A trajectory tracking control method and system for a nonholonomic wheeled mobile robot

Abstract

The present application belongs to the technical field of trajectory tracking control of nonholonomic wheeled mobile robots, and specifically discloses a trajectory tracking control method and system for nonholonomic wheeled mobile robots. In the trajectory tracking process of the nonholonomic wheeled mobile robot, the present application method converges the position tracking error and the attitude tracking error to an arbitrarily small compact set near the origin within a limited time through steps such as designing an adaptive neural state observer, a finite-time command filter, an error compensation mechanism, a virtual control input, and an actual control signal. The present application not only avoids the calculation complexity explosion problem caused by repeated derivation of the virtual control signal in the traditional backstepping method, but also guarantees that the trajectory tracking error of the nonholonomic wheeled mobile robot converges to an arbitrarily small neighborhood within a limited time under the conditions of unknown nonlinear dynamics and unmeasurable speed, and all signals in the closed-loop system are ultimately bounded.

Description

Technical Field

[0001] This invention belongs to the field of tracking and control technology for non-holonomic wheeled mobile robots, specifically relating to a trajectory tracking and control method and system for a non-holonomic wheeled mobile robot. Background Technology

[0002] Nonholonomic wheeled mobile robots have advantages such as simple structure, high mobility, and low energy consumption, and are widely used in indoor navigation, automated delivery, and service robots. However, nonholonomic wheeled mobile robots have characteristics such as nonholonomic constraints, unknown nonlinear dynamics (such as disturbances caused by wheel slip and friction), and unmeasurable velocity states. These characteristics make the design of high-performance trajectory tracking controllers extremely challenging.

[0003] In recent years, various control strategies have been applied to trajectory tracking of nonholonomic wheeled mobile robots, such as PID control, robust control, neural network adaptive control, terminal sliding mode control, and adaptive backstepping control. Among these, backstepping is an effective design method for nonlinear system controllers. However, traditional backstepping requires repeated differentiation of the virtual control signal during the design process, leading to an explosion in computational complexity. To address this issue, dynamic surface control introduces a first-order filter to generate the derivative of the virtual control signal, avoiding repeated differentiation, but neglecting the influence of filtering errors and reducing tracking accuracy.

[0004] Most of the trajectory tracking controllers mentioned above are state feedback designs, requiring measurable speed information. However, in practical applications, the speed of wheeled mobile robots is often unmeasurable due to cost, technological limitations, or environmental interference. In such cases, observer-based output feedback control is often employed, such as adaptive fuzzy output feedback methods and dynamic adaptive neural network controllers. These methods effectively handle system uncertainties using neural networks, but typically only guarantee asymptotic convergence, not finite-time convergence.

[0005] Finite-time control has faster convergence speed and higher steady-state accuracy. Existing research has carried out finite-time tracking control for nonholonomic wheeled mobile robots with disturbances, but most of them rely on full-state feedback.

[0006] To date, no research has been found that combines command filtering backstepping with adaptive neural output feedback and finite-time control to solve the trajectory tracking control of nonholonomic wheeled mobile robots under unknown dynamics and unmeasurable velocity conditions. Therefore, proposing an output feedback control method that can achieve high-precision trajectory tracking within a finite time is of great significance.

[0007] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art. Summary of the Invention

[0008] The purpose of this invention is to propose a trajectory tracking control method for a nonholonomic wheeled mobile robot. This method addresses the problems of unknown nonlinear dynamics and unmeasurable velocity in nonholonomic wheeled mobile robots. It achieves this by designing an adaptive neural state observer to estimate the unmeasurable velocity, introducing a finite-time command filter to avoid complexity explosion and generate a virtual control derivative, constructing an error compensation mechanism to eliminate filtering errors, and using a radial basis function neural network to approximate the unknown function. This enables the trajectory tracking error to converge to any small compact set near the origin within a finite time, while ensuring that all signals in the closed-loop system are eventually bounded. This improves the trajectory tracking convergence speed and control accuracy of the nonholonomic wheeled mobile robot.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A trajectory tracking control method for a nonholonomic wheeled mobile robot includes the following steps:

[0011] Step 1. Establish the kinematic and dynamic model of the nonholonomic wheeled mobile robot;

[0012] Step 2. Under the conditions of unknown nonlinear dynamics and unmeasurable velocity, design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot. The specific design process is as follows:

[0013] First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate virtual control derivatives. An error compensation mechanism is constructed to eliminate filtering errors. A radial basis function neural network is used to approximate the unknown nonlinear dynamics, while ensuring that all signals of the system are eventually bounded, thus completing the controller design.

[0014] Step 3. Using the controller built in Step 2, implement trajectory tracking control for the non-holonomic wheeled mobile robot.

[0015] Furthermore, based on the trajectory tracking control method for incomplete wheeled mobile robots, this invention also proposes a trajectory tracking control system for incomplete wheeled mobile robots that is adapted to it, which adopts the following technical solution:

[0016] A trajectory tracking control system for a non-holonomic wheeled mobile robot includes the following modules:

[0017] The model building module is used to build kinematic and dynamic models of nonholonomic wheeled mobile robots.

