Multi-robot distributed cooperative formation control method under specified time

Abstract

The invention belongs to the technical field of agent cooperative work control, and particularly relates to a multi-robot distributed cooperative formation control method under specified time. The method comprises the following steps: constructing a multi-robot dynamic model; constructing a communication topological structure of the multi-robot formation and determining an expected formation form; virtual springs are introduced between the robots to construct a potential energy function, and formation errors of a robot system are defined; designing a time-varying gain-based gradient descent distributed controller in a task level and a controller in a specified time in a joint level; estimating and compensating unknown parameters of the robot kinetic model in real time to obtain an online estimation parameter adaptive law based on time-varying gain; a formation master controller is obtained according to all the controllers and the online estimation parameter adaptive law, and multi-robot distributed cooperative formation control is achieved through the formation master controller; according to the method, the problem of rapid reconstruction of the formation form in complex dynamic environments such as dynamic obstacle avoidance of an unmanned aerial vehicle cluster and cooperative work of multiple mechanical arms is effectively solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent body collaborative work control, and specifically relates to a multi-robot distributed collaborative formation control method under a specified time. Background Art

[0002] Multi-robot cooperative formation control, a core issue in the field of distributed intelligent system control, is widely used in defense, intelligent manufacturing, and automation fields, including ship formation navigation, underwater robot cooperative exploration, mobile robots, multi-manipulator precision assembly, and drone swarm reconnaissance. Current typical control approaches mainly fall into three theoretical frameworks: state convergence achieved through local interaction protocols, but its convergence rate is limited by the consistency control of the algebraic connectivity of the network topology; leader-follower architectures that rely on preset trajectories for formation tracking, but suffer from single-point vulnerability and insufficient adaptability to dynamic environments; and approaches based on the fusion of behavioral rules such as obstacle avoidance and clustering. While highly flexible and capable of solving the nonlinear dynamics of multi-agent systems commonly encountered in engineering practice within the Euler-Lagrangian framework, they cannot guarantee system convergence time. Existing common approaches face two key challenges: First, traditional gradual convergence mechanisms cannot accurately achieve formation objectives within a limited time, especially in sudden mission scenarios, which may lead to delayed system response. Second, centralized control architectures require global communication, high computing power, and extensive hardware resources. In large-scale systems, they face limitations in communication bandwidth and exponential computational complexity. For example, although the classic collaborative algorithm based on the Lyapunov function can ensure asymptotic stability, its convergence time is strongly related to the initial state and design parameters, and it is difficult to meet the stringent requirements of industrial handling and flexible assembly for ±0.5mm synchronization accuracy.

[0003] In summary, a new multi-robot distributed collaborative formation control method is urgently needed to effectively solve the problem of rapid reconstruction of formation morphology in complex dynamic environments such as dynamic obstacle avoidance of drone clusters and collaborative work of multiple robotic arms, and provide verifiable real-time control guarantees for scenarios such as intelligent manufacturing and national defense reconnaissance. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention proposes a multi-robot distributed cooperative formation control method under a specified time, which includes:

[0005] S1: Obtain a robot system consisting of multiple robots and build a multi-robot dynamics model;

[0006] S2: Construct the communication topology of the multi-robot formation and determine the desired formation shape;

[0007] S3: Introduce virtual springs between robots to construct potential energy functions and calculate the formation error of the robot system;

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

[0009] S5: Design a controller at the joint level with a specified time based on the passive characteristics of the Euler system;

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

[0011] S7: Based on all controllers and the online estimated parameter adaptive law, the formation master controller is obtained, and the formation master controller is used to realize multi-robot distributed collaborative formation control.

[0012] Preferably, the multi-robot dynamics model is expressed as:

[0013]

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

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

[0016]

[0017] in, represents the set of desired formation forms, x represents the global state vector formed by the stacking of N robots in m-dimensional space, I N It is represented as an N×N identity matrix, R represents the rotation matrix of the desired formation transformation, x * is the reference formation configuration, m is the dimension of the Cartesian coordinate system, b is the translation vector, 1 N is a column vector of all ones; SO(m) is a rotation matrix in a special orthogonal group, Represents the linear space consisting of all m-dimensional real column vectors.

