Trajectory tracking control method for wheeled mobile robot with preset safety performance

Abstract

The invention discloses a wheeled mobile robot trajectory tracking control method with preset safety performance, and relates to the technical field of robots. Comprising the steps that S1, a robot model is established, and a robot kinematics model is obtained through coordinate transformation; s2, determining a robot trajectory tracking control target and constraint conditions, defining safety output performance and preset safety performance, and giving a hypothesis; s3, based on the robot kinematics model and the defined safety performance, planning a safety performance function, constructing a dynamic constraint boundary of an output tracking error, converting a constraint-containing tracking problem into an unconstrained system, designing a continuous state feedback control law, including normalized error processing and control law construction, and finally completing design of a robust controller; and S4, verifying the validity of the proposed safety performance preset plan and the robust controller. The attitude trajectory tracking robust controller is low in structural complexity, low in calculation cost and high in response speed, and meets safety constraints and performance constraints at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of automatic control technology, and more specifically, relates to a trajectory tracking control method for a wheeled mobile robot with preset safety performance. Background Art

[0002] Over the past decade or so, mobile robots have been widely used in various fields, from factory inspections to logistics and transportation, emergency rescue, medical care, and even the military. Consequently, mobile robots have attracted increasing attention from researchers and scholars. Trajectory tracking control, as a fundamental and important control problem for mobile robots, has long garnered extensive attention and research.

[0003] However, in the real world, mobile robots are subject to ubiquitous constraints, including performance and safety constraints, as they perform complex tasks, driven by quality, efficiency, and safety. Violations of these constraints can lead to performance degradation, system damage, and other catastrophic consequences. Therefore, designing trajectory tracking controllers for mobile robots within these constraints is of great theoretical and practical significance.

[0004] Traditionally, preset performance control, a relatively mature control method, combines other control methods such as adaptive control, proportional-integral-derivative controllers (PID), and preset time to provide a more flexible solution to mobile robot tracking control problems. However, these methods typically focus only on situations where the output error constraints do not conflict with safety constraints, ignoring safety issues in obstacles or more complex environments, leading to potential risks in practical applications. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a trajectory tracking control method for a wheeled mobile robot with preset safety performance. A state-to-error conversion mechanism is established for a wheeled mobile robot with a known model, and a performance function curve is planned using polynomial fitting technology. Based on the preset performance control (PPC) framework, a posture trajectory tracking robust controller with low structural complexity, low computational cost, and fast response speed is developed, which satisfies both safety constraints and performance constraints.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a trajectory tracking control method for a wheeled mobile robot with preset safety performance, comprising the following steps:

[0007] S1. Establish a wheeled mobile robot model, define the reference coordinate system and the body coordinate system, perform coordinate transformation, and obtain the wheeled mobile robot kinematic model;

[0008] S2. Clarify the trajectory tracking control objectives and constraints of the wheeled mobile robot, define the safety output tracking performance and preset safety performance, and provide assumptions to meet the needs of subsequent safety performance function planning and robust controller design;

[0009] S3. Based on the kinematic model of the wheeled mobile robot established in step S1 and the safety performance defined in step S2, a safety performance function is planned using polynomial fitting technology, and a dynamic constraint boundary of the output tracking error is constructed. Both offline and online situations are considered simultaneously. Using the planned dynamic safety boundary, the constrained tracking problem is converted into an unconstrained system, and a continuous state feedback control law is designed, including normalized error processing and control law construction, to finally complete the design of the robust controller.

[0010] S4. Verify the effectiveness of the proposed safety performance preset planning and robust controller, and give experimental results of the trajectory tracking process, performance function, tracking error and control input signal.

[0011] Preferably, step S1 specifically includes the following contents:

[0012] The wheeled mobile robot model consists of a rigid main frame and two running wheels, each driven by a motor;

[0013] Body coordinate system {X c , Y c The origin of X is at the center of mass of the wheeled mobile robot model. c The axis direction is the forward travel direction of the runner;

[0014] Consider a wheeled robot moving in a two-dimensional plane with a reference coordinate system Fixed on the earth; the heading direction of the wheeled robot is determined by the heading angle Determine the heading angle The heading direction of the wheeled robot and X c The angle between the axes;

[0015] In order to solve the under-actuated characteristics of the traditional wheeled mobile robot model and facilitate the subsequent robust controller design, the reference coordinate system The coordinate transformation is performed using the reference point position , the kinematic model of the wheeled mobile robot is described by the following equations:

[0016] in, , , Including speed and angular velocity , .

