An adaptive terminal sliding mode model predictive control method, device and electronic equipment

Abstract

The application provides a kind of adaptive terminal sliding mode model predictive control method, device and electronic equipment, wherein the adaptive terminal sliding mode model predictive control method comprises: for robot formation, set adaptive terminal sliding mode controller;The robot formation includes leader robot and follower robot;The adaptive terminal sliding mode controller is used to reduce the influence of external interference received by the robot formation;For leader robot in the robot formation, configure trajectory tracking controller;The trajectory tracking controller is used to optimize the actual trajectory of the leader robot;For follower robot in the robot formation, configure formation pose controller.The dynamics stability control of robot formation system is realized by the application, and the stable tracking of reference trajectory by leader robot and the stable maintenance of formation shape by follower robot are also realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, and in particular to a self-adaptive terminal sliding mode model predictive control method and device and electronic equipment. BACKGROUND

[0002] In the actual application process of the multi-mobile robot formation system, the formation system is often disturbed by various external factors, especially in complex outdoor environments, communication interference, obstacle interference, friction interference, etc. can affect the formation control effect, and the typical interference is the ground and the wheel-ground sliding friction and rolling friction interference of the mobile robot. At the kinematics level of the multi-robot formation, the terminal sliding mode model predictive control is an advanced control method, which involves concepts and methods of predictive control, sliding mode control and optimization control in control theory.

[0003] The terminal sliding mode model predictive control is a control strategy based on system mathematical model prediction and using optimization algorithm to generate control signals. The terminal sliding mode model predictive control can combine the adaptive control method to realize the adaptive adjustment of the system model uncertainty and disturbance. At the kinematics level of the multi-robot formation, there are many control algorithms now, such as: model predictive control (MPC), graph theory, nonlinear control, LQ method, adaptive control, sliding mode and artificial potential field method. For the formation of the multi-robot formation system, the constraints of the system and the collision avoidance problem need to be considered. However, in the actual application scene, the motion process of the robot formation is often affected by external interference, resulting in the deviation of the motion trajectory and affecting the normal work of the robot formation.

[0004] For the problem of external interference in the motion process of the robot formation in the prior art, there is no effective solution at present. SUMMARY

[0005] The present application provides a self-adaptive terminal sliding mode model predictive control method, device and electronic equipment to solve the defect of external interference in the motion process of the robot formation in the prior art.

[0006] In a first aspect, the present application provides a self-adaptive terminal sliding mode model predictive control method, comprising:

[0007] For the robot formation, an adaptive terminal sliding mode controller is set; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the influence of external interference on the robot formation;

[0008] Configuring a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot;

[0009] A formation posture controller is configured for the follower robots in the robot formation; the formation posture controller is used to maintain the follower robots in the formation.

[0010] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, an adaptive terminal sliding mode controller is set for a robot formation, including:

[0011] Establishing a mathematical model of the robots in the robot formation based on the dynamic equations of the robot formation;

[0012] Designing a terminal sliding surface of the dynamic control system of the robot formation and determining the control target of the robot formation;

[0013] Setting an adaptive controller for the robot formation and compensating for the uncertainty of the dynamic control system;

[0014] Designing an adaptive law, and generating an adaptive estimation representation of the robot formation subjected to external interference based on the adaptive law;

[0015] Substitute the adaptive estimation representation into the adaptive controller to obtain the adaptive terminal sliding mode controller.

[0016] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, after the adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller, the method includes:

[0017] For the adaptive terminal sliding mode controller of the robot formation, a Lyapunov function is defined;

[0018] The stability of the adaptive terminal sliding mode controller is verified based on the Lyapunov function, and the adaptive terminal sliding mode controller is fine-tuned according to the verification result.

[0019] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, a trajectory tracking controller is configured for the leader robot in the robot formation, comprising:

[0020] constructing a kinematic model of the robot formation, and determining a linear error representation of the leader robot based on the kinematic model;

[0021] discretizing a linear error representation of the leader robot;

[0022] Setting speed constraints for the movement speed of the leader robot and the speed increment within a unit sampling period;

[0023] determining a performance functional of a model predictive control of the leader robot based on the velocity constraint;

[0024] A performance functional of the leader robot model predictive control and a linear error representation of the leader robot are combined to determine an input increment sequence for trajectory control of the robot formation.