[0018] Preferably, the formation error of the robot system is obtained by scaling the original formation error in the task space with a time-varying gain function. The original formation error in the task space is expressed as:

[0019]

[0020] Among them, z k represents the actual Euclidean distance corresponding to the k-th edge, represents the expected distance corresponding to the kth edge, e k (t) is the original error signal in the task space corresponding to the k-th edge at time t;

[0021] The formation error of the robot system is expressed as:

[0022] η k (t)=μ(t)e k (t)

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

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

[0025]

[0026] Among them, u i t represents the control law of the i-th robot at the task level, K p >0 indicates positive control gain, J i (q i ,a i ) is the generalized Jacobian matrix of the i-th robot after transformation by the linear regression matrix, q i represents the generalized joint angle vector of the i-th robot, a i represents the actual vector of kinematic parameters, Represents the gradient vector of the potential energy function of the i-th robot at time t.

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

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

[0029] Among them, u i jrepresents the control law of the i-th robot at the joint level, K D >0 indicates the design control gain, ξ i represents the joint velocity vector of the i-th robot, G i (q i ,w i ) represents the gravity vector of the i-th robot system, q i represents the generalized joint rotation vector of the i-th robot, w i represents a known bounded compact set of constant system parameters of the ith robot.

[0030] Preferably, the adaptive law of online estimation parameters based on time-varying gain is expressed as:

[0031]

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

[0033] Preferably, the formation master controller is expressed as:

[0034]

[0035] Among them, u i represents the total control input vector of the i-th robot, K p >0 indicates positive control gain, represents the generalized Jacobian matrix of the i-th robot after transformation by the linear regression matrix, q i represents the generalized joint angle vector of the i-th robot, a i represents the actual vector of kinematic parameters of the i-th robot, represents the gradient vector of the potential energy function of the i-th robot at time t, K D >0 indicates the design control gain, ξ i represents the joint velocity vector of the i-th robot, G i (q i ,w i ) represents the gravity vector of the i-th robot system, w irepresents the constant system parameter vector of the known bounded compact set of the ith robot, represents the parameter estimate of the i-th robot The time derivative vector of , μ(t) represents the time-varying gain function, represents the kinematic regression matrix of the i-th robot, α>0 represents the design gain parameter, represents the kinematic parameter estimation vector of the i-th robot.

[0036] The beneficial effects of the present invention are:

[0037] This paper addresses the problem of identifying unknown parameters in a robot's dynamics model by constructing a linear observer architecture based on a regression matrix. By incorporating a time-varying gain mechanism, this observer achieves global convergence of parameter estimation errors within a user-preset time interval. Compared to existing technologies, the proposed observer achieves more accurate parameter estimation within a specified timeframe, further improving the observer's convergence speed.

[0038] Compared with the existing technology, the present invention proposes a distributed cooperative formation control method under a specified time for distributed formation control of multi-agent systems. The designed specified time gradient descent controller achieves precise convergence within the user-preset time. Through the distributed control architecture, collaborative parallel computing reduces the communication load, while increasing the system's fault tolerance and scalability to node failures and reducing the hardware requirements of the system. This method improves feasibility in practical engineering applications and provides a new methodological framework for real-time parameter identification and cooperative control of complex dynamic systems.