[0018] The controller construction module is used to design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot under unknown nonlinear dynamics and unmeasurable velocity conditions. The specific design process is as follows:

[0019] First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate virtual control derivatives. An error compensation mechanism is constructed to eliminate filtering errors. A radial basis function neural network is used to approximate the unknown nonlinear dynamics, while ensuring that all signals of the system are eventually bounded, thus completing the controller design.

[0020] And a tracking control module, which uses a finite-time adaptive neural output feedback command filtering backstepping tracking controller built using the controller construction module to realize trajectory tracking control of a nonholonomic wheeled mobile robot.

[0021] Furthermore, based on the aforementioned trajectory tracking control method for incomplete wheeled mobile robots, this invention also proposes a computer device, which includes a memory and one or more processors.

[0022] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the aforementioned finite-time adaptive neural output feedback command filtering backstepping tracking control method for a nonholonomic wheeled mobile robot.

[0023] Furthermore, based on the aforementioned trajectory tracking control method for a non-holonomic wheeled mobile robot, this invention also proposes a computer-readable storage medium storing a program thereon. When executed by a processor, this program is used to implement the steps of the aforementioned trajectory tracking control method for a non-holonomic wheeled mobile robot.

[0024] The method of the present invention has the following advantages:

[0025] As described above, this invention proposes a trajectory tracking control method for a nonholonomic wheeled mobile robot. This method introduces a novel finite-time output feedback control scheme, enabling high-precision trajectory tracking even when the velocity is unmeasurable. Compared to existing asymptotically convergent output feedback methods, this invention achieves finite-time convergence, thus exhibiting faster convergence speed and higher steady-state accuracy. Compared to existing finite-time tracking methods, this invention eliminates the need for full-state measurement, utilizing only position and attitude information to estimate the unmeasurable velocity through an adaptive neural state observer. Compared to existing backstepping methods, this invention avoids the complexity explosion problem of traditional backstepping methods by introducing a finite-time command filter and a fractional power error compensation mechanism, while also eliminating the influence of filtering errors, significantly improving tracking performance. Furthermore, this invention combines radial basis function neural networks to approximate unknown nonlinear dynamics, effectively handling uncertainties such as friction and wheel slippage, thereby achieving finite-time high-precision trajectory tracking control for a nonholonomic wheeled mobile robot under unknown dynamics and unmeasurable velocity conditions. Attached Figure Description

[0026] Figure 1 This is a flowchart of the trajectory tracking control method for a non-complete wheeled mobile robot in an embodiment of the present invention;

[0027] Figure 2 This is a graph showing the tracking error curves between the various states and the desired state of the incomplete wheeled mobile robot in the simulation example of this invention. Figure 2 (a), (b), (c), (d), and (e) in the figure respectively give Coordinates Tracking error diagram for coordinate position, yaw angle, speed, and yaw rate;

[0028] Figure 3 This is a state observer response curve diagram of a nonholonomic wheeled mobile robot in a simulation example of the present invention; wherein... Figure 3 In the figure, (a) represents the change of actual speed and estimated speed over time, and (b) represents the change of actual yaw rate and estimated yaw rate over time.

[0029] Figure 4 This invention presents a simulation example of a nonholonomic wheeled mobile robot under both a finite-time adaptive neural output feedback command filtering backstepping control scheme and an adaptive neural output feedback command filtering backstepping control scheme. Comparison chart of coordinate position tracking curves;

[0030] Figure 5 This invention presents a simulation example of a nonholonomic wheeled mobile robot under both a finite-time adaptive neural output feedback command filtering backstepping control scheme and an adaptive neural output feedback command filtering backstepping control scheme. Comparison chart of coordinate position tracking curves;

[0031] Figure 6 This is a comparison chart of the yaw angle tracking curves of a nonholonomic wheeled mobile robot under the finite-time adaptive neural output feedback command filtering backstepping control scheme and the adaptive neural output feedback command filtering backstepping control scheme in the simulation example of this invention.

[0032] Figure 7 This is a comparison chart of the speed tracking curves of a nonholonomic wheeled mobile robot under the finite-time adaptive neural output feedback command filtering backstepping control scheme and the adaptive neural output feedback command filtering backstepping control scheme in the simulation example of this invention.

[0033] Figure 8 This is a comparison chart of the yaw rate tracking curves of a nonholonomic wheeled mobile robot under the finite-time adaptive neural output feedback command filtering backstepping control scheme and the adaptive neural output feedback command filtering backstepping control scheme in the simulation example of this invention.

[0034] Figure 9 This is a comparison chart of the speed tracking curves of a nonholonomic wheeled mobile robot under the finite-time adaptive neural output feedback command filtering backstepping control scheme and the adaptive neural output feedback command filtering backstepping control scheme in the simulation example of this invention.