[0025] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, a kinematic model of the robot formation is constructed, and a linear error representation of the leader robot is determined based on the kinematic model, including:

[0026] determining a reference trajectory of the leader robot based on the kinematic model;

[0027] Based on a reference trajectory of the leader robot, a linear error representation of the leader robot is generated.

[0028] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, combining the performance functional of the leader robot model predictive control and the linear error representation of the leader robot, determining an input increment sequence for trajectory control of the robot formation, including:

[0029] determining a constrained optimization problem for the leader robot based on a performance functional and a linear error representation of the leader robot;

[0030] Transforming the constrained optimization problem of the leader robot into a quadratic programming problem;

[0031] The quadratic programming problem is solved to obtain an input increment sequence for trajectory control of the robot formation.

[0032] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, a formation pose controller is configured for the follower robot in the robot formation, comprising:

[0033] defining a system model of the robot formation, and determining a system augmented state of the follower robot based on the system model;

[0034] determining control system constraints and model predictive control performance functionals for the follower robot;

[0035] generating an optimization problem for trajectory control of the follower robot based on control system constraints and performance functionals of the follower robot;

[0036] The optimization problem is solved to determine the expected speed of each follower robot.

[0037] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, solving the optimization problem to determine the expected speed of each follower robot includes:

[0038] Converting the optimization problem into a quadratic programming problem;

[0039] Solving the quadratic programming problem to obtain an incremental control sequence of the follower robot;

[0040] A desired velocity of the follower robot is determined based on an incremental control sequence of the follower robot.

[0041] In a second aspect, the present invention further provides an adaptive terminal sliding mode model predictive control device, comprising:

[0042] a formation configuration module configured to configure an adaptive terminal sliding mode controller for a robot formation comprising a leader robot and a follower robot; the adaptive terminal sliding mode controller configured to reduce the impact of external interference on the robot formation;

[0043] A leadership configuration module, configured to configure a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is configured to optimize the actual trajectory of the leader robot;

[0044] A following configuration module is used to configure a formation posture controller for the follower robots in the robot formation; the formation posture controller is used to maintain the follower robots in the formation.

[0045] In a third aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the adaptive terminal sliding mode model predictive control method as described in the first aspect above is implemented.

[0046] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the adaptive terminal sliding mode model predictive control method as described in the first aspect above.

[0047] In a fifth aspect, the present invention further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the adaptive terminal sliding mode model predictive control method as described in the first aspect above.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The adaptive terminal sliding mode model predictive control method proposed in this paper employs real-time adaptive estimation of external uncertain disturbances at the dynamic level. This method, combined with terminal sliding mode control, results in the design of an adaptive terminal sliding mode controller. This reduces the impact of external uncertain disturbances on the robot formation system and achieves dynamic stability control of the system. Furthermore, at the kinematic level, a trajectory tracking controller and formation pose controller are designed for the leader robot and follower robots, respectively, in conjunction with model predictive control. This ensures that the leader robot stably tracks the reference trajectory and that the follower robots maintain stable formation shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0051] Figure 1 It is a flow chart of the adaptive terminal sliding mode model predictive control method provided by the present invention;

[0052] Figure 2 is a schematic diagram of an adaptive terminal sliding mode model predictive control method according to an embodiment of the present invention;

[0053] Figure 3 is an operation simulation path diagram of the adaptive terminal sliding mode model predictive control in an embodiment of the present invention;

[0054] Figure 4 is an operation simulation path diagram of the kinematic model predictive control in an embodiment of the present invention;

[0055] Figure 5 1 is a graph showing a position error change curve of a leader robot according to an embodiment of the present invention;

[0056] Figure 6 is a speed response curve diagram of the leader robot in an embodiment of the present invention;

[0057] Figure 7 is a position error curve diagram of follower robots No. 1 and No. 2 in an embodiment of the present invention;

[0058] Figure 8 is a position error curve diagram of follower robots No. 3 and No. 4 in an embodiment of the present invention;

[0059] Figure 9 is a position error curve diagram of follower robots No. 5 and No. 6 in an embodiment of the present invention;

[0060] Figure 10 is a position error curve diagram of follower robots No. 7 and No. 8 in an embodiment of the present invention;

[0061] Figure 11 is a formation distance error curve diagram in an embodiment of the present invention;

[0062] Figure 12 is a formation angle error curve diagram in an embodiment of the present invention;

[0063] Figure 13 It is a structural block diagram of the adaptive terminal sliding mode model predictive control device provided by the present invention;

[0064] Figure 14 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0065] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0066] The present invention provides an adaptive terminal sliding mode model predictive control method, Figure 1 is a flow chart of the adaptive terminal sliding mode model predictive control method provided by the present invention, such as Figure 1 As shown, the method includes the following steps:

[0067] Step S101: Setting an adaptive terminal sliding mode controller for a robot formation; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation;

[0068] Step S102, configuring a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot;

[0069] Step S103: configuring a formation pose controller for the follower robots in the robot formation; the formation pose controller is used to maintain the follower robots in the formation.

