the regression matrix observer in this invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] This invention proposes a multi-robot distributed cooperative formation control method within a specified time, such as... Figure 1 As shown, the method includes the following:

[0048] S1: Obtain a robot system consisting of multiple robots and construct a multi-robot dynamics model.

[0049] To obtain a robotic system consisting of multiple robots, the dynamic model of each robot can be represented as:

[0050]

[0051] in, Let the inertia matrix of the i-th robot be represented. Let represent the Coriolis force matrix (mainly including Coriolis force and centrifugal force) of the i-th robot. Let represent the gravitational torque of the i-th robot. i∈{1,2,3,...,N} N represents the total number of robots in the entire formation system. Let the generalized joint rotation angle, velocity, and acceleration vector of the i-th robot be represented respectively. Let W represent the known bounded compact set of the i-th robot. i The constant system parameter vector, u i The control torque (input torque) of the i-th robot arm is represented by the total control input vector, and n indicates that the i-th robot has n joints.

[0052] The time-limited convergence criterion for the control system is:

[0053]

[0054] in, Let represent the time derivative of the system's Lyapunov function, k > 0 to represent a positive constant, μ(t) to represent the time-varying gain function, U(t) to represent the system's Lyapunov function, and d(t) to represent a bounded unknown perturbation.

[0055] This can be further expressed as: Consider a time-varying function If there exists a A positive function U(t): [0,T)→[0,+∞) satisfies:

[0056] If the unknown perturbation d(t) is bounded and the positive real constant k > 0, then U(t) is bounded in [0, T), and

[0057] The expression for the time-varying gain function μ(t) is:

[0058]

[0059] In the formula, t represents the time of the system control process, T represents the user-preset convergence time, ρ represents the initial coefficient of the safe transition interval, and μ max μ is the upper limit of the time-varying gain. min This indicates the lower limit of the stable gain.

[0060] S2: Construct the communication topology of the multi-robot formation and determine the desired formation pattern;

[0061] like Figure 2 As shown, the communication topology between robot arms is derived from graph theory. Let G be an undirected graph in graph theory, satisfying either minimum rigidity or infinitesimal rigidity. The vertex set is given by... This represents the end effector of the i-th robot. (Edge set) Each edge (i,j)∈E represents the end effector i and j. j To maintain coordination, the neighbor set of end effector i can be accessed through... Indicated. Respectively using And |E| represents the number of vertices and edges in graph G, and the incidence matrix of graph G. The elements can be represented as: if vertex i is the Eth vertex... k The head of the edge, then the element b of the correlation matrix B. ik Equals 1; if vertex i is the Eth vertex k The tail of the edge, then the element b of the incidence matrix B. ik Equal to -1; otherwise element b ik It is zero.

[0062] Given a reference configuration x * Define the expected formation set may be represented as:

[0063]

[0064] where, denotes a set of desired formation shapes, where each pose x is represented by a reference formation x * generated by rotation and translation, x denotes the global state vector of the stack of N robots in m-dimensional space, i.e. I N denoted as N x N identity matrix, used to apply the rotation matrix R to all robots, R denotes the rotation matrix of desired formation transformation, is a reference formation configuration, denotes the desired relative position relationship of robots, m is the dimension of the Cartesian coordinate system, is a translation vector, denotes the translation degree of freedom of the formation as a whole, 1 N is a full 1 column vector, i.e. R ∈ SO(m) is a rotation matrix in the special orthogonal group, which satisfies: R T R = I m , det(R) = 1, I m denoted as m x m identity matrix ensures that R is an orthogonal rotation matrix, det(R) = 1 indicates that the determinant of the orthogonal rotation matrix R is 1, is a linear space composed of all m-dimensional real column vectors.

[0065] Definition is a reachable subset of end effector, which can be represented as where, is a set of generalized joint positions without kinematic singularity, which can be represented as:

[0066]

[0067] where, h i (q i ,w i ) represents forward kinematics, x i0 is the base position of the i-th robot, is represented as a set of motion singular points avoided by the robot, and its expression is:

[0068] J g,i (q i ,w i ) is the geometric Jacobian matrix of the i-th robot at joint angle q i .