[0035] Figure 10 This is a comparison chart of the yaw rate tracking curves of a nonholonomic wheeled mobile robot under the finite-time adaptive neural output feedback command filtering backstepping control scheme and the adaptive neural output feedback command filtering backstepping control scheme in the simulation example of this invention.

[0036] Figure 11 This invention presents a simulation example of a nonholonomic wheeled mobile robot under both a finite-time adaptive neural output feedback command filtering backstepping control scheme and an adaptive neural output feedback command filtering backstepping control scheme. Comparison chart of coordinate position tracking curves. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0038] Example 1

[0039] This embodiment describes a trajectory tracking control method for a nonholonomic wheeled mobile robot. During trajectory tracking, this method employs steps such as designing an adaptive neural state observer to estimate unmeasurable velocity, generating virtual control signal derivatives using a finite-time command filter, eliminating filtering errors through an error compensation mechanism, and handling virtual control input and actual control signals. This ensures that the position tracking error and attitude tracking error converge within an arbitrarily small compact set near the origin within a finite time. This method not only avoids the computational complexity explosion problem caused by repeated differentiation of the virtual control signal in traditional backstepping methods, but also guarantees that the trajectory tracking error of the nonholonomic wheeled mobile robot converges to an arbitrarily small neighborhood within a finite time, even under conditions of unknown nonlinear dynamics and unmeasurable velocity. Furthermore, all signals in the closed-loop system are ultimately bounded.

[0040] like Figure 1 As shown, the trajectory tracking control method for a non-holonomic wheeled mobile robot in this embodiment includes the following steps:

[0041] Step 1. Establish the kinematic and dynamic model of the nonholonomic wheeled mobile robot.

[0042] The kinematic and dynamic model of a nonholonomic wheeled mobile robot is defined as follows:

[0043] (1)

[0044] in and Relative coordinates to the ground Yaw angle Let be the longitudinal velocity in the volume coordinate system. Yaw rate in body coordinate system; longitudinal force and torque To control input; function and Used to describe friction and external disturbances. All position and velocity measurements are taken at the rear axle midpoint, with lateral velocity constrained to zero.

[0045] Step 2. Under the conditions of unknown nonlinear dynamics and unmeasurable velocity, design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot. The specific design process is as follows:

[0046] First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate a virtual control derivative. An error compensation mechanism is constructed to eliminate filtering errors. A radial basis function neural network is used to approximate the unknown nonlinear dynamics so that the trajectory tracking error converges to any small compact set near the origin in a finite time. At the same time, it is ensured that all signals of the closed-loop system are eventually bounded, thus completing the controller design.

[0047] For a compact set and a continuous function There exists a radial basis function neural network that approximates an unknown nonlinear function for any... There always exists a radial basis function neural network. , represented as:

[0048] ;

[0049] in To approximate the error, Ω denotes compact set. For the ideal weight vector, The first element representing the ideal weight vector One element; is the basis function vector.

[0050] in The first basis function vector represents the basis function vector. There are 1 elements, where M > 1 represents the number of neuron nodes.

[0051] Each basis function is defined as:

[0052] ;

[0053] in As the center vector, The first vector is the center vector. One element; This is the width parameter.

[0054] Therefore, for unknown nonlinear functions and There are positive numbers and , so that for any It satisfies the Lipschitz continuity condition:

[0055] (2)

[0056] in This represents the first input vector. , These represent the longitudinal velocity and yaw rate of the robot's first input vector in the volume coordinate system, respectively. This represents the second input vector. , These represent the longitudinal velocity and yaw rate of the robot's second input vector in the volume coordinate system, respectively. Represents absolute value. It represents the distance between two states (Euclidean norm).

[0057] For any positive parameter and The extended finite-time Lyapunov criterion is stated as follows:

[0058] ;

[0059] Convergence time The upper bound is: ;

[0060] in It is a Lyapunov function. It is the start time.

[0061] For the system If there exists a continuous function and normal numbers satisfy If the system trajectory is stable in a finite time, then the system trajectory is stable.

[0062] For any positive constant j > 0 and o > 0, we have:

[0063] (3)

[0064] in, Represent a scalar function that takes real values. For the variables selected later.

[0065] Step 2.1. Design an adaptive neural state observer to estimate unmeasurable velocity states.

[0066] The adaptive neural state observer is designed as follows:

[0067] (4)

[0068] in and Design parameters for observer gain. , , , They correspond to as , , , The estimate; , Represents the ideal weight vector The approximation value. and For radial basis function neural networks to handle unknown nonlinear functions and Online estimates.

[0069] .

[0070] According to the radial basis function neural network approximation principle, there exists an ideal weight vector. Make and ;in Representing the approximation error, and outputting the estimated radial basis function network by defining... );in express approximation value, .

[0071] Indicates the first The upper bound of the approximation error of a radial basis function neural network, and the approximation error is determined by... Give, and This represents the basis function vector in a radial basis function neural network.

[0072] Functional error caused by state deviation is and Provided.