[0070] Compared with other control algorithms, model predictive control (MPC) has strong prediction ability, can optimize control input under the consideration of system constraint conditions, and is suitable for complex nonlinear and constrained systems. At the same time, MPC has flexibility and adaptability, can adapt to the dynamic characteristics and uncertainty of the system, and ensures the stability and safety of the system through robust design and constraint processing. Compared with other methods, MPC has lower requirements for system model, can adjust the control strategy in real time, has multivariable control ability, and comprehensively considers the relationship between multiple variables. These advantages make MPC a powerful control method, which is widely used in industrial and automation fields.

[0071] Therefore, in the method, firstly, the external uncertain disturbance is adaptively estimated in real time on the dynamics level, and an adaptive terminal sliding mode controller is designed combined with terminal sliding mode control, which reduces the influence of external uncertain disturbance on the robot formation system and realizes the dynamic stability control of the robot formation system. Then, on the kinematics level, combined with the model predictive control method, the trajectory tracking controller and the formation pose controller are designed for the leader robot and the follower robot respectively, realizing the stable tracking of the leader robot to the reference trajectory and the stable maintenance of the formation shape of the follower robot.

[0072] Figure 2 is a schematic diagram of the adaptive terminal sliding mode model predictive control method in the embodiment of the application, as Figure 2 shown, in some embodiments, step S101, for the robot formation, an adaptive terminal sliding mode controller is set, including: based on the dynamic equation of the robot formation, a mathematical model of the robot in the robot formation is established; a terminal sliding surface of the dynamic control system of the robot formation is designed, and the control target of the robot formation is determined; an adaptive controller is set for the robot formation, and the uncertainty of the dynamic control system is compensated; an adaptive law is designed, and an adaptive estimation representation of the robot formation subjected to external disturbance is generated based on the adaptive law; the adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller.

[0073] For example, first, based on the dynamic equation of the robot formation, a mathematical model of the robot is established:

[0074]

[0075] wherein, is a positive definite inertia symmetric matrix, which represents the inertia characteristics of the mobile robot system, and the element value thereof depends on the mass distribution of the robot in actual situation, represents the velocity, Represents the input transformation matrix, which plays a key role in converting the control input into the influence on the dynamics of the robot system. Its specific form depends on the structure and drive method of the robot. Represents the control input of the mobile robot system, usually expressed as the torque output of the motor. In actual robot control systems, the control input is calculated and adjusted based on the current state of the robot and the desired motion target. Denotes the external uncertain friction force on the mobile robot. Definition is the state vector of the dynamic model, represents the longitudinal displacement of the mobile robot along the velocity direction, represents the heading angle of the mobile robot. Substituting the state vector of the dynamic model into the above mathematical model, we can obtain:

[0076]

[0077] in, is the inertia matrix of the mobile robot, for Under the external friction interference force, for The control input is , ; m Indicates quality, J represents the moment of inertia, d represents the distance between the center of mass and the center of the wheel axle, W represents the wheelbase of the mobile robot, represents the left wheel torque, represents the right wheel torque, r Indicates the radius of the driving wheel. Definition The expected value of the state is ,but , define the tracking error of the mobile robot as ,but , .

[0078] Then, the terminal sliding surface of the mobile robot dynamic control system is designed to determine the control target and sliding surface:

[0079]

[0080] in, , , is a symmetric positive definite matrix, ,in and ; sRepresents a vector containing two elements, which can be regarded as a quantity that combines the tracking error change rate and the error information after a specific transformation. E It is obtained by a specific nonlinear transformation of the tracking error. n 1. n 2 represents a symmetric matrix The diagonal elements of The elements in the transform function are used to control the tracking error. The power of , thus affecting the weighting degree of the error and the nonlinear characteristics.