[0069] S3: Introduce virtual springs between robots to construct potential energy functions and calculate the formation error of the robot system.

[0070] For each robot, in each edge E k A potential energy function V(η) is constructed for each end-effector in the edge E

[0071]

[0072] The formation error of the robot system is defined as:

[0073] The formation error of the system represents the position error e k of the end-effector of the ith robot in the task space, whose expression is:

[0074]

[0075] where e k (t) represents the position error of the kth edge of the robot end-effector at time t, i.e., the original error signal in the task space corresponding to the kth edge at time t, z k represents the actual Euclidean distance corresponding to the kth edge, i.e., z k (t) = ||x i (t) - x j (t) ||, is the position coordinate of the robot i and j at time t (m = 2 or 3) represents the expected distance corresponding to the kth edge between the robot i and the robot j, which can be expressed as d ij represents, and ||·|| represents the L2 norm (Euclidean distance). x i represents the position of the end-effector of the ith robot in the task space, which can be linearly mapped from the joint space of the robot to the task space through forward kinematics, whose expression is:

[0076] x i = h i (q i ,w i ) + x i0

[0077] where h i (q i ,w i ) is: is the forward kinematics of the robot, representing a linear mapping from the joint angle q in the joint space to the spatial position of the end-effector of the robot arm in the task space, where x i0 represents the base position of the ith robot in the task space.

[0078] The original error is scaled according to the time scaling function to obtain the scaled error, i.e., the final formation error η k of the robot system, which can be expressed as:

[0079] η k(t) = μ(t)e k (t)

[0080] where e k (t) is the original task space error signal of the kth edge at time t, and μ(t) represents the time-varying gain function.

[0081] S4: Design a task level gradient descent distributed controller based on time-varying gain based on the formation error of the robot system.

[0082] Use gradient descent as the control input for each end effector to achieve the minimum V value of the stable cooperative formation, and the potential function V(η) is the gradient of x i , which is represented by , and its expression is:

[0083]

[0084] where represents the gradient vector of the i-th robot potential function at time t, D z is a diagonal matrix, D z = block diag(z1,...,z |E| ); b ik represents the elements of the associated matrix B, represents the normalized associated matrix, i.e. η represents the error signal scaled by the time-varying gain of the task space error.

[0085] Since the virtual coupling is distributed between the end effectors, the end effector is embedded into the joint, and the distributed control law of the i-th robot in the task space can be represented as:

[0086]

[0087] where represents the control law (control input) of the i-th robot at the task level, K p > 0 represents a positive control gain, is the generalized Jacobian matrix of the i-th robot transformed by the linear regression matrix, represents the generalized joint angle of the i-th robot, represents the actual vector of kinematic parameters, including the equivalent inertia of the connecting rod, the coupling term, the gravity term, etc. The Jacobian matrix can be obtained from the expression , where h i (q i , w i ) represents the forward kinematics.

[0088] S5: Design a joint level controller with specified time using the passive characteristics of the Euler system.

[0089] To solve the static formation problem, the control law is designed to ensure that the joint velocity converges to zero, and the joint velocity of the ith robot is defined as

[0090] As a classic Euler-Lagrange system, the mechanical arm has a passive property from joint torque to joint velocity, and the specified time control law u is designed at the joint level i j which can be expressed as:

[0091] u i j = -K D ξ i + G i (q i ,w i )

[0092] wherein represents the control law (control input) of the ith robot at the joint level, K D > 0 represents the design control gain, represents the joint velocity vector of the ith robot.

[0093] Assuming that the graph theory G satisfies the minimum rigidity or infinitesimal rigidity, i.e. the minimum edge number of the undirected graph G topology structure is 2N-3, where N represents the number of agents in the entire multi-agent system, for the case where the dynamic parameters are known, for any target formation S can be solved according to the following control law:

[0094]

[0095] S6: Real-time estimation and compensation of unknown parameters of the robot dynamics model, and obtain an online estimated parameter adaptive law based on time-varying gain.

