Ground adaptive mobile robot control method based on Lyapunov stability and backstepping method

Abstract

The invention relates to a ground adaptive mobile robot control method based on Lyapunov stability and a backstepping method, and the method specifically comprises the steps: building a mobile robot motion model which comprises a mobile coordinate system and a fixed reference coordinate system, and constructing an error prediction parameter of a mobile robot; designing a Lyapunov function V1 (x) containing a saturation function according to the error prediction parameters, deducing and calculating an expected control rate omega d of the mobile robot, introducing auxiliary control input v, calculating a steering rate error e omega of the mobile robot according to the auxiliary control input v, and designing a Lyapunov function V2 (x1) containing the saturation function according to the error prediction parameters; in combination with the expected control rate omega d of the mobile robot, auxiliary control input v is obtained through deduction and calculation according to a backstepping method, and finally a real-time steering speed instruction omega c of the mobile robot is obtained through calculation according to the auxiliary control input v.

Description

Technical Field

[0001] The present invention relates to the technical field of robot control, in particular to a ground adaptive mobile robot control method based on Lyapunov stability and backstepping method. Background Art

[0002] Generally speaking, control methods can be divided into linear and nonlinear techniques. When linear methods are used, traditional proportional-integral-derivative (PID) control and some robust control methods are usually used.

[0003] Among the existing technologies, path following methods based on Lyapunov stability are particularly interesting. In "Path Following Control Algorithm for a Skid-Steering Mobile Robot Based on Adaptive Discontinuous Posture Control," Ibrahim et al. designed a point-to-point following algorithm for following a trajectory defined by a set of waypoints. In "Integrated Force Control for Four-Wheel Steered Vehicle Based on Sliding Mode Steering Control and Particle Swarm Optimization," Dai et al. applied sliding mode control techniques to derive steering control commands. In "Coupled Fractional-Order Sliding Mode Control and Obstacle Avoidance for a Four-Wheel Steerable Mobile Robot," Xie et al. developed a collision-free trajectory tracking controller for a four-wheeled mobile robot that combined a novel coupled fractional-order sliding mode control with an obstacle avoidance scheme. In "Path Following Control of a Wheeled Mobile Robot Based on Online Optimization of a Guidance Vector Field," Chen et al. proposed a controller based on a guidance vector field that enables the mobile robot to follow a desired path with acceptable error under uncertainties, including surface friction, unmodeled dynamics, and disturbances. In "Dynamic Sliding Mode Controller for Trajectory Tracking of a Nonholonomic Mobile Robot," a robust sliding mode control for following circular paths was proposed and its stability was demonstrated using a Lyapunov direct method. In the paper "Output Feedback Control of a Skid-Steering Mobile Robot Based on a Supertorsion Algorithm," Salgado et al. designed a state-feedback controller for a mobile robot based on the supertorsion algorithm and compared it with state feedback and first-order sliding mode control. In "Path Following Control of an Underactuated Robot with Arbitrary Path Curvature," Moro et al. proposed a simple path-following method that achieves asymptotic convergence for general 2D curves. For other realistic nonholonomic vehicles, vector field and nested saturation techniques were primarily investigated for linear and circular paths.

[0004] From the preceding discussion, we can see that Lyapunov stability-based methods can produce simple and useful steering control methods. Some studies consider the robot's dynamic model, but this model is too complex, requiring more accurate modeling and higher computational costs. In other studies, path-following controllers only consider the kinematic model without considering the dynamic model, which can degrade following performance. Summary of the Invention

[0005] In order to solve the problems existing in the above-mentioned prior art, this application considers the first-order approximate steering dynamic characteristics and kinematic model, and designs a steering control method using backstepping and Lyapunov stability theory; the present invention proposes a ground adaptive mobile robot control method based on Lyapunov stability and backstepping.

[0006] The technical solutions of the present invention are as follows:

[0007] The present invention proposes a ground adaptive mobile robot control method based on Lyapunov stability and backstepping method, which is characterized by the following specific steps:

[0008] A mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is established, and error prediction parameters of the mobile robot are constructed. The error prediction parameters include the virtual distance error e d and heading angle error e θ ;

[0009] According to the virtual distance error e d and heading angle error e θ Construct an error kinematics model of a mobile robot;

[0010] Based on the virtual distance error e d and heading angle error e θ Design a Lyapunov function V1(x) containing a saturation function and derive the expected control rate ω of the mobile robot d , and then combined with the error motion model to verify the stability of the mobile robot motion;