[0017] Preferably, in step S2, the trajectory tracking control goal of the wheeled mobile robot is to design a trajectory tracking robust controller, and the trajectory tracking robust controller meets the following requirements:

[0018] i) All signals in the closed-loop system of the wheeled mobile robot are globally and eventually uniformly bounded;

[0019] ii) The output tracking error meets the preset safety performance;

[0020] To this end, the following definitions and assumptions are introduced:

[0021] set up Output for the system Convex safe set of is a known and bounded desired trajectory, and is also bounded, then the output tracking error Defined as

[0022]

[0023] Definition 1: Safety output tracking performance, let represents the safe set of output tracking error, which is mathematically described as: , if satisfied ,and , then it is called safety output tracking performance;

[0024] Definition 2: Preset safety performance, set yes A preset non-empty subset, if it satisfies , it is called preset safety performance;

[0025] Assumption: Matrix is completely known and non-singular.

[0026] Preferably, step S3 specifically includes the following steps:

[0027] S31. Plan a safety performance function and obtain a dynamic safety boundary;

[0028] Mathematical expression of safety performance area: ,in, is the safety performance constraint, defined as

[0029]

[0030] in, and It is a safety performance function that needs to be planned;

[0031] Assuming the actual trajectory safety set and expected trajectory If known in advance, the safety output tracking performance can be obtained , the safety performance function can be planned as a cubic polynomial curve:

[0032]

[0033]

[0034] in, and are the polynomial coefficients, is a constant that limits the maximum allowable steady-state error, is a positive constant that determines these parameters so that:

[0035] 1) Satisfy the initial error: and , plus the initial value established based on initial error constraints, safety performance guarantees and other performance requirements 、 , the two safety performance curves of offline initial planning can be uniquely determined 、 ;

[0036] 2) Safety performance function and The rate of change at each moment is zero, which ensures a smooth transition at both ends of the time period and avoids drastic changes in the controller input due to sudden changes at the boundaries;

[0037] The cubic polynomial fit ensures that and continuity, and and It should be small enough to ensure the required transient and steady-state tracking performance indicators;

[0038] During the movement of the wheeled mobile robot, due to changes in the environment, such as the appearance of new obstacles, the safe area and It is likely to change, so that the initially set safety performance area becomes infeasible; in this case, it is necessary to adjust online by re-planning the safety performance function ;

[0039] In order to better present the safety performance function planning algorithm, it is assumed that there are only static obstacles in the environment, so that or changes at certain moments, and there is always a non-empty region , so that for all ,have , that is, the preset safety performance control problem is feasible; once in the time interval The current safety performance constraints are not met, where 、 are certain constants respectively, then the current safety performance function is recorded as 、 , violating the updated security zone or , these functions should be in the interval Re-planning within 、 , and satisfies 、 ;

[0040] In this case, there are two possibilities for adjusting the safety performance function. and is the performance function after planning;

[0041] i) Unilateral replanning: If the time interval Only one safety function is violated or , it is necessary to re-plan one of the safety performance functions without losing generality, such as :

[0042]

[0043] in, arrive are the coefficients of the polynomial to be determined, is the appropriate number of sampling points selected; Should be determined so that:

[0044] 1) The planned safety performance function is different from the initial function and The boundary values ​​of the moments are the same: ;

[0045] 2) The planned safety performance function is different from the initial function and The rate of change of time is the same: ;

[0046] For any belong , need to ensure , During WMR operation and can be physically measured, where , is a constant;

[0047] ii) Bilateral replanning: If the safety performance function and All violated , then both sides need to be replanned at the same time; choose The upper / lower regions of the time axis with higher conflict intensity are used as the concave / convex direction of the replanning function; then Will be adjusted to (7), re-planned Expressed as:

[0048]

[0049] in, arrive For polynomial coefficients, the rearranged The conditions in i) must still be met. Should be determined so that:

[0050] 1) 、 ;