[0096] The regression matrix linear observer is used to estimate and compensate the unknown parameters of the robot dynamics model in real time, and the regression matrix linear observer is expressed as:

[0097] The velocity kinematics depends on the kinematics parameter vector (i.e. there is a smooth function and ), for any vector satisfies:

[0098]

[0099] wherein Z i (·) is a known kinematics regression equation, p is the dimension of the kinematics parameter vector, and there is a smooth matrix function value Can be expressed as:

[0100]

[0101] Adopting the linear observer based on the regression matrix above, a new adaptive estimation Jacobian matrix is introduced Controller, based on the online estimation parameter of time-varying gain The adaptive law can be expressed as:

[0102]

[0103] Wherein, Indicates the parameter estimation value of the i th robot The time derivative vector of (i.e., the update speed), Indicates the linear regression matrix of the i th robot, which depends on the generalized joint angle q i And the gradient of the i th robot potential energy function at time t Alpha greater than 0 indicates a positive design gain parameter, Indicates the kinematic parameter estimation vector of the i th robot.

[0104] The estimation error of the kinematic parameters Can be expressed as:

[0105]

[0106] S7: Obtain the formation total controller according to all controllers and online estimation parameter adaptive laws, and realize the distributed cooperative formation control of multi-robot system using the formation total controller.

[0107] Consider a group of N robot dynamics model parameters unknown, and the graph theory G formed between the robots satisfies the minimum rigidity or infinitesimal rigidity, select appropriate gain parameter For the reference configuration x * The formation formed can be solved by the following prescribed time controller, i.e., the formation total controller:

[0108]

[0109] Based on the control law above, the cooperative formation control of multi-robot system within a prescribed time can be finally realized.

[0110] Simulation verification is carried out on the present application:

[0111] In order to verify the effectiveness of the method of the present application, simulation experiments are carried out by using Matlab2024a, and the specific process is as follows:

[0112] Four sets of numerical simulation experiments of two-degree-of-freedom manipulator systems are constructed by selecting model parameters to systematically verify the proposed distributed cooperative formation control method under the specified time. The parameters of the four sets of two-degree-of-freedom manipulators are consistent, and the dynamic parameters are shown in Table 1. The total simulation time of the system is set to 10 s, i.e., t = 10 s, and the sampling period is Δt = 0.01 s. Other related simulation parameters are shown in Tables 1, 2, and 3. Table 1 lists the parameters of the two-degree-of-freedom manipulator system, Table 2 lists the nominal model parameters of the regression matrix observer, and other related parameters are shown in Table 3.

[0113] Table 1 Parameters of the two manipulator system

[0114]

[0115] In Table 1, only the system parameters of a single two-degree-of-freedom manipulator are listed, and the system parameters of the other three manipulators are completely consistent with the above. Among them, m i represents the mass of the i-th link in the manipulator, I ci represents the moment of inertia of the i-th link in the manipulator, l i represents the length of the i-th link, l ci represents the distance from the i-th link to its center of mass.

[0116] Table 2 Nominal model parameters of the regression matrix observer

[0117]

[0118] Note that Table 2 also only lists the nominal model of the regression matrix observer of a single two-degree-of-freedom manipulator, and the nominal models of the regression matrix observers of the other three manipulators are completely consistent with Table 2. Among them, a i1 represents the equivalent inertia of link 1 in the i-th manipulator, a i2 represents the equivalent inertia of link 2 in the i-th manipulator, a i3 represents the coupling inertia term (i.e., the Coriolis force and centrifugal force coefficients) in the i-th manipulator, a i4 represents the gravity term of joint 1 in the i-th manipulator, a i5 represents the gravity term of joint 2 in the i-th manipulator.