[0011] The first-order approximate model of steering dynamics and the auxiliary control input v are introduced, and the steering rate error e of the mobile robot is calculated according to the auxiliary control input v. ω , and then build the steering dynamics model of the mobile robot in combination with the error kinematics model of the mobile robot;

[0012] Based on the steering rate error e ω , virtual distance error e d and heading angle error e θ Design a Lyapunov function V2(x1) containing a saturation function, derive and calculate the auxiliary control input v of the mobile robot using the backstepping method, and then verify the stability of the mobile robot's motion by combining it with the steering dynamics model;

[0013] In a mixed road environment, the adaptive variation coefficient of the first-order approximate model of steering dynamics is identified and adjusted by a controlled experiment method, and then combined with the expected control rate ω of the mobile robot dThe real-time steering speed instruction ω of the mobile robot is calculated by the auxiliary control input v c .

[0014] As a preferred embodiment, the establishment of a mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is specifically as follows:

[0015] Define a fixed reference coordinate system XOY, and establish a mobile coordinate system xoy with the center of mass of the mobile robot as the origin;

[0016] The calculation formulas for the mobile robot's moving speed V and rotation speed ω are as follows:

[0017]

[0018] Where, ω l is the rotation speed of the left wheel of the mobile robot, ω r The rotation speed of the right wheel of the mobile robot; R is the wheel radius, 2f is the distance between the left and right wheels;

[0019] The kinematic model of the mobile robot is established based on the mobile coordinate system xoy:

[0020]

[0021] Where x and y are the coordinates of the center of mass of the mobile robot in the fixed reference coordinate system XOY, θ is the heading of the mobile robot in the two-dimensional coordinate system, ω is the rotation speed of the mobile robot, and l is the distance between the rotation center and the center of mass of the mobile robot;

[0022] When the distance between the rotation center and the center of mass of the mobile robot is less than a preset threshold, the above formula is simplified to:

[0023]

[0024] The simplified formula is used as the final kinematic model of the mobile robot.

[0025] As a preferred embodiment, the virtual distance error e d and heading angle error e θ The calculation formula is as follows:

[0026] Define the virtual distance error e d The calculation formula is as follows:

[0027] e d =f(x,y);

[0028] Where f(x,y) is a continuous quadratically differentiable function;

[0029] Virtual distance error ed Taking the derivative, the calculation formula is as follows:

[0030]

[0031] Where, f x and f y are the first-order partial derivatives of the function f(x,y) with respect to the variables x and y, V is the moving speed of the mobile robot, θ is the actual heading of the mobile robot, is the gradient modulus of the function f(x,y);

[0032] Among them, the gradient mode The calculation formula is as follows:

[0033] Preset heading angle error e θ The calculation formula is as follows:

[0034] e θ =θ-θ d ;

[0035] Where θ is the actual heading of the mobile robot, θ d is the desired heading of the mobile robot; the desired heading of the mobile robot is calculated according to the first-order partial derivatives of the desired trajectory function with respect to the variables x and y.

[0036] As a preferred embodiment, the virtual distance error e d and heading angle error e θ The specific steps to construct the error kinematics model of the mobile robot are:

[0037] Virtual distance error e d and heading angle error e θ The derivatives of together constitute the error kinematics model of the mobile robot, and the function formula is as follows:

[0038]

[0039] As a preferred embodiment, the virtual distance error e d and heading angle error e θ The specific steps for designing the Lyapunov function V1(x) including the saturation function are:

[0040] Define the set D1 = {(e d ,e θ )||e d ≤e d0 ,|e θ |<π}, where e d0 is a fixed positive number; let x=(e d ,e θ )T , construct the Lyapunov function V1(x) containing the saturation function, the function formula is as follows:

[0041]

[0042] In the formula, k1 is a fixed positive number, f sat (y) is the saturation function; x is the virtual distance error e d and heading angle error e θ The variable point constructed together, x=(e d ,e θ ) T , T is the transposition mark;

[0043] Among them, the saturation function f sat The definition formula of (y) is as follows:

[0044]

[0045] Where the parameter y0 is a given positive constant.

[0046] As a preferred embodiment, the expected control rate ω of the mobile robot is derived and calculated. d The specific steps are:

[0047] The derivative of the Lyapunov function V1(x) containing the saturation function with respect to time is obtained. The specific formula is as follows:

[0048]

[0049] according to Non-positive definite selection of expected control rate ω d , the specific selection formula is as follows:

[0050]

[0051] Where k2 is a known positive constant.