[0081] Then, an adaptive controller is designed to implement sliding mode control and compensate for the uncertainty of the robot formation system. The specific formula is as follows:

[0082]

[0083] in, u represents the control input, 、 They are all symmetric positive definite matrices, used to provide related positive design parameters; 、 It means that they play the role of providing relevant positive design parameters in the control algorithm. The elements in these matrices are used to adjust the influence of the control input on the system state, thereby affecting the performance of the control system, such as response speed, stability and robustness. 、 It is related to the linear speed control of the robot. When the parameter is large, the system's sensitivity to linear speed tracking error increases, which will prompt the robot to adjust the linear speed faster.

[0084] In order to solve the problem of external uncertain friction disturbance, an adaptive law is designed to estimate and compensate for the uncertainty of the system. The adaptive estimation of the external uncertain friction disturbance is expressed as:

[0085]

[0086] in, , They are the wheel-ground sliding interference estimation coefficient and the wheel-ground rolling interference estimation coefficient respectively. The larger the estimation coefficient, the shorter the convergence time of the external interference force estimation. However, an excessively large estimation coefficient will lead to an increase in the error between the estimated value and the actual value. Therefore, it is necessary to select an appropriate estimation coefficient value based on the actual movement conditions of the mobile robot.

[0087] Finally, substituting the adaptive disturbance estimate into the adaptive controller, the adaptive terminal sliding mode controller is obtained as:

[0088]

[0089] Furthermore, after the adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller, the method includes: defining a Lyapunov function for the adaptive terminal sliding mode controller of the robot formation; verifying the stability of the adaptive terminal sliding mode controller based on the Lyapunov function, and fine-tuning the adaptive terminal sliding mode controller according to the verification results.

[0090] For example, the stability of the adaptive terminal sliding mode controller is proved, and the Lyapunov function is defined as:

[0091]

[0092] in, V represents the Lyapunov function, which is a function that comprehensively considers multiple factors such as system state deviation, robot inertia, and external friction interference. Substituting the adaptive terminal sliding mode controller into the above formula, we can obtain:

[0093]

[0094] From the above formula, according to Lyapunov stability theory and Russell invariance principle, it can be deduced that the control system is asymptotically stable.

[0095] In some embodiments, step S102, at the kinematic level, configures a trajectory tracking controller for the leader robot in the robot formation, including: constructing a kinematic model of the robot formation, and determining the linear error representation of the leader robot based on the kinematic model; discretizing the linear error representation of the leader robot; setting speed constraints for the movement speed of the leader robot and the speed increment within a unit sampling period; based on the speed constraints, determining the performance functional of the leader robot model predictive control; combining the performance functional of the leader robot model predictive control and the linear error representation of the leader robot, determining the input increment sequence for trajectory control of the robot formation.

[0096] Specifically, a kinematic model of the robot formation is constructed, and the linear error representation of the leader robot is determined based on the kinematic model, including: determining the reference trajectory of the leader robot based on the kinematic model; and generating the linear error representation of the leader robot based on the reference trajectory of the leader robot.

[0097] Combining the performance functional of the leader robot model predictive control and the linear error representation of the leader robot, the input incremental sequence for trajectory control of the robot formation is determined, including: determining the constrained optimization problem for the leader robot based on the performance functional and linear error representation of the leader robot; formally transforming the constrained optimization problem of the leader robot to generate a quadratic programming problem; and solving the quadratic programming problem to obtain the input incremental sequence for trajectory control of the robot formation.

[0098] For example, first, a robot kinematic model is established. The specific formula is as follows:

[0099]

[0100] in, x Represents the horizontal coordinate of the robot in the plane coordinate system, y represents the horizontal coordinate of the robot in the plane coordinate system, θ represents the heading angle of the mobile robot, v represents the linear velocity of the mobile robot, Represents the angular velocity of the mobile robot. From the above formula, the reference trajectory state differential equation of the leader robot can be obtained as:

[0101]

[0102] in, is a state vector, is the state transition function, represents the linear velocity of the leader robot, represents the horizontal coordinate of the leader robot in the plane coordinate system, Represents the ordinate of the leader robot in the plane coordinate system, represents the heading angle of the leader robot in the plane coordinate system, represents the linear velocity of the leader robot in the plane coordinate system, represents the angular velocity of the leader robot in the plane coordinate system. Based on the above state differential equation, the linear error differential equation can be obtained as:

[0103]