[0051] 2) 、 ;

[0052] The boundary conditions require that the fitted function 、 exist and When the derivative condition is satisfied, it matches the boundary value of the original curve to ensure the continuity of the safety performance function before and after. In addition, the derivative condition stipulates that and The first derivative of must be and This ensures the smoothness of the safety performance function; Ensure the safety performance of the system, Ensure that the re-planned curves do not intersect, thereby ensuring that the safety performance function does not violate the output tracking error Evolving within a specified area to ensure system security;

[0053] S32. Using dynamic safety margins, we transform the constrained tracking problem into an unconstrained problem and design a low-complexity robust controller.

[0054] Using the planned safety performance boundary function and , the tracking error constraint can be established as

[0055]

[0056] in, and Represents the latest performance function after re-planning and When an obstacle appears in the environment, the safety performance curve is adjusted in real time through unilateral or bilateral replanning in step S31 to ensure that the error is always within the preset safety area to avoid collision between the robot and the obstacle.

[0057] Preferably, step S32 includes the following steps:

[0058] S321, Normalization error processing: Introducing normalization variables , the error is scaled by the safety margin function, and the constrained problem is transformed into an unconstrained problem;

[0059] In the design of robust controllers, in order to transform a constrained problem with a preset tracking error constraint into an unconstrained problem, it is necessary to use and right Normalize,

[0060]

[0061] in , ;

[0062] Obviously, from formula (10) we can know that Has the following properties:

[0063] i) If for have ,but ;

[0064] ii) If near or ,but tends toward 1 or -1;

[0065] pass The sign and absolute value of the error reflect the direction of deviation and the degree of approach to the boundary, which converts the boundary constraint of the original error into unconstrained problem for subsequent robust controller design; define As auxiliary variables

[0066]

[0067] pass The sign and absolute value of the error reflect the direction of deviation and the degree of approach to the boundary, which converts the boundary constraint of the original error into Unconstrained problem for subsequent robust controller design;

[0068] S322, Construction Control Law

[0069] For the kinematic model of the wheeled mobile robot in step S1, the control input of the robust controller is constructed as

[0070]

[0071] in, For design parameters, reasonable selection can achieve a balance between response speed and system stability, ensuring that the error converges quickly and stably to the preset safety area; adding The matrix makes Directly with Linear relationship, eliminating posture Interference with the control process makes the control more direct and simple; negative feedback makes the control input and The direction of change is opposite; when When it increases (indicating a departure from the safe area), It will act on the robot with a known kinematic model and drive it to adjust its posture in the opposite direction. Reduce; final tracking error It will always converge to the preset safe area, forming a closed-loop link of "constraint programming-error conversion-robust control".

[0072] The beneficial effects of adopting the above technical solution are:

[0073] 1. The present invention solves the problem of separation of safety and performance constraints in traditional methods by combining dynamic programming of safety performance functions with low-complexity robust control, and significantly improves the adaptability, safety and control efficiency of wheeled mobile robots in environments with obstacles.

[0074] 2. This invention uses coordinate transformation to convert the original three-dimensional state vector based on the Earth coordinate system into a two-dimensional state vector based on the vehicle body coordinate system. This solves the under-actuated characteristic of the model and facilitates the subsequent control scheme design.

[0075] 3. By establishing a mapping relationship between state and tracking error, the system state is indirectly constrained, avoiding the separation of performance and safety constraints in traditional methods and achieving the unification of safety and performance constraints. This provides a theoretical basis for subsequent safety performance function planning and controller design.

[0076] 4. Dynamic programming of safety performance function (offline + online). In offline polynomial fitting programming, a cubic polynomial curve is used to program the safety performance function. By adjusting the polynomial coefficients and the steady-state tracking error constant, The sum and transition times allow for flexible control of tracking error convergence speed and steady-state accuracy to meet diverse mission requirements. During online replanning, when obstacles appear in the environment, the safety performance function is replanned unilaterally or bilaterally to dynamically adjust the tracking error bounds, ensuring that the tracking error remains within the safe set and preventing collisions between the wheeled mobile robot and obstacles. Safety performance takes precedence over tracking performance; when the two conflict, bounds are adjusted to ensure safety, mitigating risks in practical applications.