[0052] As a preferred embodiment, the steps of introducing the first-order approximate model of steering dynamics and the auxiliary control input v, and constructing the steering dynamics model of the mobile robot according to the auxiliary control input ν and the error kinematics model of the mobile robot are specifically as follows:

[0053] The first-order dynamic approximation model is specifically:

[0054]

[0055] Where, ω c is the speed command, α ω Adaptive change coefficient according to the change of road conditions; ω is the rotation speed of the mobile robot;

[0056] The calculation formula of the preset auxiliary control input ν is specifically:

[0057]

[0058] At the same time, the steering rate error e is preset ω The calculation formula is:

[0059] e ω =ω-ω d ;

[0060] The steering rate error e ω Take the derivative:

[0061]

[0062] Combined with the error kinematics model of the mobile robot, the steering dynamics model of the mobile robot can be obtained. The specific function formula is as follows:

[0063]

[0064] As a preferred embodiment, the steering rate error e ω , virtual distance error e d and heading angle error ν θ The specific steps for designing the Lyapunov function V2(x1) including the saturation function are:

[0065] Definition D2 = {(e d ,e θ ,e ω )||e d |≤e d1 ,|e θ |<π,|e ω |≤e ω1}, where e ω1 is a normal quantity; preset x1=(e d ,e θ ,e ω ) T , construct the Lyapunov function V2(x1) containing the saturation function, the function formula is as follows:

[0066]

[0067] As a preferred embodiment, the step of deriving and calculating the auxiliary control input v of the mobile robot according to the backstepping method is specifically as follows:

[0068] The derivative of the Lyapunov function V2(x1) containing the saturation function with respect to time is obtained. The specific formula is as follows:

[0069]

[0070] The desired control rate ω is selected d Substituting into the derivative, we get:

[0071]

[0072] Based on The auxiliary control input v is selected as non-positive definite. The specific selection formula is as follows:

[0073]

[0074] Where k ω is a known normal quantity.

[0075] As a preferred embodiment, the real-time steering speed instruction ω of the mobile robot c The specific calculation formula is:

[0076]

[0077] Where ω is the real-time steering speed of the mobile robot.

[0078] The present invention has the following beneficial effects:

[0079] 1. The present invention considers both steering dynamics and kinematic models, avoiding simplification errors of pure kinematic models and improving dynamic response performance.

[0080] 2. The present invention improves the control accuracy and stability of the mobile robot by presetting Lyapunov functions V1(x) and V2(x1) containing saturation functions.

[0081] 3. The present invention identifies the changes in the adaptive variation coefficient under different road conditions, synchronously adjusts the control rate of the mobile robot, and then dynamically adjusts the steering speed instruction of the mobile robot. The mobile robot will modify its route according to the changes in the ground to adapt to the changes in the ground friction coefficient.

[0082] 4. Compared with the prior art, the present invention has lower computational complexity and meets the real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 Schematic diagram of the steps of the present invention;

[0084] Figure 2 Schematic diagram of the speed, position and parameters of the mobile robot;

[0085] Figure 3 This is a physical picture of the pavement test bench;

[0086] Figure 4 Schematic diagram of the mobile robot used in the experiment;

[0087] Figure 5 To use α ω_fixed and α ω_change Comparative diagram of following straight lines in four directions under the two methods;

[0088] Figure 6 is the parameter α in the linear path following control ω Schematic diagram of the change over time, where (a) the straight line heading 0°, (b) the straight line heading 45°, (c) the straight line heading 90°, and (d) the straight line heading 135°;

[0089] Figure 7 To use α ω_fixed and α ω_change Distance error e of the two methods for linear path following d Schematic comparison diagram, where (a) a straight line with a heading of 0°, (b) a straight line with a heading of 45°, (c) a straight line with a heading of 90°, and (d) a straight line with a heading of 135°. DETAILED DESCRIPTION

[0090] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0091] It should be understood that the step numbers used herein are only for convenience of description and are not intended to limit the order in which the steps are to be executed.

[0092] It should be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0093] The terms “include” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0094] The term "and / or" refers to and includes any and all possible combinations of one or more of the associated listed items.