[0119] Table 3 Other related parameters

[0120] Parameter name Parameter value Parameter name Parameter value Parameter name Parameter value K P ]]> 1000 K D ]]> 1300 α 0.02 Parameter name Parameter value Parameter name Parameter value Parameter name Parameter value μ max ]]> 100 μ min ]]> 40 p 0.985

[0121] As shown in Table 3, K P represents the first design gain parameter, K D represents the second design gain parameter, α represents the third design gain parameter, μ maxThis represents the upper bound of the adjustment of the time-varying gain function, preventing the time-varying gain from growing unbounded. μ min ρ represents the steady-state lower limit of the time-varying gain, and ρ represents the initial coefficient of the safe transition range of the time-varying gain.

[0122] To further illustrate, the kinematic model of each two-joint robotic arm can be represented as:

[0123]

[0124] The Jacobian matrix can be represented as:

[0125]

[0126] Where, q i =[q i1 q i2 ] T The length of the connecting rod is a i =[l1 l2] T Then the set of singularity configurations for robot motion is The initial joint angles of each robotic arm in this simulation are q1(0) = [0, π / 3]. T q2(0) = [π / 2, π / 3] T q3(0) = [π, π / 3] T q4(0) = [3π / 2, π / 3] T The initial base coordinates of the four robotic arms are (0,0), (8,0), (8,8), and (0,8), respectively. The initial joint velocities of all robotic arms are zero, and the initial kinematic parameter estimates are... Considering the desired formation of the robots is a square with a side length of 4cm, the corresponding formation correlation matrix B is:

[0127]

[0128] Since all robots are considered to operate in a horizontal plane, the gravity matrix is ​​always zero, i.e., G. i (q i ,w i )≡0 where i=1,2,3,4.

[0129] Simulation results are as follows Figures 3 to 6 As shown, Figure 3 The graphs show the position and velocity variations of all robotic arm end effectors. It can be clearly observed from the graphs that the time-varying gain function effectively defines the position and velocity fluctuation errors, effectively enabling each robotic arm to reach the target position within a specified time and converge its motion speed to zero.

[0130] Figure 4In the middle, the motion trajectory of the robot end effector clearly shows the convergence process from the initial pose (marked as "x") to the target pose (marked as "o"). The experimental data show that in the two-dimensional workspace, the formation of the desired formation is achieved, verifying the feasibility of the proposed formation control method. Figure 5 The error graphs under different user preset times are shown (a is the error graph under the specified convergence time T=2s, and b is the error graph under the specified convergence time T=1.5s), as shown in Figure 5 As shown in a, when the preset time T=2s, the relative distance between the end effectors of the four mechanical arms can accurately match the set relative expected distance, as shown in Figure 5 As shown in b, when the preset convergence time is shortened to T=1.5s, the system shows strong stability, and the formation error can accurately converge to zero within 1.5s, fully verifying the high precision and fast response capability of the system. Figure 6 The kinematic parameter estimation error dynamic characteristic curve obtained by the regression matrix observer is shown, and the results show that the parameter estimation has certain fluctuations in the initial stage, but with the action of the time-varying gain, the kinematic parameter estimation value is effectively converged to the nominal value within the specified time T.

[0131] In summary, the present application combines the specified time convergence mechanism, distributed control architecture and adaptive parameter estimation, and proposes a multi-robot distributed cooperative formation control method under the specified time, which provides a possible solution for the requirement of millimeter-level response and synchronization in the field of industrial automation and national defense cluster detection. First, the specified time control constructs a time base function or a time-varying control gain, so that the entire system error signal strictly converges to zero within the user preset time T, breaking through the limitations of traditional gradual convergence time uncertainty, finite time convergence dependence on initial conditions, design parameters, etc.; secondly, based on the neighborhood information interaction, a distributed control strategy is constructed, which reduces the communication load through cooperative parallel computing, while increasing the fault tolerance and scalability of the system to node failures; finally, in view of the parameter perturbation of the system dynamics model, load changes and environmental interaction disturbances and other uncertainties in actual engineering, an adaptive observer based on regression matrix is designed to estimate the kinematic parameters of the Jacobian matrix online, effectively compensating for the uncertainty of the dynamic model and adapting to the unstructured environment. The cooperative design of the three effectively solves the problem of rapid reconstruction of the formation shape in complex dynamic environments such as unmanned aerial vehicle cluster dynamic obstacle avoidance and multi-robot cooperative work, and provides a verifiable real-time control guarantee for intelligent manufacturing, national defense detection and other scenes, showing significant practical application value.