[0073] Based on formulas (1) and (4), the dynamic derivation of the observer error is as follows:

[0074] (5)

[0075] Define Lyapunov functions :

[0076] (6)

[0077] Differentiating formula (6) and applying Young's inequality, we get:

[0078] (7)

[0079] The variable representing the tracking error is introduced as follows:

[0080] (8)

[0081] in For the desired trajectory value, This is the filtered output. These represent the virtual yaw angle, virtual longitudinal velocity, and virtual yaw rate after processing by the command filter, respectively.

[0082] Step 2.2. Introduce a finite-time command filter.

[0083] make For virtual control vectors, For the filtered output, where , , These represent the virtual yaw angle, virtual longitudinal speed, and virtual yaw rate, respectively.

[0084] The finite-time command filter is designed in the following form:

[0085] (9)

[0086] in Indicates the output of the filter. It is an auxiliary variable. and A positive constant; This represents the output derivative estimate of the filter. ,and Selecting positive design parameters and In the case where the input disturbance is absent, the following relationship holds exactly after a transient phase of finite duration:

[0087] (10)

[0088] Furthermore, the solution of the corresponding dynamic system reaches stability in a finite time; where This represents the virtual control vector.

[0089] Consider satisfying The input noise; after reaching finite-time stability, the following inequalities hold:

[0090] (11)

[0091] in and This indicates that it depends only on the positive constant of the selected parameter of the differentiator. A positive constant; This represents the upper bound constant of the input noise amplitude.

[0092] Step 2.3. Controller signal design.

[0093] For ease of subsequent analysis, the dynamic position is restated as follows:

[0094] (12)

[0095] in express derivative, express Derivative.

[0096] The virtual control variables and command filter variables are expressed using the same function, as shown in formula (13):

[0097] (13)

[0098] in and Indicates virtual control input. and This represents the filtered virtual control input.

[0099] Virtual longitudinal velocity and virtual yaw angle By reversing the previous equation of formula (13), its calculation formula is as follows:

[0100] (14)

[0101] The following error signals are defined as:

[0102] (15)

[0103] in Represents the global Directional velocity tracking error, Represents the global Directional velocity tracking error.

[0104] and The position is dynamically represented as:

[0105] (16)

[0106] For the design of control signals, virtual control input The construction is as follows:

[0107] (17)

[0108] in It is about controlling the gain. and It is a positive constant.

[0109] and The position error is dynamically given as follows:

[0110] (18)

[0111] item and By adding or subtracting vectors The transformation results in the following form:

[0112] (19)

[0113] in:

[0114] and (20)

[0115] Defined as:

[0116] (twenty one)

[0117] Then, substituting formulas (16), (17), and (19) into (18), we get:

[0118] (twenty two)

[0119] For yaw control, define the following signals:

[0120] (twenty three)

[0121] in It is about controlling the gain. ,and It is a positive constant.

[0122] Tracking error The time derivative is described as follows:

[0123] (twenty four)

[0124] The longitudinal force and torque are designed as follows:

[0125] (25)

[0126] in , It is the control gain; under this control input design, and The time derivative of the tracking error is:

[0127] (26)

[0128] Finally, the finite-time adaptive neural output feedback command filtering backstepping controller is designed as follows: (27)

[0129] in and Indicates the inverse term. and This indicates a signal to compensate for tracking errors. , These represent longitudinal force and torque, respectively. For the desired trajectory value, the parameters and Indicates a positive design gain;

[0130] constant satisfy ,and A positive constant; a user-defined parameter Used to determine the sign of the desired longitudinal velocity in the body coordinate system; Used to calculate the angle corresponding to the difference between two coordinates.

[0131] Step 2.4. Error compensation signal design.

[0132] Compensation tracking error signal and The definition is as follows:

[0133] (28)

[0134] in , , , , This represents the error compensation signal; the error compensation signal and Defined as:

[0135] (29)

[0136] in initial value , initial value ; and It is a normal number.

[0137] The time derivative for compensating for tracking errors is expressed as follows:

[0138] (30)

[0139] Error compensation signal The definition is as follows:

[0140] (31)

[0141] in initial value , It is a positive constant; The time derivative is as follows:

[0142] (32)

[0143] Error compensation signal and The error is always equal to zero, and the compensation tracking error dynamically becomes:

[0144] (33)

[0145] The command filtering backstepping method proposed in this invention not only solves the complexity explosion problem through the command filter, but also introduces an error compensation mechanism to eliminate filtering errors and improve the system tracking performance.

[0146] After constructing a finite-time adaptive neural output feedback command filtering backstepping controller, a stability analysis is performed on the constructed finite-time adaptive neural output feedback command filtering backstepping controller. The specific process is as follows:

[0147] Define Lyapunov functions :

[0148] (34)

[0149] in and Indicates a positive design parameter.

[0150] The derivative is:

[0151] (35)

[0152] To offset the sign uncertainty in the aforementioned expression, the backstep error variable is introduced as follows:

[0153] (36)

[0154] Unknown parameters and Further estimation is performed using the following adaptive law:

[0155] (37)

[0156] in and Indicates a positive design parameter.

