Adaptive terminal sliding mode model prediction control method and device and electronic equipment

Abstract

The invention provides a self-adaptive terminal sliding mode model prediction control method and device and electronic equipment, and the method comprises the steps: setting a self-adaptive terminal sliding mode controller for a robot formation; the robot formation comprises a leader robot and a follower robot; the adaptive terminal sliding mode controller is used for reducing the influence 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 for optimizing the actual trajectory of the leader robot; and configuring a formation pose controller for the follower robots in the robot formation. According to the invention, the dynamic stability control of the robot formation system is realized, and the stable tracking of the leader robot to the reference trajectory and the stable maintenance of the follower robot to the formation are also realized.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to an adaptive terminal sliding mode model predictive control method, device and electronic equipment. Background Art

[0002] In the actual application of multi-mobile robot formation systems, the formation system is often interfered by various external factors, especially in complex field environments. Communication interference, obstacle interference, friction interference, etc. will affect the formation control effect. The more typical interference is the sliding friction and rolling friction interference between the ground and the mobile robot. At the level of multi-robot formation motion dynamics, terminal sliding mode model predictive control is an advanced control method, involving concepts and methods such as predictive control, sliding mode control and optimization control in control theory.

[0003] Terminal sliding mode model predictive control is a control strategy that uses an optimization algorithm to generate control signals based on a system mathematical model. Terminal sliding mode model predictive control can be combined with adaptive control methods to achieve adaptive adjustment of system model uncertainty and disturbances. At the kinematic level of multi-robot formations, there are many control algorithms, 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 a multi-robot formation system, it is necessary to consider two issues: system constraints and collision avoidance. However, in actual application scenarios, the movement of the robot formation is often affected by external interference, resulting in a deviation in the motion trajectory, which affects the normal operation of the robot formation.

[0004] There is no effective solution to the problem of external interference in the robot formation movement process in the prior art. Summary of the invention

[0005] The present invention provides an adaptive terminal sliding mode model predictive control method, device and electronic equipment, which are used to solve the defect of external interference in the robot formation movement process in the prior art.

[0006] In a first aspect, the present invention provides an adaptive terminal sliding mode model predictive control method, comprising: 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 influence of external interference on the robot formation; 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; 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 formation.

[0007] 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: Based on the dynamic equation of the robot formation, a mathematical model of the robots in the robot formation is established; Designing a terminal sliding surface of a dynamic control system of the robot formation and determining a control target of the robot formation; Setting an adaptive controller for the robot formation and compensating for the uncertainty of the dynamic control system; Designing an adaptive law, and generating an adaptive estimation representation of the robot formation subjected to external interference based on the adaptive law; The adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller.

[0008] 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 comprises: 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.

[0009] 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: 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 a speed constraint for the movement speed of the leader robot and a speed increment within a unit sampling period; determining a performance functional of a model predictive control of the leader robot based on the speed 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.

[0010] 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: Based on the kinematic model, determining a reference trajectory of the leader robot; Based on a reference trajectory of the leader robot, a linear error representation of the leader robot is generated.

[0011] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, the performance functional of the leader robot model predictive control and the linear error representation of the leader robot are combined to determine the input increment sequence for trajectory control of the robot formation, including: 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.

[0012] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, a formation posture controller is configured for a follower robot in the robot formation, comprising: 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 performance functionals of a model predictive control of 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.

[0013] According to an adaptive terminal sliding mode model predictive control method provided by the present invention, 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; A desired velocity of the follower robot is determined based on an incremental control sequence of the follower robot.

[0014] In a second aspect, the present invention further provides an adaptive terminal sliding mode model predictive control device, comprising: A formation configuration module, used 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 for reducing the influence of external interference on the robot formation; A leadership configuration module, configured to configure a trajectory tracking controller for a leader robot in the robot formation; the trajectory tracking controller is used 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.

[0015] In a third aspect, the present invention further 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.

[0016] 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.

[0017] 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.