[0095] Example 1:

[0096] See also Figure 1 A path following control method for a ground adaptive wheeled mobile robot is provided, and the specific steps include:

[0097] A mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is established, and error prediction parameters of the mobile robot are constructed. The error prediction parameters include the virtual distance error e d and heading angle error e θ ;

[0098] According to the virtual distance error e d and heading angle error e θ Construct an error kinematics model of a mobile robot;

[0099] Based on the virtual distance error e d and heading angle error e θ Design the Lyapunov function V1(x) containing the saturation function, and derive the expected control rate ω of the mobile robot according to the backstepping method. d , and then combined with the error motion model to verify the stability of the mobile robot motion;

[0100] The first-order approximate model of steering dynamics and the auxiliary control input v are introduced, and the steering rate error e of the mobile robot is calculated according to the auxiliary control input v. ω , and then build the steering dynamics model of the mobile robot in combination with the error kinematics model of the mobile robot;

[0101] Based on the steering rate error e ω , virtual distance error e d and heading angle error e θ Design a Lyapunov function V2(x1) containing a saturation function, derive and calculate the auxiliary control input v of the mobile robot using the backstepping method, and then verify the stability of the mobile robot's motion by combining it with the steering dynamics model;

[0102] In a mixed road environment, the adaptive variation coefficient of the first-order approximate model of steering dynamics is identified and adjusted by a controlled experiment method, and then combined with the expected control rate ω of the mobile robot d The real-time steering speed command of the mobile robot is calculated by the auxiliary control input v.

[0103] As a preferred implementation of this embodiment, the establishment of a mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is specifically as follows:

[0104] Define a fixed reference coordinate system XOY, and establish a mobile coordinate system xoy with the center of mass of the mobile robot as the origin;

[0105] The calculation formulas for the mobile robot's moving speed V and rotation speed ω are as follows:

[0106]

[0107] Where, ω l is the rotation speed of the left wheel of the mobile robot, ω r The rotation speed of the right wheel of the mobile robot; R is the wheel radius, 2f is the distance between the left and right wheels;

[0108] In this embodiment, the wheel rotation speed instruction can be calculated based on the movement speed and rotation speed instructions.

[0109] The kinematic model of the mobile robot is established based on the mobile coordinate system xoy:

[0110]

[0111] Where x and y are the coordinates of the center of mass of the mobile robot in the fixed reference coordinate system XOY, θ is the heading of the mobile robot in the two-dimensional coordinate system, ω is the rotation speed of the mobile robot, and l is the distance between the rotation center and the center of mass of the mobile robot;

[0112] In this embodiment, the movement and rotation speed of the mobile robot are controlled by a path following controller. The left and right robot wheels are controlled using a PID speed controller. The speed and position of the mobile robot and the parameters are shown in the following example. Figure 2 shown.

[0113] When the distance between the rotation center and the center of mass of the mobile robot is less than a preset threshold, the above formula is simplified to:

[0114]

[0115] The simplified formula is used as the final kinematic model of the mobile robot.

[0116] As a preferred implementation of this embodiment, the virtual distance error e d and heading angle error e θ The calculation formula is as follows:

[0117] Preset virtual distance error e d The calculation formula is as follows:

[0118] e d =f(x,y);

[0119] Where f(x,y) is a continuous quadratically differentiable function;

[0120] Virtual distance error e dTaking the derivative, the calculation formula is as follows:

[0121]

[0122] Where, f x and f y are the first-order partial derivatives of the function f(x,y) with respect to the variables x and y, respectively. V is the moving speed of the mobile robot, and θ is the heading of the mobile robot in the two-dimensional coordinate system. is the gradient modulus of the function f(x,y);

[0123] Among them, the gradient mode The calculation formula is as follows:

[0124] In this embodiment, due to the moving speed V of the mobile robot and its derivative Bounded and satisfies V P1 ≥V≥V P2 >0, where V P1 and V P2 All are normal. r ={(x,y)|f(x,y)=0,x,y∈R} is an implicit expression of the reference path, where f(x,y) is a continuous quadratically differentiable function.

[0125] In this solution, the robot's safe movement area is defined as Where λ is a positive constant. This means that safe motion control is possible only when the robot is at a point where the gradient modulus is greater than or equal to λ. In, f x ,f y ,f xx ,f xy and f yy They are all bounded.

[0126] Preset heading angle error e θ The calculation formula is as follows:

[0127] e θ =θ-θ d ;

[0128] Where θ is the heading of the mobile robot in the two-dimensional coordinate system, θ d is the desired heading of the mobile robot; the desired heading of the mobile robot is calculated according to the first-order partial derivatives of the desired trajectory function with respect to the variables x and y.