[0157] Then, substituting formulas (36) and (37) into (35), and based on Young's inequality, we obtain:

[0158] (38)

[0159] For error compensation systems, the Lyapunov function is chosen. for:

[0160] (39)

[0161] Then we have:

[0162] (40)

[0163] function For all Bounded; , This indicates the error compensation signal.

[0164] Due to the properties of trigonometric functions and the removal of singularities through limit analysis, Each component remains finite.

[0165] For a finite-time command filter, it is known that the command filter variable... Bounded; therefore, from formula (20), we know that It is a bounded matrix; therefore, it has positive constants. and Make The absolute values ​​of the components satisfy And it satisfies the inequality. and In a limited time Post-satisfaction .

[0166] in Indicates the filtered result Directional velocity components and the original The maximum permissible deviation of the directional velocity component. Indicates the filtered result Directional velocity components and the original The maximum permissible deviation of the directional velocity component. This indicates the maximum permissible deviation between the filtered yaw angle and the original yaw angle command. Subsequently, for... ,have:

[0167] (41)

[0168] Then, Substituting (41) into (40) and based on Young's inequality, we get:

[0169] (42)

[0170] also:

[0171] (43)

[0172] Consider the following Lyapunov functions :

[0173] (44)

[0174] Differentiate the Lyapunov function (44) along the closed-loop system, and add and subtract nonnegative terms in the analysis. , .in , , , , , , , , , , , .

[0175] This represents a positive design gain parameter, and To facilitate analysis within a limited timeframe.

[0176] According to formula (3), where ,have:

[0177] (45)

[0178] Apply inequality (45) to define the introduced terms. And rearrange, Rewritten in a compact form:

[0179] (46)

[0180] Define the parameter set as follows:

[0181] (47)

[0182] Then in formula (46) , and Compact representation is:

[0183] (48)

[0184] Therefore, (46) is represented as:

[0185] (49)

[0186] or:

[0187] (50)

[0188] The estimation error, the compensation tracking error signal, the tracking error, and the error compensation signal are defined as follows:

[0189] (51)

[0190] in .

[0191] if Then (49) equals: .

[0192] According to the finite-time stability theory given above, The reduction will make , , , Enter exist Inside.

[0193] if Then (50) equals ;

[0194] Similarly, The reduction will make , , , Enter exist Inside.

[0195] therefore, , It will converge to:

[0196] (52)

[0197] exist ,have:

[0198] (53)

[0199] Signal and It is always equal to zero; therefore:

[0200] (54)

[0201] (55)

[0202] In a limited time Within this loop, all closed-loop signals eventually become bounded; this completes the proof.

[0203] Step 3. Using the finite-time adaptive neural output feedback command filtering backstepping controller constructed in Step 2, the trajectory tracking control of the nonholonomic wheeled mobile robot is realized.

[0204] First, using the position and attitude data transmitted back by the nonholonomic wheeled mobile robot, the unmeasurable velocity state is estimated through an adaptive neural state observer, and the virtual control input, neural network approximation signal, and adaptive compensation signal are calculated.

[0205] Using the virtual control input as the input to the finite-time command filter, the filtered virtual control derivative and the filtered output signal are obtained. At the same time, the error compensation signal is calculated to eliminate the filtering error, and finally the actual control signal (longitudinal force and torque) is obtained. The calculated control signal is then transmitted to the nonholonomic wheeled mobile robot to achieve control.

[0206] The method of this invention ensures that the position tracking error and attitude tracking error of a nonholonomic wheeled mobile robot converge to an arbitrarily small compact set near the origin within a finite time. This method not only effectively avoids the computational complexity explosion problem caused by repeated differentiation of virtual control signals in traditional backstepping methods, but also eliminates the filtering error introduced by the finite-time command filter through an error compensation mechanism. Furthermore, it effectively handles unknown nonlinear dynamics (such as friction and wheel slip) using a radial basis function neural network. Therefore, the control method of this invention not only has excellent uncertainty resistance but also strong practicality.

[0207] The present invention method will be compared with the adaptive neural output feedback command filtering backstepping tracking control scheme that removes the finite time term (hereinafter referred to as the comparison scheme) by conducting simulation analysis and experimental verification.

[0208] It should be noted that the comparison scheme here is not an existing technical solution, but is only used to verify the improvement of the steady-state accuracy and convergence speed of the system by the finite time term in the method of the present invention. Therefore, only the finite time term has been removed.

[0209] In the simulation, the model parameters of the method of the present invention and the comparative scheme for a non-complete wheeled mobile robot are shown in Table 1.

[0210] Table 1. Comparison of model parameters of nonholonomic wheeled mobile robots under the control of the method of the present invention and the comparative scheme.

[0211]

[0212] In this embodiment, external interference is defined as: =1, friction force is defined as: =1.

[0213] The initial state is defined as: .