[0039] This invention effectively solves the problem of rapid reconstruction of formation morphology in complex dynamic environments such as dynamic obstacle avoidance of drone clusters and collaborative work of multiple robotic arms. It also provides verifiable real-time control guarantees for scenarios such as intelligent manufacturing and national defense reconnaissance, demonstrating significant practical engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the multi-robot distributed cooperative formation control method under specified time in the present invention;

[0041] Figure 2 Schematic diagram of the virtual coupling and topological communication relationship between multiple robots in the present invention;

[0042] Figure 3 Schematic diagram of position and velocity simulation of multi-robot end effectors in the present invention;

[0043] Figure 4 Schematic diagram of the control formation and trajectory of a multi-robot collaborative formation under a specified time in the present invention;

[0044] Figure 5 This is a comparison diagram of the errors of the multi-robot collaborative formation under different prescribed times in the present invention;

[0045] Figure 6 Schematic diagram of the change in the estimated value of the kinematic parameters estimated by the regression matrix observer in the present invention. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0047] The present invention proposes a multi-robot distributed cooperative formation control method under a specified time, such as Figure 1 As shown, the method includes the following contents:

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

[0049] Get a robot system composed of multiple robots. The dynamic model of each robot can be expressed as:

[0050]

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

[0052] The control system specifies the time convergence criterion as:

[0053]

[0054] in, represents the time derivative of the system Lyapunov function, k>0 represents a positive constant, μ(t) represents the time-varying gain function, U(t) represents the system Lyapunov function, and d(t) represents a bounded unknown disturbance.

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

[0056] For an unknown perturbation d(t) that is bounded and a positive real constant k>0, then U(t) is bounded in [0,T), and

[0057] Among them, the expression of the time-varying gain function μ(t) is:

[0058]

[0059] Where t is the time of the system control process, T is the convergence time preset by the user, ρ is the starting coefficient of the safe transition interval, μ is max is the upper limit of time-varying gain, μ min Indicates the lower limit of stable gain.

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

[0061] like Figure 2 As shown in the figure, the communication topology between the robot arms is represented by graph theory. Represents that the graph theory G is an undirected graph and satisfies minimum rigidity or infinitesimal rigidity. represents the end effector of the i-th robot. Each edge (i,j)∈E represents the end effector i and j The need to maintain a collaborative relationship between them, the neighbor set of end effector i can be Indicated by and |E| represents the number of vertices and edges of the graph G, the incidence matrix of the graph G The elements can be expressed as follows: If vertex i is the E k The head of the edge, then the element b of the incidence matrix B ik Equal to 1; if vertex i is the E k The tail of the edge, then the element b of the incidence matrix B ik Equal to -1; otherwise element b ik is zero.

[0062] Given a reference configuration x * , define the desired formation shape set It can be expressed as:

[0063]

[0064] in, represents the set of desired formations, where each configuration x is represented by the reference formation x * After rotation and translation, x represents the global state vector formed by stacking N robots in m-dimensional space, that is, I N It is represented as an N×N identity matrix, which is used to apply the rotation matrix R to all robots. R represents the rotation matrix of the desired formation transformation. is the reference formation configuration, which represents the expected relative position relationship of the robots, m is the dimension of the Cartesian coordinate system, is the translation vector, which represents the translational freedom of the formation as a whole, 1 N is a column vector of all ones, i.e. R∈SO(m) is a rotation matrix in a special orthogonal group, satisfying: R T R=I m ,det(R)=1,I m The identity matrix represented as m×m ensures that R is an orthogonal rotation matrix. det(R)=1 means that the determinant of the orthogonal rotation matrix R is 1. It is a linear space consisting of all m-dimensional real column vectors.

[0065] definition is the reachable subset of the end effector, which can be expressed as in, is a set of generalized joint positions without kinematic singularities, which can be expressed as:

[0066]

[0067] Among them, h i (q i ,w i ) represents forward kinematics, x i0 is the base coordinate position of the i-th robot, It is represented as the set of robot avoidance motion singular points, and its expression is:

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

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

[0070] For each robot, on its edge E k = Each end effector in (i, j) constructs the potential energy function V(η):

[0071]

[0072] Define the formation error of the robot system:

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

[0074]

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

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

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

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

[0079] η k(t)=μ(t)e k (t)

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

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

[0082] Gradient descent is used as the control input for each end effector to achieve the minimum V value for a stable cooperative formation. The potential energy function V(η) is used for x i The gradient of The expression is:

[0083]

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

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

[0086]

[0087] in, represents the control law (control input) of the i-th robot at the task level, K p >0 indicates positive control gain, is the generalized Jacobian matrix of the i-th robot after transformation by the linear regression matrix, represents the generalized joint rotation angle of the i-th robot, Represents the actual vector of kinematic parameters, including the equivalent inertia of the connecting rod, coupling terms, gravity terms, etc. The Jacobian matrix can be expressed by Find, where h i (q i ,w i ) represents forward kinematics.