[0129] Among them, the desired heading θ of the mobile robot d The calculation formula is as follows:

[0130] The desired heading θ of the mobile robot d The calculation formula is as follows:

[0131]

[0132] Among them, the denominators in the calculation formulas are not zero.

[0133] In this embodiment, the heading angle error e can also be θ To find the derivative, specifically:

[0134]

[0135] As a preferred implementation of this embodiment, the virtual distance error e d and heading angle error e θ The specific steps to construct the error kinematics model of the mobile robot are:

[0136] Virtual distance error e d and heading angle error e θ The derivatives of together constitute the error kinematics model of the mobile robot, and the function formula is as follows:

[0137]

[0138] As a preferred implementation of this embodiment, the virtual distance error e d and heading angle error e θ The specific steps for designing the Lyapunov function V1(x) including the saturation function are:

[0139] Define the set D1 = {(e d ,e θ )||e d ≤e d0 ,|e θ |<π}, where e d0 is a fixed positive number; let x=(e d ,e θ ) T , construct the Lyapunov function V1(x) containing the saturation function, the function formula is as follows:

[0140]

[0141] In the formula, k1 is a fixed positive number, f sat (y) is the saturation function; x is the virtual distance error e d and heading angle error e θ The variable point constructed together, x=(e d ,e θ ) T , T is the transposition mark;

[0142] Among them, the saturation function f sat The definition formula of (y) is as follows:

[0143]

[0144] Where the parameter y0 is a given positive constant.

[0145] In this embodiment, the steps of verifying the stability of the mobile robot motion in combination with the error motion model are as follows: for V1(x), it is in D1-{(0,0) T}, the value of the Lyapunov function V1(x) is greater than 0. The derivative of V1(x) with respect to time is:

[0146]

[0147] according to Non-positive definite select the following control law ω d :

[0148]

[0149] Where k2 is a known positive constant. d Replacing the rotational velocity ω in the error kinematics model, the formula of the error kinematics model becomes:

[0150]

[0151] It can be noted that (0,0) T is the only equilibrium point of the error kinematics model in D1. In addition,

[0152]

[0153] From this we can find that is semi-negative definite. According to Barbalat's lemma, when t→∞, Furthermore, the control law shown in the formula of the error kinematics model can asymptotically transform e d and e θ Approaching zero.

[0154] As a preferred implementation of this embodiment, the expected control rate ω of the mobile robot is derived and calculated. d The specific steps are:

[0155] The derivative of the Lyapunov function V1(x) containing the saturation function with respect to time is obtained. The specific formula is as follows:

[0156]

[0157] according to Non-positive definite selection of expected control rate ω d , the specific selection formula is as follows:

[0158]

[0159] Where k2 is a known positive constant.

[0160] As a preferred implementation of this embodiment, the steps of introducing the first-order approximate model of steering dynamics and the auxiliary control input v, and constructing the steering dynamics model of the mobile robot according to the auxiliary control input v and the error kinematics model of the mobile robot are specifically as follows:

[0161] The first-order dynamic approximation model is specifically:

[0162]

[0163] Where, ω c is the speed command, α ω Adaptive change coefficient according to the change of road conditions; ω is the rotation speed of the mobile robot;

[0164] The calculation formula of the preset auxiliary control input v is specifically:

[0165]

[0166] At the same time, the steering rate error e is preset ω The calculation formula is:

[0167] e ω =ω-ω d ;

[0168] The steering rate error e ω Take the derivative:

[0169]

[0170] Combined with the error kinematics model of the mobile robot, the steering dynamics model of the mobile robot can be obtained. The specific function formula is as follows:

[0171]

[0172] As a preferred implementation of this embodiment, the steering rate error e ω , virtual distance error e d and heading angle error e θ The specific steps for designing the Lyapunov function V2(x1) including the saturation function are:

[0173] Definition D2 = {(e d ,eθ ,e ω )||e d |≤e d1 ,|e θ |<π,|e ω |≤e ω1}, where e ω1 is a normal quantity; preset x1=(e d ,e θ ,e ω ) T , construct the Lyapunov function V2(x1) containing the saturation function, the function formula is as follows:

[0174]

[0175] As a preferred implementation of this embodiment, the step of deriving and calculating the auxiliary control input v of the mobile robot according to the backstepping method is specifically as follows:

[0176] The derivative of the Lyapunov function V2(x1) containing the saturation function with respect to time is obtained. The specific formula is as follows:

[0177]

[0178] The desired control rate ω is selected d Substituting into the derivative, we get:

[0179]

[0180] Based on The auxiliary control input v is selected as non-positive definite. The specific selection formula is as follows:

[0181]

[0182] Where k ω is a known normal quantity.