[0214] Expectation is defined as: , Desired yaw angle linear velocity and yaw rate From the expected trajectory Generation, i.e. and These represent the expected positions of the reference trajectories. Coordinates, desired location Coordinates, desired yaw angle, desired longitudinal speed, and desired yaw rate.

[0215] In the simulation, the parameter selection of the controller in the method of the present invention and the comparison scheme is shown in Table 2:

[0216] Table 2 Parameters of the controller in the method of the present invention and the comparative scheme

[0217]

[0218] In the experiment, the model parameters of the incomplete wheeled mobile robot of the method of the present invention and the comparative scheme are shown in Table 3:

[0219] Table 3. Model parameters of the incomplete wheeled mobile robot of the present invention method and comparative scheme.

[0220] External interference is defined as: =1, friction force is defined as: =1;

[0221] The initial state is defined as: .

[0222] Expectation is defined as: , Reference yaw angle linear velocity and yaw rate From the expected trajectory generate.

[0223] In the experiment, the parameter selection of the controller under the method of the present invention and the comparative scheme is shown in Table 4.

[0224] Table 4 Parameters of the controller in the method of the present invention and the comparative scheme

[0225] Simulation results are as follows Figures 2 to 8 As shown, where:

[0226] Figure 2 (a), (b), (c), (d), and (e) in the figure give the states respectively. Coordinates The tracking error graph (coordinate position, yaw angle, speed, yaw rate) confirms that it converges to the desired trajectory quickly and accurately.

[0227] Figure 3 The response curves of the state observer are given, where Figure 3 In the figure, (a) represents the changes in actual speed and estimated speed over time. Figure 3 In the figure, (b) shows the changes in the actual yaw rate and the estimated yaw rate over time.

[0228] Depend on Figure 3 As can be seen from (a) and (b) in the figure, the present invention achieves accurate estimation of unmeasurable velocity states.

[0229] Figure 4 The response curves of the x-coordinate of the method of the present invention and the comparative scheme are presented.

[0230] The x-coordinate controlled by this invention can quickly and smoothly approximate the desired trajectory, with the curve almost coinciding with the desired value. The convergence process is smooth and without obvious deviation, fully demonstrating the rapid tracking capability and high precision of this method in the x-direction.

[0231] Figure 5 The response curves of the y-coordinate of the method of the present invention and the comparative scheme are presented.

[0232] This invention exhibits extremely high tracking accuracy in the y-direction, with the response curve closely following the expected value and a very smooth transition, with almost no overshoot or fluctuations, demonstrating the excellent adaptability and control effect of this method for dynamic changes in the y-direction.

[0233] Figure 6 The response curves of the yaw angle for the method of the present invention and the comparative scheme are presented.

[0234] This invention enables the yaw angle to be quickly adjusted to the desired value, with agile and stable curve changes. Errors are effectively suppressed in a short time, almost coinciding with the desired trajectory, demonstrating excellent dynamic response capabilities when dealing with yaw adjustments caused by nonholonomic constraints.

[0235] Figure 7 The response curves of the longitudinal velocity of the method of the present invention and the comparative scheme are presented.

[0236] The longitudinal speed change controlled by this invention is extremely smooth, and it can quickly reach and stabilize near the desired speed. The curve transition is natural, without overshoot or obvious fluctuations, which reflects the accuracy and robustness of this method in speed control.

[0237] Figure 8 The response curves of the yaw rate for the method of the present invention and the comparative scheme are presented.

[0238] The method of this invention provides the most precise control over yaw rate, with the response curve closely following the expected value. The changes are rapid and stable, with almost no oscillations or overshoot, fully demonstrating the high efficiency and high performance of this method under torque input control.

[0239] Experimental results are as follows Figure 9-11 As shown, Figure 9-11 The speeds of the method of this invention and the comparative scheme are given. Yaw rate and The response curves of the trajectory show that the method of the present invention can achieve faster convergence speed and higher tracking performance.

[0240] Example 2

[0241] This embodiment 2 describes a trajectory tracking control system for a non-complete wheeled mobile robot, which is based on the same inventive concept as the trajectory tracking control method for the non-complete wheeled mobile robot in embodiment 1 above.

[0242] A trajectory tracking control system for a non-holonomic wheeled mobile robot includes the following modules:

[0243] The model building module is used to build kinematic and dynamic models of nonholonomic wheeled mobile robots.

[0244] The controller construction module is used to design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot under unknown nonlinear dynamics and unmeasurable velocity conditions. The specific design process is as follows:

[0245] First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate virtual control derivatives. An error compensation mechanism is constructed to eliminate filtering errors. Radial basis function neural networks are used to approximate the unknown nonlinear dynamics so that the trajectory tracking error converges to any small compact set near the origin in a finite time. At the same time, it is ensured that all signals of the closed-loop system are eventually bounded, thus completing the controller design.

[0246] And a tracking control module, which uses a finite-time adaptive neural output feedback command filtering backstepping tracking controller built using the controller construction module to realize trajectory tracking control of a nonholonomic wheeled mobile robot.