[0018] Compared with the prior art, the present invention has the following beneficial effects: The adaptive terminal sliding mode model predictive control method provided by the present invention performs adaptive real-time estimation of external uncertain interference at the dynamic level, and combines terminal sliding mode control to design an adaptive terminal sliding mode controller, thereby reducing the impact of external uncertain interference on the robot formation system and realizing the dynamic stability control of the robot formation system. Then, at the kinematic level, combined with the model predictive control method, a trajectory tracking controller and a formation posture controller are designed for the leader robot and the follower robot, respectively, to realize the stable tracking of the reference trajectory by the leader robot and the stable maintenance of the formation formation by the follower robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0020] Figure 1 It is a flow chart of the adaptive terminal sliding mode model predictive control method provided by the present invention; Figure 2 is a schematic diagram of an adaptive terminal sliding mode model predictive control method in an embodiment of the present invention; 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 is an operation simulation path diagram of the kinematic model predictive control in an embodiment of the present invention; Figure 5 is a graph showing a change in position error of a leader robot in an embodiment of the present invention; Figure 6 is a speed response curve diagram of the leader robot in an embodiment of the present invention; Figure 7 is a position error curve diagram of follower robots No. 1 and No. 2 in an embodiment of the present invention; Figure 8 is a position error curve diagram of follower robots No. 3 and No. 4 in an embodiment of the present invention; Fig. 9 is a position error curve diagram of follower robots No. 5 and No. 6 in an embodiment of the present invention; Fig.10 is a position error curve diagram of follower robots No. 7 and No. 8 in an embodiment of the present invention; Fig.11 is a formation distance error curve diagram in an embodiment of the present invention; Fig.12 is a curve diagram of formation angle error in an embodiment of the present invention; Fig.13 It is a structural block diagram of the adaptive terminal sliding mode model predictive control device provided by the present invention; Fig.14 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0022] The present invention provides an adaptive terminal sliding mode model predictive control method. Figure 1is 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 comprises the following steps: 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; 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; Step S103, configuring 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.

[0023] Compared with other control algorithms, the model predictive control algorithm (MPC) has powerful predictive capabilities, can optimize control inputs under system constraints, and is suitable for complex nonlinear and constrained systems. At the same time, MPC is flexible and adaptable, can adapt to the dynamic characteristics and uncertainties of the system, and ensure system stability and safety through robust design and constraint processing. Compared with other methods, MPC has lower requirements for system models, can adjust control strategies in real time, has multivariable control capabilities, and comprehensively considers the relationship between multiple variables. These advantages make MPC a powerful control method that is widely used in industry and automation.

[0024] Therefore, in this method, firstly, at the dynamic level, the external uncertain interference is adaptively estimated in real time, and combined with the terminal sliding mode control, an adaptive terminal sliding mode controller is designed to reduce the impact of external uncertain interference on the robot formation system and realize the dynamic stability control of the robot formation system. Then, at the kinematic level, combined with the model predictive control method, the trajectory tracking controller and the formation posture controller are designed for the leader robot and the follower robot respectively, realizing the stable tracking of the reference trajectory by the leader robot and the stable maintenance of the formation formation by the follower robot.

[0025] Figure 2 is a schematic diagram of an adaptive terminal sliding mode model predictive control method in an embodiment of the present invention, such as Figure 2As shown, in some of the 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 robots in the robot formation is established; the terminal sliding mode 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 interference is generated based on the adaptive law; the adaptive estimation representation is brought into the adaptive controller to obtain an adaptive terminal sliding mode controller.

[0026] Exemplarily, first, based on the dynamic equation of the robot formation, a mathematical model of the robot is established:

[0027] in, represents the positive definite inertia symmetric matrix, which represents the inertial characteristics of the mobile robot system. In actual situations, its element values ​​depend on the mass distribution of the robot. Indicates speed, 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 mode of the robot. Represents the control input of the mobile robot system, usually expressed in the form of motor torque output. 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. represents the external uncertain friction force on the mobile robot. Definition is the state vector of the dynamics 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 get:

[0028] in, is the inertia matrix of the mobile robot, for The external friction disturbance force under 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 mobile robot tracking error as ,but , .

[0029] Then, the terminal sliding surface of the mobile robot dynamics control system is designed to determine the control target and sliding surface:

[0030] 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.

[0031] Then design an adaptive controller to realize sliding mode control and compensate for the uncertainty of the robot formation system. The specific formula is as follows:

[0032] in, u represents the control input, , are all symmetric positive definite matrices, used to provide related positive-valued 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 larger, the system's sensitivity to linear speed tracking error increases, which will prompt the robot to adjust the linear speed faster.

[0033] 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:

[0034] in, , They are the wheel-ground sliding interference estimation coefficient and the wheel-ground rolling interference estimation coefficient respectively. The larger the estimation coefficient is, the shorter the convergence time for estimating the external disturbance force will be. However, too large an 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.

[0035] Finally, substituting the adaptive disturbance estimate into the adaptive controller, the adaptive terminal sliding mode controller is obtained as:

[0036] 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 result.

[0037] Exemplarily, the stability of the adaptive terminal sliding mode controller is proved, and the Lyapunov function is defined as:

[0038] 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 get:

[0039] From the above formula, according to Lyapunov stability theory and Russell invariance principle, it can be deduced that the control system is asymptotically stable.

[0040] In some of the 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.

[0041] Specifically, 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: determining a reference trajectory of the leader robot based on the kinematic model; and generating a linear error representation of the leader robot based on the reference trajectory of the leader robot.