[0077] 5. Tracking error is normalized using a planned safety performance function, converting the bounded tracking error into an unconstrained auxiliary variable, simplifying controller design. The constructed control law eliminates attitude angle interference, making control more direct and simple. A negative feedback mechanism ensures rapid error convergence to a pre-set safety zone. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a schematic diagram of the structure of a wheeled mobile robot;

[0079] Figure 2 It is the initialization of the preset safety performance function;

[0080] Figure 3 It is a unilateral replanning schematic diagram;

[0081] Figure 4 It is a schematic diagram of bilateral re-planning;

[0082] Figure 5 It is a flow chart of the experimental process;

[0083] Figure 6 yes Performance functions;

[0084] Figure 7 yes Performance functions;

[0085] Figure 8 It is the robot trajectory tracking process;

[0086] Figure 9 is the control input signal; DETAILED DESCRIPTION

[0087] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0088] The present invention comprises the following steps:

[0089] S1: A wheeled mobile robot is selected as the research object for modeling. The reference coordinate system and the body coordinate system are defined. In order to solve the under-actuated characteristics of the original model and facilitate the subsequent controller design, coordinate transformation is performed to obtain the kinematic model of the wheeled mobile robot.

[0090] The wheeled mobile robot model studied in this paper is as follows Figure 1 As shown in Figure 2. The robot consists of a rigid main frame and two wheels, each driven by a motor. The origin of the body coordinate system is at the center of mass of the mobile robot model. The axis direction is the forward driving direction of the robot's wheels. In this section, we will derive a two-degree-of-freedom model for a wheeled mobile robot.

[0091] Consider a wheeled robot moving in a two-dimensional plane with a reference coordinate system Fixed on the earth. The heading direction of the robot is fixed to the reference coordinate system of the vehicle body The heading direction is determined by the heading angle Decide.

[0092] In order to solve the under-actuated characteristics of the traditional model of wheeled mobile robots and facilitate the subsequent robust controller design, we Perform coordinate transformation on the position of the reference point: .

[0093] When the position, velocity and state changes of the robot are of interest, a kinematic model is usually used. , Then Taking derivatives, we get the kinematic model of the mobile robot:

[0094]

[0095] in, , , Including speed and angular velocity , .

[0096] S2: Clarify the trajectory tracking control objectives and constraints of the wheeled mobile robot, define the safety output performance and preset safety performance, and provide assumptions to meet the needs of subsequent safety performance function planning and controller design.

[0097] The goal of trajectory tracking control for a wheeled mobile robot is to design a trajectory tracking robust controller that meets the following requirements:

[0098] i) All signals in the closed-loop system of the wheeled mobile robot are globally eventually uniformly bounded (GUUB).

[0099] ii) The output tracking error satisfies the preset safety performance (Definition 2).

[0100] To this end, this paper needs to introduce the following definitions and assumptions.

[0101] set up Output for the system Convex safe set of is a known and bounded desired trajectory, and is also bounded. Then the output tracking error Defined as

[0102]

[0103] Definition 1: Safety output tracking performance: Assume represents the safe set of output tracking error, which is mathematically described as: If satisfied ,and , it is called safety output tracking performance.

[0104] Definition 2: Preset safety performance. yes A preset non-empty subset, if it satisfies , it is called preset safety performance.

[0105] Assumption 1: Matrix is completely known and non-singular.

[0106] S3: Based on the mobile robot kinematic model established in step S1 and the safety performance defined in step S2, a safety performance function is planned using polynomial fitting techniques to construct a dynamic constraint bound for the output tracking error. Considering both offline and online scenarios, the planned dynamic safety bound is used to transform the constrained tracking problem into an unconstrained system. A continuous state feedback control law is then designed, including normalized error processing and control law construction, ultimately completing the robust controller design. This includes the following steps:

[0107] S31. Plan the safety performance function and obtain the dynamic safety boundary

[0108] In this paper, the safety performance area is mathematically expressed as: .in is the safety performance constraint, defined as

[0109]

[0110] in and It is a safety performance function that needs to be planned.