[0247] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0248] Example 3

[0249] This embodiment 3 describes a computer device used to implement the steps of the trajectory tracking control method for the incomplete wheeled mobile robot described in embodiment 1 above.

[0250] The computer device includes a memory and one or more processors. Executable code is stored in the memory, which, when executed by the processor, provides steps for implementing a trajectory tracking control method for a nonholonomic wheeled mobile robot.

[0251] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0252] Example 4

[0253] This embodiment 4 describes a computer-readable storage medium for implementing the steps of the trajectory tracking control method for the non-holonomic wheeled mobile robot described in embodiment 1 above.

[0254] The computer-readable storage medium in this embodiment 4 stores a program that, when executed by a processor, implements the steps of a trajectory tracking control method for a non-holonomic wheeled mobile robot.

[0255] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0256] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A trajectory tracking control method for a non-holonomic wheeled mobile robot, characterized in that, Includes the following steps: Step 1. Establish the kinematic and dynamic model of the nonholonomic wheeled mobile robot; Step 2. Under the conditions of unknown nonlinear dynamics and unmeasurable velocity, design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot. The specific design process is as follows: First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate virtual control derivatives. An error compensation mechanism is constructed to eliminate filtering errors. A radial basis function neural network is used to approximate the unknown nonlinear dynamics, while ensuring that all signals of the system are eventually bounded, thus completing the controller design. The finite-time adaptive neural output feedback command filtering backstepping controller is designed as follows: ; in , , These represent the virtual yaw angle, virtual longitudinal speed, and virtual yaw rate, respectively. and Indicates the inverse term. and This indicates a signal to compensate for tracking errors. , These represent longitudinal force and torque, respectively. The desired trajectory value; parameters and Indicates a positive design gain; and For radial basis function neural networks and Online estimation; These represent the virtual yaw angle, virtual longitudinal velocity, and virtual yaw rate after processing by the command filter, respectively. , , , , Variables representing tracking error; constant satisfy ,and A positive constant; a user-defined parameter Used to determine the sign of the desired longitudinal velocity in the body coordinate system; Used to calculate the angle corresponding to the difference between two coordinates; Step 3. Using the controller built in Step 2, implement trajectory tracking control for the non-holonomic wheeled mobile robot.

2. The trajectory tracking control method for a non-holonomic wheeled mobile robot according to claim 1, characterized in that, Step 1 specifically involves: The kinematic and dynamic model of a nonholonomic wheeled mobile robot is defined as follows: (1) in and Relative coordinates to the ground; Yaw angle Let be the longitudinal velocity in the robot's body coordinate system. Yaw rate in the robot's body coordinate system; longitudinal force and torque For control input; and Both are unknown nonlinear functions, and are used to describe friction and external disturbances, respectively.

3. The trajectory tracking control method for a complete wheeled mobile robot according to claim 2, characterized in that, In step 2, for a compact set and a continuous function There exists a radial basis function neural network that approximates an unknown nonlinear function for any... There always exists a radial basis function neural network. : ； in To approximate the error, Ω denotes compact set. For the ideal weight vector, The first element representing the ideal weight vector One element; A vector of basis functions; The first basis function vector represents the basis function vector. There are elements, where M > 1 represents the number of neuron nodes; each basis function is defined as: ； in As the center vector, The first vector is the center vector. One element; For width parameters; Therefore, for unknown nonlinear functions and There are positive numbers and , such that for any It satisfies the Lipschitz continuity condition: (2) in This represents the first input vector. This represents the second input vector; , These represent the longitudinal velocity and yaw rate of the robot's first input vector in the volume coordinate system, respectively. , These represent the longitudinal velocity and yaw rate of the robot's second input vector in the volume coordinate system, respectively. This indicates the calculation of absolute value. This indicates the calculation of the distance between two states; For any positive parameter , and The extended finite-time Lyapunov criterion is stated as follows: ； Convergence time The upper bound is: ； in It is a Lyapunov function. It is the start time; For the system If there exists a continuous function and normal numbers , , , satisfy Then the system trajectory is actually stable in a finite time; For any positive constant j > 0 and o > 0, we have: (3) in, Represent a scalar function that takes real values. For the variables selected later.

4. The trajectory tracking control method for a non-holonomic wheeled mobile robot according to claim 3, characterized in that, In step 2, an adaptive neural state observer is designed to estimate the unmeasurable velocity state; The adaptive neural state observer is designed as follows: (4) in , , , They correspond to as , , , The estimate; and Design parameters for observer gain; , Represents the ideal weight vector Approximation value; and For radial basis function neural networks and Online estimation; ； According to the radial basis function neural network approximation principle, there exists an ideal weight vector. Make: and ; in The approximation error is represented by the estimated radial basis function network output as follows: );in express Approximation value; Indicates the first The upper bound of the approximation error of a radial basis function neural network, and the approximation error is determined by... Give; and This represents the basis function vector in a radial basis function neural network. 1,2; Functional error caused by state deviation is and Give; Based on formulas (1) and (4), the dynamic derivation of the adaptive neural state observer error is as follows: (5) Define Lyapunov functions : (6) Differentiating formula (6) and applying Young's inequality, we get: (7) Introduce a variable to represent tracking error , , , , They are respectively: (8) in For the desired trajectory value, This is the filtered output.