[0042] Combined with 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; solving the quadratic programming problem to obtain the input incremental sequence for trajectory control of the robot formation.

[0043] Exemplarily, first, a robot kinematic model is established, and the specific formula is as follows:

[0044] 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:

[0045] 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:

[0046] 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 set the sampling time period of MPC to , then after discretizing the above linear error differential equation, we can get:

[0047]

[0048]

[0049] At any sampling time k , and . The augmented matrix of the system state is defined as:

[0050] Substituting the augmented matrix into the above formula, the augmented state equation of the robot formation system can be obtained as follows:

[0051] in, , , , According to the above analysis, it can be deduced that at any sampling time k When , the discrete state output of the robot formation system can be expressed as:

[0052] 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.

[0053] Then, set constraints on the movement speed of the leader robot and the speed increment within the unit sampling period to prevent the output power and output torque of the drive motor from being too large and causing the motor to burn out. The speed constraint can be expressed as:

[0054] 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.

[0055] When designing the MPC performance functional, the leader robot’s trajectory tracking error and the system’s control input need to be considered. The system’s control input is the velocity increment within a unit sampling period. Therefore, at any sampling time k , the leader robot MPC performance functional can be designed as:

[0056] 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. , represents the speed increment of the leader robot in the unit sampling period. In model predictive control, the control input is usually related to the dynamic changes of the system. Provides reference motion trajectories 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.

[0057] 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:

[0058] in, , N c In order 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:

[0059] 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 the problem, it can be concluded that at any sampling time k In , the control input increment sequence of the robot formation system generated by MPC is:

[0060] 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. During the sampling time, the actual control input of the system is:

[0061] By repeating the above optimization and solving steps, the actual trajectory of the leader robot can be optimally converged to the reference trajectory.

[0062] In some of the embodiments, step S103, configuring a formation posture controller for the follower robots in the robot formation, includes: 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; solving the optimization problem to determine the expected speed of each follower robot.

[0063] 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.

[0064] For example, let is the multi-mobile robot formation system vector, where , are the actual distance and 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:

[0065] 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 system state quantity augmented. The system augmented state equation of the follower robot can be expressed as:

[0066] 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 constraints, speed increment constraints, and system output state constraints. The follower robot formation control system constraints can be expressed as:

[0067] in, , They represent the minimum and maximum values ​​of the output state of the follower robot respectively.

[0068] According to the design of the leader robot MPC kinematic controller, the MPC performance functional of the follower robot mainly considers the error of the actual position of the follower robot to the expected formation posture and the system control input. Therefore, the MPC performance functional of the follower robot can be obtained as follows:

[0069] 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. According to the system constraints and performance functionals of the formation state equation of the follower robot, the prediction optimization problem of the formation control of the follower robot can be obtained in the same way. For the convenience of solving, it is converted into a quadratic programming problem as shown below:

[0070] 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, and the actual control input of the robot formation system can be obtained as follows:

[0071] By repeating the above optimization steps, the expected speed of each follower robot can be obtained, so that the multi-mobile robot formation system can maintain a stable formation.

[0072] In order to verify the effectiveness and superiority of the adaptive terminal sliding mode model predictive control method proposed in the present invention in solving the problem of multi-machine system formation control stability under interference environment, this embodiment conducts a multi-machine formation control simulation comparison experiment, uses MATLAB R2021a software to write simulation code, and conducts experiments on a PC based on WINDOWS10, R7-5800H. Figure 3 and Figure 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.

[0073] For the convenience of comparison, this simulation comparison experiment sets the mobile robot's predetermined speed to 0.4m / s, the maximum moving speed to 2m / s, and the initial heading angle to 45 degrees. Since this method adds dynamic control, dynamic-related parameters need to 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:

[0074] 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 to restore the stable formation from the start of obstacle avoidance to the end of obstacle avoidance is taken as the convergence time, and the mean square error of the formation error of the entire system 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 5is 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.

[0075] In view of the adaptive terminal sliding mode model predictive control method proposed in the present invention, this simulation experiment artificially adds external interference to the multi-machine formation system at the 200th control cycle. In this case, simulation comparison experiments are conducted on the adaptive terminal sliding mode model predictive control (ATSMMPC) and the single kinematic model predictive control (MPC). The single kinematic model predictive control only has kinematic stability control but no dynamic stability control. Figure 7-12 As shown, Figure 7 is a position error curve diagram of follower robots No. 1 and No. 2 in an 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, Fig. 9 is a position error curve diagram of follower robots No. 5 and No. 6 in the embodiment of the present invention, Fig.10 is a position error curve diagram of follower robots No. 7 and No. 8 in an embodiment of the present invention; Fig.11 is a formation distance error curve diagram in an embodiment of the present invention, Fig.12 It is a curve diagram of 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.

