A finite-time consensus control method for multi-robot system with output constraints

Abstract

This invention provides a finite-time consistency control method for multi-manipulator systems with output constraints. Addressing the cooperative control problem of multi-manipulator systems with model uncertainties, external disturbances, and output constraints, this invention proposes a finite-time convergent adaptive control strategy based on a backstepping design framework, combined with an event-triggered mechanism and a fuzzy logic system. First, a dynamic model of the follower manipulator is established, and the synchronization state error is defined. Second, a cascaded Lyapunov function is designed to handle the output constraints, and the fuzzy logic system is used to approximate the model uncertainties. Third, an event-triggered mechanism is constructed to save communication resources, and control and adaptive laws are designed based on finite-time convergence theory. Simulation results show that the proposed method enables multiple manipulators to achieve high-precision trajectory tracking consistency within a finite time, with the tracking error strictly controlled within a minimal range. The control voltage always meets the output constraints, improving system safety and engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of multi-manipulator cooperative control, and specifically relates to a finite-time consistency control method for multi-manipulator systems with output constraints. Background Technology

[0002] With the development of robotic arms in the industrial field, tasks are becoming increasingly complex, and single robotic arms cannot perform well. Multi-robotic arm collaboration is the future trend. Multi-robotic arm systems, due to their advantages such as flexible structure, large operating space, and strong collaborative capabilities, have been widely used in aerospace assembly, material handling, flexible manufacturing, and service robots. In practical applications, to complete complex collaborative tasks, multiple robotic arms need to achieve the desired coordination and consistency within a limited time. However, due to the inherent coupling, nonlinearity, uncertainty, and the influence of external disturbances within the system, achieving stable and rapid collaborative control presents significant challenges.

[0003] Existing multi-robot consensus control methods primarily employ asymptotic stability-based control strategies. While these strategies can guarantee eventual convergence to the desired consensus state, the convergence speed is slow, failing to meet the finite-time convergence requirements of practical engineering. Furthermore, during task execution, the end effector outputs of the robot arm typically exhibit physical constraints such as position, velocity, and force. Ignoring these constraints can lead to performance degradation and even safety hazards. Therefore, designing a control method that achieves consensus in a multi-robot system within a finite time while considering output constraints has become a crucial problem urgently needing to be solved in the field of multi-robot cooperative control. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the purpose of the present invention is to provide a finite-time consistency control method for a multi-manipulator system with output constraints to solve the problems mentioned in the background art.

[0005] This invention provides a finite-time consistency control method for a multi-manipulator system with output constraints, comprising the following steps:

[0006] S1: Consider including a leader and A multi-arm robotic system with multiple followers, where the robotic arms are connected via a directed communication topology network. Each has... A robotic arm with degrees of freedom can only obtain state information from either the leader or the neighbors. The leader is represented as 0, and the followers as... For followers Establish a dynamic model;

[0007] S2: Define the follower based on backstepping iteration technique. Synchronization state error and Considering system output constraints, design a cascaded Lyapunov function. and Design virtual control law And use fuzzy logic system to approximate the model's uncertainties;

[0008] S3: Design the event triggering mechanism for the robotic arm and define the overall Lyapunov function. Based on the fast finite-time convergence theory, design the final control law. Intermediate control law And adaptive law ;

[0009] S4: Simulation analysis shows that if all estimation errors and state errors of the system can converge to the zero neighborhood in a finite time and no Zeno phenomenon occurs, then it can be concluded that the finite-time consistency control method for the multi-manipulator system with output constraints can achieve the actual finite-time consistency of the system.

[0010] This invention provides a finite-time consistency control method for a multi-robotic arm system with output constraints, which has the following advantages: the designed controller enables the follower to track the leader's expected trajectory well and ensures that the multi-robotic arm system achieves consistency within a finite time. In addition, the method proposed in this invention fully considers the output constraints of the robotic arm system, effectively avoids the problem of output exceeding limits, and enhances the safety and engineering applicability of the method. Attached Figure Description

[0011] Figure 1 It is the experimental topology network and motion scenario of a multi-robotic arm system;

[0012] Figure 2 This is a schematic diagram of the follower robotic arm;

[0013] Figure 3 It consists of the position response and tracking error of the two joints of the two followers;

[0014] Figure 4 These are the control variables for the two joints of follower 1 and the event triggering time interval;

[0015] Figure 5 These are the control variables for the two joints of Follower 2 and the event triggering time interval;

[0016] Figure 6 The results are experimental comparisons of tracking errors obtained when controlling two followers using a finite-time controller (FTC), a non-event-triggered controller (NETC), and a non-finite-time controller (NFTC), respectively.