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

[0089] To solve the static formation problem, the control law needs to be designed to ensure that the joint velocity converges to zero. The joint velocity of the i-th robot is defined as

[0090] As a classic Euler-Lagrangian system, the robotic arm is designed with a prescribed time control law u at the joint level based on the passive characteristics of the joint torque to joint velocity. i j It can be expressed as:

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

[0092] in, represents the control law (control input) of the i-th robot at the joint level, K D >0 indicates the design control gain, represents the joint velocity vector of the i-th robot.

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

[0094]

[0095] S6: Real-time estimation and compensation of unknown parameters of the robot dynamics model, and obtaining an online estimation 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. The regression matrix linear observer is expressed as:

[0097] Velocity kinematics depends on the kinematic parameter vector (That is, there is a smooth function and ), for any vector satisfy:

[0098]

[0099] where Z i (·) is a known kinematic regression equation, p is the dimension of the kinematic parameter vector, and there exists a smooth matrix function value It can be expressed as:

[0100]

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

[0102]

[0103] in, represents the parameter estimate of the i-th robot The time derivative vector of (i.e., update speed), represents the linear regression matrix of the i-th robot, which depends on the generalized joint angle q i and the gradient of the potential energy function of the i-th robot at time t α>0 indicates a positive design gain parameter, represents the kinematic parameter estimation vector of the i-th robot.

[0104] Estimation error of kinematic parameters It can be expressed as:

[0105]

[0106] S7: Based on all controllers and the online estimated parameter adaptive law, the formation master controller is obtained, and the formation master controller is used to realize multi-robot distributed collaborative formation control.

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

[0108]

[0109] Based on the above control law, the collaborative formation control of the multi-robot system can be finally achieved within the specified time.

[0110] The present invention is simulated and verified:

[0111] In order to verify the effectiveness of the method of the present invention, a simulation experiment was carried out using Matlab2024a, as follows:

[0112] By selecting model parameters to construct a numerical simulation experiment of four groups of two-degree-of-freedom manipulator systems, the proposed distributed cooperative formation control method under a specified time was systematically verified. Considering that the parameters of the four groups of two-degree-of-freedom manipulators are consistent, their dynamic parameters are shown in Table 1. The total simulation time of the system is set to 10s, that is, t = 10s, and the sampling period is Δt = 0.01s. 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 dual-manipulator system

[0114]

[0115] In Table 1, only the system parameters of a single two-DOF manipulator are listed. The system parameters of the other three manipulators are exactly the same as above. i Expressed as the mass of the i-th link in the robotic arm, I ci Expressed as the moment of inertia of the i-th link in the robotic arm, l i Expressed as the length of the i-th connecting rod, 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 lists only the regression matrix observer nominal model of a single two-DOF manipulator. The regression matrix observer nominal models of the other three manipulators are exactly the same as those in Table 2, where a i1 represents the equivalent inertia of link 1 in the i-th robotic arm, a i2 represents the equivalent inertia of link 2 in the i-th robotic arm, a i3 represents the coupled inertia term (i.e., the Coriolis force and centrifugal force coefficient) in the i-th manipulator, a i4 represents the gravity term of joint 1 in the i-th robotic arm, a i5 represents the gravity term of joint 2 in the i-th robotic arm.

[0119] Table 3 Other related parameters

[0120] Parameter name Parameter value Parameter name Parameter value Parameter name Parameter value <![CDATA[K P ]]> 1000 <![CDATA[K D ]]> 1300 α 0.02 Parameter name Parameter value Parameter name Parameter value Parameter name Parameter value <![CDATA[μ max ]]> 100 <![CDATA[μ min ]]> 40 ρ 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 maxIndicates the upper bound of the time-varying gain function to avoid the unbounded growth of the time-varying gain, μ min It represents the steady-state lower limit of the time-varying gain, and ρ represents the starting coefficient of the safe transition interval of the time-varying gain.