[0104] in, represents the state error vector in the robot formation system, A represents the system matrix, B represents the input matrix, t Indicates time, Represents the velocity error vector. Since MPC is a discrete control, it is necessary to discretize the robot formation system and let the sampling time period of MPC be , then after discretizing the above linear error differential equation, we can get:

[0105]

[0106]

[0107]

[0108] At any sampling time k , and The augmented matrix of the system state is defined as:

[0109]

[0110] Substituting the augmented matrix into the above formula, the augmented state equation of the robot formation system can be obtained as follows:

[0111]

[0112] in, , , , According to the above analysis and derivation, at any sampling time k When , the discrete state output of the robot formation system can be expressed as:

[0113]

[0114] in, represents the discrete state output of the robot formation system at any sampling time k, is a coefficient matrix used to weight the input changes. It is also the coefficient matrix, which is used in the output equation to weight the input changes.

[0115] Then, set constraints on the leader robot's movement speed and the speed increment within a unit sampling period to prevent the output power and output torque of the drive motor from being too large, which may cause the motor to burn out. The speed constraint can be expressed as:

[0116]

[0117] in, and are the maximum and minimum values ​​of the mobile robot's control speed, and They are the maximum and minimum values ​​of the speed increment controlled within a unit sampling period, respectively. The speed constraint value is related to the performance parameters of the drive motor.

[0118] When designing the MPC performance functional, the trajectory tracking error of the leader robot and the control input of the system must be considered. The system control input is the velocity increment within the unit sampling period. Therefore, at any sampling time k , the leader robot MPC performance functional can be designed as:

[0119]

[0120] in, J represents the MPC (Model Predictive Control) performance functional of the leader robot. It is a comprehensive indicator used to measure the performance of the system at any sampling time k. Indicates the velocity increment of the leader robot in a unit sampling period. In model predictive control, the control input is usually related to the dynamic changes of the system. Reference motion trajectory for the leader robot, is the predicted trajectory of the output, 、 are the system state error weight matrix and system control input weight matrix of the leader robot respectively.

[0121] Through the above analysis of the system constraints and performance functionals of the leader robot's trajectory tracking error state equation, it can be synthesized into the following constrained optimization problem:

[0122]

[0123] in, , N c Represents the prediction time domain. To facilitate the solution and reduce the computational difficulty, the solution to the discrete state output of the robot formation system can be transformed into the solution to the following quadratic programming problem:

[0124]

[0125] in, , There are many algorithms for solving quadratic programming problems, such as Lagrange method, interior point method, and effective set method. The present invention omits the solution process of the quadratic programming problem and does not describe it in detail. After solving, it can be concluded that at any sampling time k The incremental sequence of control inputs for the robot formation system generated by MPC is:

[0126]

[0127] The first control increment in the control input increment sequence of the robot formation system is used as the actual control input increment of the system at the next moment, and the actual control input of the system can be obtained. At the sampling moment, the actual control input of the system is:

[0128]

[0129] By repeating the above optimization and solution steps, the actual trajectory of the leader robot can be optimally converged to the reference trajectory.

[0130] In some embodiments, step S103 configures a formation pose controller for the follower robots in the robot formation, including: defining a system model of the robot formation, and determining the system augmented state of the follower robot based on the system model; determining the control system constraints of the follower robot and the performance functional of the model predictive control; generating an optimization problem for trajectory control of the follower robot based on the control system constraints and performance functional of the follower robot; and solving the optimization problem to determine the expected speed of each follower robot.

[0131] Specifically, the optimization problem is solved to determine the expected speed of each follower robot, including: converting the optimization problem into a quadratic programming problem; solving the quadratic programming problem to obtain an incremental control sequence of the follower robot; and determining the expected speed of the follower robot based on the incremental control sequence of the follower robot.

[0132] For example, let is the multi-mobile robot formation system vector, where 、 are the actual distance and actual angle of the follower robot formation, is the heading angle of the leader robot, is the heading angle of the follower robot, and , then the multi-mobile robot formation system model can be expressed as:

[0133]

[0134] in, , represents the angular velocity of the leader robot, represents the angular velocity of the follower robot, represents the linear velocity of the follower robot, represents the linear velocity of the leader robot. The above formula is Taylor expanded, linearized, discretized, and the system state quantity is augmented. The system augmented state equation of the follower robot can be expressed as:

[0135]

[0136] in, i Indicates the follower robot number, , , The constraints of the follower robot formation control system must take into account the robot's motion speed constraint, speed increment constraint, and system output state constraint. The follower robot formation control system constraints can be expressed as:

[0137]

[0138] in, , They represent the minimum and maximum values ​​of the follower robot's output state respectively.