[0017] Figure 7 The statistics are the number of triggers and IAE values ​​when controlling two followers using a finite-time controller (FTC), a non-event-triggered controller (NETC), and a non-finite-time controller (NFTC), respectively.

[0018] Figure 8 These are experimental results on the trajectory position tracking of the end effector and the performance of the corresponding joints of the two followers;

[0019] Figure 9 It is the tracking error between the two followers;

[0020] Figure 10 These are the control variables and event triggering time intervals for the three joints of Follower 1 with output constraints. Detailed Implementation

[0021] The embodiments of the present invention will be described in detail below. The embodiments described below are implemented based on the technical solution of the present invention, and detailed implementation methods and specific operation processes are given. However, the protection scope of the present invention is not limited to the embodiments described below.

[0022] A finite-time consistency control method for a multi-manipulator system with output constraints includes the following steps:

[0023] S1: Consider including a leader and A multi-arm robotic system with multiple followers, where the robotic arms are connected via a directed communication topology network, such as... Figure 1 As shown, N = 2 in this example. A schematic diagram of the follower robotic arm is shown below. Figure 2 As shown. The base 11 includes a panel 12; a shoulder 13 of the robotic arm is mounted on the top of the base 11; the shoulder 13 is connected to an elbow 16, and the elbow 16 is connected to a wrist 15; the robotic arm sends and receives data via a circuit board 14. Each has... A robotic arm with degrees of freedom can only obtain state information from either the leader or the neighbors. The leader is represented as 0, and the followers as... For followers Establish a dynamic model;

[0024] S2: Define the follower based on backstepping iteration technique. Synchronization state error and Considering system output constraints, design a cascaded Lyapunov function. and Design virtual control law And use fuzzy logic system to approximate the model's uncertainties;

[0025] S3: Design the event triggering mechanism for the robotic arm and define the overall Lyapunov function. Based on the fast finite-time convergence theory, design the final control law. Intermediate control law And adaptive law ;

[0026] S4: Simulation analysis.

[0027] In step S1, the follower The dynamic model is as follows

[0028] in, It is the position information of the robotic arm joints. and These represent the joint velocity and acceleration information of the robotic arm, respectively. , and Let these represent the inertia matrix, Coriolis matrix, and gravity term, respectively. This represents the term of joint friction. This indicates the control torque.

[0029] In step S2, the follower The synchronization state error is defined as:

[0030] in, For joint tracking error, For relative speed error, For virtual control variables, For followers The information transmission coefficient between leaders For followers Neighborhood set, For the leader's output, For the neighbors The output, For followers and neighbors The information transmission coefficient between them.

[0031] In step S2, the cascaded Lyapunov function design considering output constraints is as follows:

[0032] Among them, constraint parameters , Through the Find the derivative and design the virtual control law. as follows:

[0033] Among them, the design parameters satisfy , , .

[0034] In step S2, the designed cascaded Lyapunov function is... Taking the derivative yields a function containing the model's uncertainty terms, as follows:

[0035] Using a fuzzy logic system to approximate the uncertainties in the model, as shown below:

[0036] in, For the number of neurons, Represents the input vector. Represents a known basis function vector. Represents an unknown ideal weight vector. It represents a finite approximation error.

[0037] In step S3, to conserve system communication resources, the event triggering mechanism is designed as follows:

[0038] in, Intermediate control rate, The final control law under the event-triggered mechanism. To account for measurement error, the design parameters must meet the following requirements. , , ; Indicates the time when a certain event is triggered. , This is the initial time.

[0039] The final control law under the event-triggered mechanism can be derived. as follows:

[0040] in, and These are design parameters with time-varying characteristics. In S3, the weight estimation error of the fuzzy logic system is considered. Design the overall Lyapunov function as follows:

[0041] in, , It is a constant.

[0042] intermediate control law of design and adaptive rate The design is as follows:

[0043] Among them, the design parameters satisfy , , , .

[0044] Furthermore, in step S4, a multi-arm robotic system with one leader and two followers is considered, and the system dynamics equations are given as follows:

[0045] in, and The masses of connecting rod 1 and connecting rod 2 are respectively. and These are the lengths of the two connecting rods, and These are the moments of inertia of the two connecting rods, and These are the positions of the centers of mass of the two connecting rods, such as... Figure 2 As shown. The leader's output trajectory is .