[0111] Assuming the actual trajectory safety set and expected trajectory If it is known in advance, then Definition 1 can be used to obtain The safety performance function can be formulated as a cubic polynomial curve

[0112]

[0113]

[0114] in and are the polynomial coefficients, is a constant that limits the maximum allowable steady-state error. is a positive constant. These parameters should be determined appropriately so that

[0115] 1) The initial error satisfies: and , plus an initial value established based on performance requirements 、 , the two safety performance curves of offline initial planning can be uniquely determined 、 .

[0116] 2) Safety performance function and The rate of change at each moment is zero, which ensures a smooth transition at both ends of the time period and avoids drastic changes in the controller input due to boundary mutations.

[0117] The cubic polynomial fit ensures that and continuity, and and should be small enough to ensure the required transient and steady-state tracking performance indicators, such as Figure 2 shown.

[0118] During the operation of the system, due to changes in the environment, such as the emergence of new obstacles, the safe area and It is likely to change, so that the initially set safety performance area In this case, it is necessary to adjust the safety performance function online by re-planning the safety performance function. .

[0119] In order to better present the safety performance function planning algorithm, this paper assumes that there are only static obstacles in the environment, so that (or ) changes at some point. And there is always a non-empty region , so that for all ,have , that is, the PSPC problem is feasible. Once in the time interval The current safety performance constraints are not met, where 、 are certain constants respectively, then the current safety performance function is recorded as 、 , violating the updated security zone or . These functions should be in the interval Re-planning within 、 , and satisfies 、 .

[0120] In this case, there are two possibilities for adjusting the safety performance function. and is the performance function after planning. Figure 3 This is a schematic diagram for unilateral replanning. Figure 4 Re-planning schematic diagram for both sides.

[0121] i) Unilateral replanning: If the time interval Only one safety function is violated or , it is necessary to re-plan one of the safety performance functions without losing generality.

[0122]

[0123] in arrive are the coefficients of the polynomial to be determined, is the appropriate number of sampling points selected. should be determined to enable

[0124] 1) The planned safety performance function is different from the initial function and The boundary values ​​of the moments are the same:

[0125] 2) The planned safety performance function is different from the initial function and The rate of change of time is the same:

[0126] For any belong , need to ensure , During WMR operation and can be physically measured, where , is a constant.

[0127] ii) Bilateral replanning: If the safety performance function and All violated , then both sides need to be replanned at the same time. The upper / lower regions of the time axis with higher conflict intensity are used as the convex direction of the replanning function. Then Will be adjusted to (7), re-planned Expressed as

[0128]

[0129] in arrive For polynomial coefficients, the rearranged The conditions in i) must still be met. should be determined to enable

[0130] 1) 、

[0131] 2) 、

[0132] The boundary conditions require that the fitted function 、 exist and When the derivative condition is satisfied, it matches the boundary value of the original curve to ensure the continuity of the safety performance function before and after. and The first derivative of must be and This ensures the smoothness of the safety performance function. Ensure the safety performance of the system, Ensure that the re-planned curves do not intersect, thereby ensuring that the safety performance function does not violate the output tracking error Evolving within the specified area, thus ensuring the security of the system.

[0133] S32. Using the dynamic safety boundary planned in step S31, the constrained tracking problem is converted into an unconstrained problem, and a low-complexity robust controller is designed.

[0134] Using the planned safety performance boundary function and , the tracking error constraint can be established as

[0135]

[0136] in and Represents the latest performance function after re-planning and When obstacles appear in the environment, the safety performance curve is adjusted in real time through unilateral or bilateral replanning to ensure that the error is always within the preset safety area and avoid collision between the robot and the obstacle.

[0137] S321, Normalization error processing: Introducing normalization variables , the error is scaled by the safety margin function, and the constrained problem is transformed into an unconstrained problem.

[0138] In order to transform the original system with preset tracking error constraints into an unconstrained system, it is necessary to use and right Normalize

[0139]

[0140] in , .

[0141] Obviously, from (10) we can know that Has the following properties

[0142] i) If for have ,but .

[0143] ii) If near or ,but tends toward 1 or -1.

[0144] pass The sign and absolute value of the error reflect the direction of deviation and the degree of approach to the boundary, which converts the boundary constraint of the original error into The unconstrained problem of , so as to facilitate the subsequent controller design. Definition As auxiliary variables

[0145]

[0146] pass The sign and absolute value of the error reflect the direction of deviation and the degree of approach to the boundary, which converts the boundary constraint of the original error into unconstrained problem for subsequent controller design.