[0139] According to the design of the leader robot's MPC kinematic controller, the follower robot's MPC performance functional mainly considers the error of the follower robot's actual position to the expected formation posture and the system control input. Therefore, the follower robot's MPC performance functional can be obtained as follows:

[0140]

[0141] in, is the desired formation pose of the follower robot, 、 are the system state error weight matrix and system control input weight matrix of the follower robot, respectively. Based on the system constraints and performance functionals of the follower robot formation state equation, the follower robot formation control prediction optimization problem can be obtained in the same way. For the convenience of solution, it is converted into a quadratic programming problem as shown below:

[0142]

[0143] After solving the above equation, the control sequence of the follower robot can be obtained. According to the MPC control principle, the first control increment in the system control input increment sequence is used as the actual control input increment of the system at the next moment. The actual control input of the robot formation system can be obtained as follows:

[0144]

[0145] By repeating the above optimization and solving steps, the expected speed of each follower robot can be obtained, so that the multi-mobile robot formation system can maintain a stable formation.

[0146] In order to verify the effectiveness and superiority of the adaptive terminal sliding mode model predictive control method proposed in this invention in solving the stability problem of multi-machine system formation control in interference environment, this embodiment conducts a multi-machine formation control simulation comparison experiment, uses MATLAB R2021a software to write simulation code, and conducts the experiment on a PC based on WINDOWS10, R7-5800H. Figure 3 andFigure 4 As shown, Figure 3 is an operation simulation path diagram of the adaptive terminal sliding mode model predictive control in an embodiment of the present invention, Figure 4 It is an operation simulation path diagram of the kinematic model predictive control in an embodiment of the present invention.

[0147] For comparison purposes, this simulation experiment sets the robot's predetermined speed to 0.4 m / s, its maximum speed to 2 m / s, and its initial heading angle to 45 degrees. Since this method incorporates dynamic control, dynamic-related parameters must be added during the experiment, as shown below: , , , , According to the simulation experiment environment of this embodiment, the relevant design parameters in the kinematic controller can be defined as: , , , , , , ; The relevant design parameters in the dynamic controller can be defined as: , , , , , Since the simulation experiment needs to be carried out in an interference environment, it can be assumed that the external interference is the sum of a constant interference and a sinusoidal interference, which can be specifically expressed as:

[0148]

[0149] In order to evaluate the performance of the formation stability control method in the multi-machine system formation motion process, the mean square error of the position error of each robot during the motion process is taken as the average position error, the mean square error of the velocity error is taken as the average velocity error, the time taken from the start of obstacle avoidance to the end of obstacle avoidance to restore the stable formation is taken as the convergence time, and the mean square error of the system's overall formation error is taken as the average formation error. The smaller the average position error, the smaller the average velocity error, the shorter the convergence time, and the smaller the average formation error, the better the stability control effect of the formation control method, the stronger the robustness, and the better the anti-interference ability. Figure 5 and Figure 6 As shown, Figure 5 is a graph showing the position error variation of the leader robot in an embodiment of the present invention. Figure 6 4 is a speed response curve diagram of the leader robot in an embodiment of the present invention.

[0150] In this simulation experiment, the adaptive terminal sliding mode model predictive control method proposed in this invention artificially adds external interference to the multi-aircraft formation system at the 200th control cycle. In this case, the adaptive terminal sliding mode model predictive control (ATSMMPC) and the single kinematic model predictive control (MPC) are simulated and compared. The single kinematic model predictive control only has kinematic stability control but no dynamic stability control. Figures 7-12 As shown, Figure 7 is a position error curve diagram of follower robots No. 1 and No. 2 in the embodiment of the present invention, Figure 8 is a position error curve diagram of follower robots No. 3 and No. 4 in the embodiment of the present invention, Figure 9 is a position error curve diagram of follower robots No. 5 and No. 6 in the embodiment of the present invention, Figure 10 is a position error curve diagram of follower robots No. 7 and No. 8 in an embodiment of the present invention; Figure 11 is a formation distance error curve diagram in an embodiment of the present invention, Figure 12 This is a curve diagram of the formation angle error in the embodiment of the present invention. Through the above comparative experiments, the effectiveness and superiority of the adaptive terminal sliding mode model predictive control method can be verified.