[0046] from Figures 3 to 10 It can be seen that all signals in a closed-loop system are bounded. From Figure 3 As can be seen, by using the designed controller, the two joint angles of the robotic arm can track the desired output angle very well, and the tracking error is controlled within a certain range. Within this range, the convergence time is close to . Figure 4 and Figure 5 These are the control variables and event triggering time intervals for the two joints of follower 1 and follower 2, respectively. It can be seen that due to harmonic noise in the servo motor, there is some jitter between the two control voltages, and the maximum event triggering time interval is... The minimum time interval is . Figure 6 The results are a comparison of the tracking errors obtained when controlling two followers using a finite-time controller (FTC), a non-event-triggered controller (NETC), and a non-finite-time controller (NFTC). It can be seen that the system's state error converges rapidly to the zero neighborhood. Figure 7 These are the corresponding number of triggers and IAE values. The designed finite-time controller (FTC) has significantly fewer event triggers than the non-event-triggered controller (NETC) and the non-finite-time controller (NFTC), and has the best tracking capabilities. Figure 8 These are experimental results regarding the trajectory and position tracking of the end effector and the performance of the corresponding joints of the two followers. Figure 9 This corresponds to the tracking error. It can be seen that the tracking error is controlled within... Within, the convergence time is approximately . Figure 10 These are the control variables and event triggering time intervals of the three joints with output constraints for follower 1. The control voltages of both followers are controlled within... Within this range, the maximum time interval for event triggering is [missing information]. The minimum time interval is Therefore, no Zeno phenomenon occurs. Finally, compared with the traditional time-triggered control method, the number of event triggers for both methods was statistically analyzed. In comparison, the method provided by this invention saves more than 50% of communication resources.

[0047] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A finite-time consistency control method for a multi-manipulator system with output constraints, characterized in that, Includes the following steps: S1: Consider including a leader and A multi-arm robotic system with multiple followers, where the robotic arms are connected via a directed communication topology network. Each has... A robotic arm with degrees of freedom can only obtain state information from either the leader or the neighbors. The leader is represented as 0, and the followers as... For followers Establish a dynamic model; S2: Define the follower based on backstepping iteration technique. Synchronization state error and Considering system output constraints, design a cascaded Lyapunov function. and Design virtual control law And use fuzzy logic system to approximate the model's uncertainties; S3: Design the event triggering mechanism for the robotic arm and define the overall Lyapunov function. Based on the fast finite-time convergence theory, design the final control law. Intermediate control law And adaptive law ; S4: Simulation analysis shows that if all estimation errors and state errors of the system can converge to the zero neighborhood in a finite time and no Zeno phenomenon occurs, then it can be concluded that the finite-time consistency control method for the multi-manipulator system with output constraints can achieve the actual finite-time consistency of the system.

2. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S1, the follower The dynamic model is as follows: in, This indicates the joint position information of the robotic arm. and These represent the joint velocity and acceleration information of the robotic arm, respectively. , and Let these represent the inertia matrix, Coriolis matrix, and gravity term, respectively. This represents the term of joint friction. This indicates the control torque.

3. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S2, the follower The synchronization state error is defined as: in, For joint tracking error, For relative speed error, For virtual control variables, For followers The information transmission coefficient between leaders For followers Neighborhood set, For the leader's output, For the neighbors The output, For followers and neighbors The information transmission coefficient between them.

4. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S2, the cascaded Lyapunov function design considering output constraints is as follows: Among them, constraint parameters Through the Find the derivative and design the virtual control law. as follows: Among them, the design parameters satisfy , , .

5. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S2, the designed cascaded Lyapunov function is... Taking the derivative yields a function containing the model's uncertainty terms, as follows: Using a fuzzy logic system to approximate the uncertainties in the model, as shown below: in, For the number of neurons, Represents the input vector. Represents a known basis function vector. Represents an unknown ideal weight vector. It represents a finite approximation error.

6. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S3, to conserve system communication resources, the event triggering mechanism is designed as follows: in, Intermediate control rate, The final control law under the event-triggered mechanism. To account for measurement error, the design parameters must meet the following requirements. , , ; Indicates the time when a certain event is triggered. , This is the initial time. The final control law under the event-triggered mechanism can be derived. as follows: in, and These are design parameters that have time-varying characteristics.

7. The finite-time consistency control method for a multi-manipulator system with output constraints according to claim 1, characterized in that, In step S3, the weight estimation error of the fuzzy logic system is considered. Design the overall Lyapunov function as follows: in, , It is a constant. intermediate control law of design and adaptive rate The design is as follows: Among them, the design parameters satisfy , , , .

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