[0147] S322, Control Law Construction

[0148] For the kinematic model of the wheeled mobile robot in step S1, the control input of the robust controller is constructed as

[0149]

[0150] in, For design parameters, reasonable selection can achieve a balance between response speed and system stability, ensuring that the error converges quickly and stably to the preset safety area. The matrix makes Directly with Linear relationship, eliminating posture The interference to the control process makes the control more direct and simple. Negative feedback makes the control input and The direction of change is opposite. When it increases (indicating a departure from the safe area), It will act on the robot with a known kinematic model and drive it to adjust its posture in the opposite direction. Reduce. Final tracking error It will always converge to the preset safe area, forming a closed-loop link of "constraint programming-error conversion-robust control".

[0151] S4. Physical verification.

[0152] In this section, we verify the effectiveness of the proposed robust controller and present experimental results on the trajectory tracking process, performance function, tracking error, and control input signal. The experiment is based on ROS (Robot Operating System) and the NOKOV motion capture system and is applied to the Turtlebot-3 Burger mobile robot. Control commands are issued by a computer, and the ROS platform serves as the transmission medium to generate data. The data is transmitted in a period of 0.01 seconds. The experimental process is as follows: Figure 5 Assume that external disturbances are negligible, including external forces, control signal corruption, and wheel slip and sliding.

[0153] The design parameters are chosen as , and The expected trajectory is set to The initial state is set to .for and , , The obstacle is a cube with a side length of 0.07 meters and the center coordinates are (1.89, 1.55). The number of sampling points is selected as 5. The experimental results are shown as follows Figure 6 , Figure 7 , Figure 8 , Figure 9 shown.

[0154] Figure 6 , Figure 7 Wheeled mobile robots , From the performance function diagram, we can see that after encountering an obstacle, the performance curve can be replanned in time, and , Always subject to performance functions. Figure 8 This is a diagram of the trajectory tracking control process of a wheeled mobile robot. Figure 8 It can be seen that the mobile robot can bypass obstacles according to the performance curve. After completely avoiding the obstacles, the robot can continue to track the original expected trajectory and output the trajectory Final and expected trajectory consistent. Figure 9 This is a control input signal diagram for a wheeled mobile robot. Figure 9 It can be seen that the control input signal It is bounded in the control process.

[0155] The above are only preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A trajectory tracking control method for a wheeled mobile robot with preset safety performance, characterized in that: The following steps are involved: S1. Establish a wheeled mobile robot model, define the reference coordinate system and the body coordinate system, perform coordinate transformation, and obtain the wheeled mobile robot kinematic model; S2. Clarify the trajectory tracking control objectives and constraints of the wheeled mobile robot, define the safety output performance and preset safety performance, and provide assumptions; S3. Based on the kinematic model of the wheeled mobile robot established in step S1 and the safety performance defined in step S2, a safety performance function is planned using polynomial fitting technology, and a dynamic constraint boundary of the output tracking error is constructed. Both offline and online situations are considered simultaneously. Using the planned dynamic safety boundary, the constrained tracking problem is converted into an unconstrained system, and a continuous state feedback control law is designed, including normalized error processing and control law construction, to complete the design of the robust controller. S4. Verify the effectiveness of the proposed safety performance preset planning and robust controller, and provide experimental results of the trajectory tracking process, performance function, tracking error and control input signal.

2. A wheeled mobile robot trajectory tracking control method with preset safety performance according to claim 1, characterized in that: Step S1 specifically includes the following contents: The wheeled mobile robot model consists of a rigid main frame and two running wheels, each driven by a motor; Body coordinate system {X c , Y c The origin of X is at the center of mass of the wheeled mobile robot model. c The axis direction is the forward travel direction of the runner; A wheeled mobile robot moves in a two-dimensional plane, and its reference coordinate system Fixed on the earth; the heading direction of the wheeled mobile robot is determined by the heading angle Determine the heading angle The heading direction of the wheeled mobile robot and X c The angle between the axes; Relative to the reference coordinate system The coordinate transformation is performed using the reference point position , we get the kinematic model of the wheeled mobile robot: in, , , Including speed and angular velocity , .