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

[0123]

[0124] The Jacobian matrix can be expressed as:

[0125]

[0126] Among them, q i =[q i1 q i2 ] T , the connecting rod length is a i =[l1 l2] T , then the robot motion singular point configuration set is The initial joint angles of each robot 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 coordinate positions of the four groups of manipulators are (0,0), (8,0), (8,8), (0,8), and the initial joint velocities of all manipulators are zero. The initial kinematic parameter estimation is Considering that the desired formation of the robots is a square with a side length of 4 cm, the corresponding correlation matrix B of the formation diagram is:

[0127]

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

[0129] The simulation results are as follows Figures 3 to 6 As shown, Figure 3 The position and velocity change diagrams of all robot arm end effectors are displayed. It can be clearly observed from the figure that the time-varying gain function effectively defines the fluctuation errors of position and velocity, effectively enabling each robot arm to reach the target position within the specified time and the movement speed to converge to zero.

[0130] Figure 4In the figure, the trajectory of the robot's end-effector clearly illustrates the convergence process from the initial pose (marked by "×") to the target pose (marked by "○"). Experimental data shows that the desired formation shape is achieved within the two-dimensional workspace, 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, b is the error graph under the specified convergence time T = 1.5s), as shown in the figure. Figure 5 As shown in Figure a, when the preset time T = 2s, the relative distances between the end effectors of the four robotic arms can accurately match the set relative expected distances, as shown in Figure 2. Figure 5 As shown in Figure 2b, 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 rapid response capability of the system. Figure 6 The dynamic characteristic curve of the kinematic parameter estimation error obtained by the regression matrix observer is presented. The results show that there are certain fluctuations in the parameter estimation in the initial stage, but with the effect 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, this paper combines a time-based convergence mechanism, a distributed control architecture, and adaptive parameter estimation to propose a multi-robot distributed collaborative formation control method under time-based convergence. This method offers a potential solution for the millimeter-level response and synchronization requirements of industrial automation and defense cluster reconnaissance. First, time-based control constructs a time basis function or time-varying control gain to ensure that the entire system error signal converges strictly to zero within a user-preset time T, overcoming the limitations of traditional asymptotic convergence time uncertainty and finite-time convergence dependence on initial conditions and design parameters. Second, a distributed control strategy is constructed based on neighborhood information interaction, reducing communication load through collaborative parallel computing while increasing the system's fault tolerance and scalability to node failures. Finally, to address the uncertainties of system dynamics model parameter perturbations, load variations, and environmental interaction disturbances in actual engineering, a regression matrix-based adaptive observer is designed to online estimate the Jacobian matrix kinematic parameters, effectively compensating for the uncertainties of the dynamic model and improving adaptability to unstructured environments. The collaborative design of the three effectively solves the problem of rapid reconstruction of formation forms in complex dynamic environments such as dynamic obstacle avoidance of drone clusters and collaborative work of multiple robotic arms. It also provides verifiable real-time control guarantees for scenarios such as intelligent manufacturing and national defense reconnaissance, demonstrating significant practical engineering application value.

[0132] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation plans of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-robot distributed cooperative formation control method under a specified time, characterized in that: include: S1: Obtain a robot system consisting of multiple robots and build a multi-robot dynamics model; S2: Construct the communication topology of the multi-robot formation and determine the desired formation shape; S3: Introduce virtual springs between robots to construct potential energy functions and calculate the formation error of the robot system; S4: Designing a time-varying gain-based gradient descent distributed controller at the task level based on the formation error of the robot system; S5: Design a controller at the joint level with a specified time based on the passive characteristics of the Euler system; S6: Real-time estimation and compensation of unknown parameters of the robot dynamics model, and obtaining an online estimation parameter adaptive law based on time-varying gain; S7: Based on all controllers and the online estimated parameter adaptive law, the formation master controller is obtained, and the formation master controller is used to realize multi-robot distributed collaborative formation control.

2. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The multi-robot dynamics model is expressed as: Among them, M i (q i ,w i ) represents the inertia matrix of the i-th robot, represents the Coriolis force matrix of the i-th robot, G i (q i ,w i ) represents the gravity moment of the i-th robot; N represents the total number of robots in the entire formation system, q i , Represent the generalized joint angle, velocity and acceleration vector of the i-th robot, w i represents the constant system parameter vector of the known bounded compact set of the i-th robot, u i represents the total control input vector of the ith robot.

3. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The desired formation of the robot system is expressed as: in, represents the set of desired formation forms, x represents the global state vector formed by the stacking of N robots in m-dimensional space, I N It is represented as an N×N identity matrix, R represents the rotation matrix of the desired formation transformation, x * is the reference formation configuration, m is the dimension of the Cartesian coordinate system, b is the translation vector, 1 N is a column vector of all ones; SO(m) is a rotation matrix in a special orthogonal group, Represents the linear space consisting of all m-dimensional real column vectors.

4. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The formation error of the robot system is obtained by scaling the original formation error in the task space with the time-varying gain function. The original formation error in the task space is expressed as: Among them, z k represents the actual Euclidean distance corresponding to the k-th edge, represents the expected distance corresponding to the kth edge, e k (t) is the original error signal in the task space corresponding to the k-th edge at time t; The formation error of the robot system is expressed as: or k (t)=μ(t)e k (t) Among them, η k (t) represents the formation error corresponding to the kth edge at time t, and μ(t) represents the time-varying gain function.

5. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The control law of the gradient descent distributed controller based on time-varying gain at the task level is expressed as: Among them, u i t represents the control law of the i-th robot at the task level, K p >0 indicates positive control gain, J i (q i ,a i ) is the generalized Jacobian matrix of the i-th robot after transformation by the linear regression matrix, q i represents the generalized joint angle vector of the i-th robot, a i represents the actual vector of kinematic parameters, Represents the gradient vector of the potential energy function of the i-th robot at time t.

6. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The control law of the controller at the specified time at the joint level is expressed as: Among them, u i j represents the control law of the i-th robot at the joint level, K D >0 indicates the design control gain, ξ i represents the joint velocity vector of the i-th robot, G i (q i ,w i ) represents the gravity vector of the i-th robot system, q i represents the generalized joint rotation vector of the i-th robot, w i represents a known bounded compact set of constant system parameters of the ith robot.

7. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The online estimation parameter adaptation law based on time-varying gain is expressed as: in, represents the parameter estimate of the i-th robot The time derivative vector of , μ(t) represents the time-varying gain function, represents the linear regression matrix of the i-th robot, represents the gradient vector of the potential energy function of the i-th robot, α>0 indicates a positive design gain parameter, q i represents the generalized joint angle vector of the i-th robot, represents the kinematic parameter estimation vector of the i-th robot, ξ i represents the joint velocity vector of the i-th robot.

8. The method for controlling a multi-robot distributed cooperative formation under a specified time according to claim 1, characterized in that: The formation master controller is expressed as: Among them, u i represents the total control input vector of the i-th robot, K p >0 indicates positive control gain, represents the generalized Jacobian matrix of the i-th robot after transformation by the linear regression matrix, q i represents the generalized joint angle vector of the i-th robot, a i represents the actual vector of kinematic parameters of the i-th robot, represents the gradient vector of the potential energy function of the i-th robot at time t, K D >0 indicates the design control gain, ξ i represents the joint velocity vector of the i-th robot, G i (q i ,w i ) represents the gravity vector of the i-th robot system, w i represents the constant system parameter vector of the known bounded compact set of the ith robot, represents the parameter estimate of the i-th robot The time derivative vector of , μ(t) represents the time-varying gain function, represents the kinematic regression matrix of the i-th robot, α>0 represents the design gain parameter, represents the kinematic parameter estimation vector of the i-th robot.

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