[0076] In summary, the present invention proposes an adaptive terminal sliding mode control method, and at the same time, adds adaptive real-time estimation of external uncertain friction interference at the dynamic level, and the designed dynamic controller has fast stability and strong robustness. Moreover, the present invention combines the leader-follower method and the MPC method at the kinematic level, and designs kinematic controllers for the leader and the follower respectively, realizing stable trajectory tracking of the leader robot and stable formation maintenance of the follower robot. In addition, the present invention can be widely used in the collaborative control of multiple mobile robots, and has great effectiveness and superiority in the stability control of multi-machine formations under fault and interference environments.

[0077] 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. Fig.13 is a structural block diagram of the adaptive terminal sliding mode model predictive control device provided by the present invention, such as Fig.13 As shown, the device comprises: 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; A leader configuration module 1302 is used to configure a trajectory tracking controller for a leader robot in a robot formation; the trajectory tracking controller is used to optimize the actual trajectory of the leader robot; The following configuration module 1303 is used to configure a formation posture controller for the follower robot in the robot formation; the formation posture controller is used to maintain the follower robot in the formation.

[0078] When the device is used, first, at the dynamic level, the formation configuration module 1301 performs adaptive real-time estimation of external uncertain interference, and combines terminal sliding mode control to design an adaptive terminal sliding mode controller, thereby reducing the impact of external uncertain interference on the robot formation system and realizing the dynamic stability control of the robot formation system. Then, at the kinematic level, the leadership configuration module 1302 and the follower configuration module 1303 combine the model predictive control method to design a trajectory tracking controller and a formation posture controller for the leader robot and the follower robot, respectively, thereby realizing the stable tracking of the reference trajectory by the leader robot and the stable maintenance of the formation formation by the follower robot.

[0079] Fig.14 An example of a physical structure diagram of an electronic device is shown in FIG. Fig.14 As shown, the electronic device may include: a processor (processor) 1401, a communication interface (Communications Interface) 1402, a memory (memory) 1403 and a communication bus 1404, wherein the processor 1401, the communication interface 1402, and the memory 1403 communicate with each other through 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: 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; 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; 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.

[0080] In addition, the logic instructions in the above-mentioned memory 1403 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0081] On the other hand, the present invention further provides a computer program product, the computer program product includes a computer program, the computer program can be stored in a non-transitory computer-readable storage medium, when the computer program is executed by a processor, the computer can execute the adaptive terminal sliding mode model predictive control method provided by the above methods, the method includes: 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; 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; 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.

[0082] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when the computer program is executed by a processor to execute the adaptive terminal sliding mode model predictive control method provided by the above methods, the method comprising: 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; 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; 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.

[0083] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0084] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0085] 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 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 influence of external interference on the robot formation; 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; 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 formation.

2. The adaptive terminal sliding mode model predictive control method according to claim 1, characterized in that: For robot formation, an adaptive terminal sliding mode controller is set up, including: Based on the dynamic equation of the robot formation, a mathematical model of the robots in the robot formation is established; Designing a terminal sliding surface of a dynamic control system of the robot formation and determining a control target of the robot formation; Setting an adaptive controller for the robot formation and compensating for the uncertainty of the dynamic control system; Designing an adaptive law, and generating an adaptive estimation representation of the robot formation subjected to external interference based on the adaptive law; The adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller.

3. The adaptive terminal sliding mode model predictive control method according to claim 2, characterized in that: After the adaptive estimation representation is brought into the adaptive controller to obtain the adaptive terminal sliding mode controller, the method 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.

4. The adaptive terminal sliding mode model predictive control method according to claim 1, characterized in that: Configuring a trajectory tracking controller for a 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 a speed constraint for the movement speed of the leader robot and a speed increment within a unit sampling period; determining a performance functional of a model predictive control of the leader robot based on the speed 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.

5. The adaptive terminal sliding mode model predictive control method according to claim 4, 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: Based on the kinematic model, determining a reference trajectory of the leader robot; Based on a reference trajectory of the leader robot, a linear error representation of the leader robot is generated.

6. The adaptive terminal sliding mode model predictive control method according to claim 4, characterized in that: Determining an input increment sequence 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, including: 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.

7. 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, including: 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 performance functionals of a model predictive control of 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.

8. The adaptive terminal sliding mode model predictive control method according to claim 7, 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.

9. An adaptive terminal sliding mode model predictive control device, characterized in that: include: A formation configuration module, used 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 influence of external interference on the robot formation; A leadership configuration module, configured to configure a trajectory tracking controller for a leader robot in the robot formation; the trajectory tracking controller is used 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.

10. 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 8 is implemented.

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