3. The trajectory tracking control method of a wheeled mobile robot with preset safety performance according to claim 1, characterized in that: In step S2, the trajectory tracking control goal of the wheeled mobile robot is to design a trajectory tracking robust controller that meets the following requirements: i) All signals in the closed-loop system of the wheeled mobile robot are globally and eventually uniformly bounded; ii) The output tracking error meets the preset safety performance; Output for the system Convex safe set of is a known and bounded desired trajectory, and is also bounded, then the output tracking error Defined as To define safety output tracking performance: represents the safe set of output tracking error, which is mathematically described as: ,when ,and , called safety output tracking performance; Define pre-set safety features: yes A preset non-empty subset, if it satisfies , called preset safety performance; matrix is completely known and non-singular.

4. The trajectory tracking control method of a wheeled mobile robot with preset safety performance according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Plan a safety performance function and obtain a dynamic safety boundary; Mathematical expression of safety performance area: ,in, is the safety performance constraint, defined as in, and It is a safety performance function that needs to be planned; Actual trajectory safety set and expected trajectory Known in advance, the safety output tracking performance , the safety performance function is planned as a cubic polynomial curve: in, and are the polynomial coefficients, is a constant that limits the maximum allowable steady-state error, is a positive constant that satisfies the following conditions: 1) Satisfy the initial error: and , the initial value established based on initial error constraints and safety performance guarantees 、 , the two safety performance curves that uniquely determine the offline initial planning 、 ; 2) Safety performance function and The rate of change at each moment is zero; Safe Area and Changes occur so that the initial safety performance area It becomes infeasible and the safety performance function needs to be re-planned and adjusted online. ; Assume that there are only static obstacles in the environment. or changes, and there is a non-empty area , so that all ,have , that is, the preset safety performance control problem is feasible; in the time interval The current safety performance constraints are not met, where 、 are certain constants respectively, and the current safety performance function is recorded as 、 , violating the updated security zone or , these functions are in the interval Re-planning within 、 , and satisfies 、 ; There are two cases for adjusting the safety performance function. and is the performance function after planning; i) Unilateral replanning: If the time interval There is only one safety performance function that violates or , without losing generality, re-plan the safety performance function : in, arrive are the coefficients of the polynomial to be determined, is the appropriate number of sampling points selected; Make the following conditions true: 1) The planned safety performance function is different from the initial function and The boundary values ​​of the moments are the same: ; 2) The planned safety performance function is different from the initial function and The rate of change of time is the same: ; belong , , ; , is a constant; ii) Bilateral Replanning: Safety Performance Function and All violated , and re-plan both sides at the same time; choose relative to The concave / convex direction of the upper / lower regions of the time axis with high conflict intensity as a function of replanning; Adjusted to (7), re-planned Expressed as: in, arrive For polynomial coefficients, the rearranged The conditions in i) must still be met. Make the following conditions true: 1) 、 ； 2） 、 ； S32. Using the dynamic safety margin planned in step S31, the constrained tracking problem is converted into an unconstrained problem, and a low-complexity robust controller is designed; Using the planned safety performance boundary function and , establish the tracking error constraint as in, and Represents the latest performance function after re-planning and .

5. The trajectory tracking control method of a wheeled mobile robot with preset safety performance according to claim 4, characterized in that: Step S32 includes the following steps: S321, Normalization error processing: Introducing normalization variables , the error is scaled by the safety margin function, and the constrained problem is transformed into an unconstrained problem; In robust controller design, the constrained problem with preset tracking error constraints is converted into an unconstrained problem by and right Normalize, in, , ; From formula (10), we know that Has the following properties: i) hour, , ; ii) near or hour, tends toward 1 or -1; definition As auxiliary variables S322, Control Law Construction For the kinematic model of the wheeled mobile robot in step S1, the control input of the robust controller is constructed as in, To design parameters, make the error converge to the preset safe area, add The matrix makes Directly with In a linear relationship, negative feedback makes the control input and The change direction is opposite, the tracking error It always converges to the preset safe area, forming a closed-loop link of "constraint programming-error conversion-robust control".

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