[0151] In summary, the present invention proposes an adaptive terminal sliding mode control method, while also incorporating adaptive real-time estimation of external uncertain friction interference at the dynamic level. The designed dynamic controller possesses rapid stability and strong robustness. Furthermore, at the kinematic level, the present invention combines the leader-follower method with the MPC method to design kinematic controllers for the leader and follower, respectively, achieving stable trajectory tracking for the leader robot and stable formation maintenance for the follower robots. Furthermore, the present invention can be widely applied in the collaborative control of multiple mobile robots, demonstrating significant effectiveness and superiority in controlling the stability of multi-robot formations in fault and interference environments.

[0152] The present invention also provides an adaptive terminal sliding mode model predictive control device. The adaptive terminal sliding mode model predictive control device provided by the present invention is described below. The adaptive terminal sliding mode model predictive control device described below and the adaptive terminal sliding mode model predictive control method described above can be referenced to each other. Figure 13 This is a structural block diagram of the adaptive terminal sliding mode model predictive control device provided by the present invention, such as Figure 13 As shown, the device includes:

[0153] The formation configuration module 1301 is used to set an adaptive terminal sliding mode controller for the robot formation; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation;

[0154] A leader configuration module 1302 is configured to configure a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is configured to optimize the actual trajectory of the leader robot;

[0155] The following configuration module 1303 is used to configure a formation pose controller for the follower robots in the robot formation; the formation pose controller is used to maintain the follower robots in the formation.

[0156] When using this device, first, at the dynamic level, the formation configuration module 1301 performs adaptive real-time estimation of external uncertain interference and, combined with terminal sliding mode control, designs an adaptive terminal sliding mode controller. This reduces the impact of external uncertain interference on the robot formation system and achieves dynamic stability control of the robot formation system. Then, at the kinematic level, the leader configuration module 1302 and follower configuration module 1303, combined with model predictive control, design a trajectory tracking controller and formation pose controller for the leader robot and follower robots, respectively. This ensures that the leader robot stably tracks the reference trajectory and that the follower robots maintain stable formation shape.

[0157] Figure 14 An example of a physical structure diagram of an electronic device is shown below. Figure 14 As shown, the electronic device may include: a processor 1401, a communication interface 1402, a memory 1403, and a communication bus 1404, wherein the processor 1401, the communication interface 1402, and the memory 1403 communicate with each other via the communication bus 1404. The processor 1401 may call the logic instructions in the memory 1403 to execute the adaptive terminal sliding mode model predictive control method, which includes:

[0158] For the robot formation, an adaptive terminal sliding mode controller is set; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation;

[0159] A trajectory tracking controller is configured for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot;

[0160] A formation pose controller is configured for the follower robots in the robot formation; the formation pose controller is used to maintain the follower robots in the formation.

[0161] Furthermore, the logic instructions in the aforementioned memory 1403 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product, stored in a storage medium, includes instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0162] On the other hand, the present invention further provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform the adaptive terminal sliding mode model predictive control method provided by the above methods, which includes:

[0163] For the robot formation, an adaptive terminal sliding mode controller is set; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation;

[0164] A trajectory tracking controller is configured for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot;

[0165] A formation pose controller is configured for the follower robots in the robot formation; the formation pose controller is used to maintain the follower robots in the formation.

[0166] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the adaptive terminal sliding mode model predictive control method provided by the above methods is implemented, and the method includes:

[0167] For the robot formation, an adaptive terminal sliding mode controller is set; the robot formation includes a leader robot and a follower robot; the adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation;

[0168] A trajectory tracking controller is configured for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot;

[0169] A formation pose controller is configured for the follower robots in the robot formation; the formation pose controller is used to maintain the follower robots in the formation.