5. The trajectory tracking control method for a non-holonomic wheeled mobile robot according to claim 4, characterized in that, In step 2, a finite-time command filter is introduced, as follows: make For virtual control vectors, For filtered output; The finite-time command filter is designed in the following form: (9) in Indicates the output of the filter. It is an auxiliary variable. and A positive constant; This represents the output derivative estimate of the filter. ,and Selecting positive design parameters and In the case where the input disturbance is absent, the following relationship holds exactly after a transient phase of finite duration: (10) Furthermore, the solution of the corresponding dynamic system reaches stability in a finite time; where Represent the virtual control vector; consider satisfying The input noise; after reaching finite-time stability, the following inequalities hold: (11) in and This indicates that it depends only on the positive constant of the selected parameter of the differentiator. A positive constant; This represents the upper bound constant of the input noise amplitude.

6. The trajectory tracking control method for a non-holonomic wheeled mobile robot according to claim 5, characterized in that, In step 2, the controller signal design process is as follows: For ease of subsequent analysis, the dynamic position is restated as follows: (12) in express derivative, express Derivative; The virtual control variables and command filter variables are expressed using the same function, as shown in formula (13): (13) in and Indicates virtual control input. and This represents the filtered virtual control input; Virtual longitudinal velocity and virtual yaw angle By reversing the previous equation of formula (13), its calculation formula is as follows: (14) The following error signals are defined as: (15) in Represents the global Directional velocity tracking error, Represents the global Directional velocity tracking error; and The position is dynamically represented as: (16) For the design of control signals, virtual control input The construction is as follows: (17) in It is about controlling the gain. and It is a positive constant; and The position error is dynamically given as follows: (18) item and By adding or subtracting vectors The transformation results in the following form: (19) in: and (20) Defined as: (21) Then, substituting formulas (16), (17), and (19) into (18), we get: (22) For yaw control, define the following signals: (23) in It is about controlling the gain. ,and It is a positive constant; Tracking error The time derivative is described as follows: (24) The longitudinal force and torque are designed as follows: (25) in , It is the control gain; under this control input design, and The time derivative of the tracking error is: (26) Finally, the finite-time adaptive neural output feedback command filtering backstepping controller is designed as follows: (27) in and Indicates the inverse term. and This indicates a signal to compensate for tracking errors. , These represent longitudinal force and torque, respectively. For the desired trajectory value, the parameters and Indicates a positive design gain; constant satisfy ,and A positive constant; a user-defined parameter Used to determine the sign of the desired longitudinal velocity in the body coordinate system; Used to calculate the angle corresponding to the difference between two coordinates.

7. The trajectory tracking control method for a non-holonomic wheeled mobile robot according to claim 6, characterized in that, In step 2, the error compensation signal design process is as follows: Compensation tracking error signal and The definition is as follows: (28) in , , , , This represents the error compensation signal; the error compensation signal and Defined as: (29) in initial value , initial value ; and It is a positive number; The time derivative for compensating for tracking errors is expressed as follows: (30) Error compensation signal The definition is as follows: (31) in initial value , It is a positive constant; The time derivative is as follows: (32) Error compensation signal and The value is always equal to zero, and the compensation tracking error dynamically becomes: (33)。 8. A trajectory tracking control system for a nonholonomic wheeled mobile robot for implementing the trajectory tracking control method for a nonholonomic wheeled mobile robot as described in claim 1, characterized in that, The trajectory tracking control system of the incomplete wheeled mobile robot includes the following modules: The model building module is used to build kinematic and dynamic models of nonholonomic wheeled mobile robots. The controller construction module is used to design a finite-time adaptive neural output feedback command filtering backstepping tracking controller for a nonholonomic wheeled mobile robot under unknown nonlinear dynamics and unmeasurable velocity conditions. The specific design process is as follows: First, an adaptive neural state observer is designed to estimate the unmeasurable velocity state. Then, a finite-time command filter is introduced to avoid complexity explosion and generate virtual control derivatives. An error compensation mechanism is constructed to eliminate filtering errors. A radial basis function neural network is used to approximate the unknown nonlinear dynamics, while ensuring that all signals of the system are eventually bounded, thus completing the controller design. And a tracking control module, which uses a finite-time adaptive neural output feedback command filtering backstepping tracking controller built using the controller construction module to realize trajectory tracking control of a nonholonomic wheeled mobile robot.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the trajectory tracking control method for a non-holonomic wheeled mobile robot as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the trajectory tracking control method for a non-holonomic wheeled mobile robot as described in any one of claims 1 to 7.

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