[0132] The above examples further illustrate the objects, technical solutions and advantages of the present application. It should be understood that the above examples are only preferred embodiments of the present application and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A multi-robot distributed cooperative formation control method under a given time, characterized in that, Comprise: S1: acquire a robot system composed of multiple robots and construct a multi-robot dynamics model; S2: construct a communication topology of the multi-robot formation and determine a desired formation mode; S3: introduce a virtual spring between the robots to construct a potential energy function and calculate the formation error of the robot system; S4: design a task-level gradient descent distributed controller based on time-varying gain based on the formation error of the robot system; the control law of the task-level gradient descent distributed controller based on time-varying gain is represented as: ； in, Indicates the first Control laws for a robot at the task level Indicates positive control gain. For the first The generalized Jacobian matrix of the robot after transformation by the linear regression matrix. Indicates the first The generalized joint rotation vector of a robot. Represents the actual vector of kinematic parameters. Represents the time t. The gradient vector of the potential energy function of each robot; S5: design a joint-level controller under prescribed time based on the passive characteristics of the Euler system; the control law of the joint-level controller under prescribed time is represented as: ； in, Indicates the first Control laws for a robot at the joint level Indicates the design control gain. Indicates the first The joint velocity vectors of the robot. Indicates the first The gravity vector of the robot system Indicates the first A known bounded compact set of constant system parameter vectors for a robot; S6: real-time estimate and compensate the unknown parameters of the robot dynamics model to obtain an online estimated parameter adaptive law based on time-varying gain; the online estimated parameter adaptive law based on time-varying gain is represented as: ； in, Indicates the first Parameter estimates for each robot The time derivative vector, Represents the time-varying gain function. Indicates the first The linear regression matrix of the robots, Indicates the first The gradient vector of the potential energy function of each robot. This represents a positive design gain parameter. Indicates the first The kinematic parameter estimation vector of a robot; S7: obtain a formation total controller according to all the controllers and the online estimated parameter adaptive law, and realize the distributed cooperative formation control of the multi-robot using the formation total controller; the formation total controller is represented as: ； wherein, denotes the total control input vector of the robot, denotes the gradient vector of the potential energy function of the robot at time t.

2. The method according to claim 1, wherein, The multi-robot dynamics model is represented as: ； wherein, denotes the inertia matrix of the th robot, denotes the Coriolis matrix of the th robot, denotes the gravity matrix of the th robot; denotes the total number of robots in the entire formation system, denotes the generalized joint angle, velocity and acceleration vectors of the th robot, respectively, denotes the constant system parameter vector of the known bounded compact set of the th robot, denotes the total control input vector of the th robot.

3. The method according to claim 1, wherein, The desired formation mode of the robot system is represented as: ； wherein, denotes a set of desired formation shapes, denotes a global state vector of a stack of robots in dimensional space, denotes an identity matrix of dimension, denotes a rotation matrix of a desired formation transformation, is a reference formation configuration, is a dimension of a Cartesian coordinate system, is a translation vector, is an all-ones column vector; is a rotation matrix in the special orthogonal group, denotes a linear space spanned by all dimensional real column vectors.

4. The method according to claim 1, wherein, The formation error of the robot system is obtained by scaling the task space original formation error through a time-varying gain function, and the task space original formation error is represented as: ； wherein, represents the actual Euclidean distance corresponding to the kth edge, represents the expected distance corresponding to the kth edge, is the task space raw error signal corresponding to the kth edge at the instant The formation error of the robot system is represented as: ； wherein, denotes the platoon error corresponding to the kth edge at time instant, denotes a time-varying gain function.

Images