[0170] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0171] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An adaptive terminal sliding mode model predictive control method, characterized in that: include: For a robot formation, an adaptive terminal sliding mode controller is set; the robot formation includes a leader robot and a follower robot; The adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation; Configuring a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot; configuring a formation pose controller for the follower robots in the robot formation; The formation posture controller is used to maintain the follower robots in formation; For robot formation, an adaptive terminal sliding mode controller is set up, including: Establishing a mathematical model of the robots in the robot formation based on the dynamic equations of the robot formation; Design the terminal sliding surface of the dynamic control system of the robot formation and determine the control target of the robot formation: in, , , is a symmetric positive definite matrix, ,in and ; s Represents a vector containing two elements, which can be regarded as a quantity that combines the tracking error change rate and the error information after a specific transformation; E It is obtained by a specific nonlinear transformation of the tracking error. n 1. n 2 represents a symmetric matrix The diagonal elements of The elements in the transform function are used to control the tracking error. The power of , thus affecting the weighting degree of the error and the nonlinear characteristics; Setting an adaptive controller for the robot formation and compensating for the uncertainty of the dynamic control system; Design an adaptive law, and generate an adaptive estimation representation of the robot formation subjected to external interference based on the adaptive law: in, , They are the wheel-ground sliding interference estimation coefficient and the wheel-ground rolling interference estimation coefficient. The larger the estimation coefficient, the shorter the convergence time of the external disturbance force estimation. However, an excessively large estimation coefficient will increase the error between the estimated value and the actual value. Therefore, it is necessary to select an appropriate estimation coefficient value based on the actual motion conditions of the mobile robot. Substituting the adaptive estimation representation into the adaptive controller, the adaptive terminal sliding mode controller is obtained: Substituting the adaptive estimation representation into the adaptive controller to obtain the adaptive terminal sliding mode controller includes: For the adaptive terminal sliding mode controller of the robot formation, a Lyapunov function is defined; The stability of the adaptive terminal sliding mode controller is verified based on the Lyapunov function, and the adaptive terminal sliding mode controller is fine-tuned according to the verification result.

2. The adaptive terminal sliding mode model predictive control method according to claim 1, characterized in that: Configuring a trajectory tracking controller for the leader robot in the robot formation, including: constructing a kinematic model of the robot formation, and determining a linear error representation of the leader robot based on the kinematic model; discretizing a linear error representation of the leader robot; Setting speed constraints for the movement speed of the leader robot and the speed increment within a unit sampling period; determining a performance functional of a model predictive control of the leader robot based on the velocity constraint; A performance functional of the leader robot model predictive control and a linear error representation of the leader robot are combined to determine an input increment sequence for trajectory control of the robot formation.

3. The adaptive terminal sliding mode model predictive control method according to claim 2, characterized in that: Constructing a kinematic model of the robot formation and determining a linear error representation of the leader robot based on the kinematic model, comprising: determining a reference trajectory of the leader robot based on the kinematic model; Based on a reference trajectory of the leader robot, a linear error representation of the leader robot is generated.

4. The adaptive terminal sliding mode model predictive control method according to claim 2, characterized in that: Determining a sequence of input increments for trajectory control of the robot formation by combining a performance functional of the leader robot model predictive control and a linear error representation of the leader robot includes: determining a constrained optimization problem for the leader robot based on a performance functional and a linear error representation of the leader robot; Transforming the constrained optimization problem of the leader robot into a quadratic programming problem; The quadratic programming problem is solved to obtain an input increment sequence for trajectory control of the robot formation.

5. The adaptive terminal sliding mode model predictive control method according to claim 1, characterized in that: Configuring a formation pose controller for a follower robot in the robot formation includes: defining a system model of the robot formation, and determining a system augmented state of the follower robot based on the system model; determining control system constraints and model predictive control performance functionals for the follower robot; generating an optimization problem for trajectory control of the follower robot based on control system constraints and performance functionals of the follower robot; The optimization problem is solved to determine the expected speed of each follower robot.

6. The adaptive terminal sliding mode model predictive control method according to claim 5, characterized in that: Solving the optimization problem to determine the expected speed of each follower robot includes: Converting the optimization problem into a quadratic programming problem; Solving the quadratic programming problem to obtain an incremental control sequence of the follower robot; A desired velocity of the follower robot is determined based on an incremental control sequence of the follower robot.

7. An adaptive terminal sliding mode model predictive control device, used to implement the adaptive terminal sliding mode model predictive control method according to any one of claims 1 to 6, characterized in that: include: a formation configuration module for setting an adaptive terminal sliding mode controller for a robot formation; the robot formation includes a leader robot and a follower robot; The adaptive terminal sliding mode controller is used to reduce the impact of external interference on the robot formation; A leadership configuration module, configured to configure a trajectory tracking controller for the leader robot in the robot formation; the trajectory tracking controller is configured to optimize the actual trajectory of the leader robot; A following configuration module is used to configure a formation posture controller for the follower robots in the robot formation; the formation posture controller is used to maintain the follower robots in the formation.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the adaptive terminal sliding mode model predictive control method according to any one of claims 1 to 6 is implemented.

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