[0183] In this embodiment, steering control is achieved by controlling the rotational speed of the robot's left and right wheels. The robot's wheel speed is controlled by a tuned PID speed controller. Therefore, the steering dynamics can be approximated by a first-order system.

[0184] The calculation formula of the preset auxiliary control input v is specifically:

[0185]

[0186] At the same time, the error of the steering rate is preset ω The calculation formula is:

[0187] e ω =ω-ω d.

[0188] In this embodiment, the process of verifying the stability of the mobile robot's motion in combination with the steering dynamics model is as follows:

[0189] It can be found that V2(x1) is in D2-{(0,0,0) T} is always greater than 0. In addition, the derivative of V2(x1) with respect to time is:

[0190]

[0191] The control rate ω of the Lyapunov function V1(x) d Substituting into the time derivative formula of V2(x1), we can get:

[0192]

[0193] Based on Non-positive definite selection of auxiliary control input v:

[0194]

[0195] where k ω is a positive constant. The above selection formula can be transformed into:

[0196]

[0197] From the above derivation, (0,0,0) T is the only equilibrium point of the nonlinear system shown in the above formula at D2. In addition:

[0198]

[0199] According to Barbalat's lemma, when t→∞, Furthermore, the error e d 、e θ and e ω asymptotically approaches zero.

[0200] As a preferred implementation of this embodiment, the real-time steering speed instruction ω of the mobile robot c The specific calculation formula is:

[0201]

[0202] Where ω is the real-time steering speed of the mobile robot.

[0203] Example 2:

[0204] In the first embodiment, the adaptive variation coefficient of the first-order approximate model of steering dynamics is identified and adjusted by a control experiment in a mixed road environment, the control rate of the mobile robot is adjusted synchronously, and the steering speed instruction of the mobile robot is adjusted dynamically. In this embodiment, a simulation experiment is performed:

[0205] Three different types of pavement test benches were built. The benches are designed to be 4 meters long, 4 meters wide, and 15 centimeters high, and different types of materials need to be laid on them, including wood, floor leather, and rubber. The specific bench pictures are as follows Figure 3 shown.

[0206] The platform is modular, with each module measuring 1 meter long, 1 meter wide, and 15 centimeters high, and is made of aluminum profiles. The materials laid on the platform are also modular, with each wooden board measuring 1 meter long and 1 meter wide; each floor covering measuring 1 meter long and 1 meter wide; and each rubber mat measuring 50 centimeters long and 50 centimeters wide. Figure 4 shown.

[0207] Before the experiment begins, the α under different road conditions will be identified by offline identification method. ω The values ​​are shown in Table 1 below. After the experiment begins, the experiment will be divided into an experimental group and a control group. During the operation of the robot, the experimental group assigns the corresponding α to different road surfaces in real time according to the different road surfaces actually detected. ω The control group has α ω The value is fixed to 5. The experimental group will be referred to as α ω_change group, the control group will be referred to as α ω_fixed Group.

[0208] Table 1 Parameters α identified under three road conditions ω Value

[0209]

[0210] In straight line path following, we move the robot forward with a linear velocity command V c Set to 0.1m / s. Figure 5 Shows the use of α ω_fixed and α ω_change When using two methods, α ω Time-varying conditions, where (a) a straight line heading 0°, (b) a straight line heading 45°, (c) a straight line heading 90°, and (d) a straight line heading 135°. Figure 6 Compared with the use of α ω_fixed and α ω_change The responses of following a straight path in four directions using the two methods. The robot’s initial position and orientation are set to (0,0) and 0 degrees, respectively. Figure 7 Shown is the corresponding distance error e d Comparison of the following situations: (a) a straight line with a heading of 0°, (b) a straight line with a heading of 45°, (c) a straight line with a heading of 90°, and (d) a straight line with a heading of 135°.

[0211] We use rise time, convergence time and overshoot to evaluate the robot's response to the target direction path. Table 2 shows the statistics of the use of α ω_fixed and α ω_change The performance indicators of the two methods for following straight paths in four different directions. When following straight paths in four directions such as 0°, 45°, 90° and 135°, except for following the straight path in the direction of 135°, α ω_fixed The rise time of the method is better than that of the method using α ω_change However, using α ω_fixed The convergence time of the method is shorter than that of using α ω_change method is longer. In addition, using α ω_change The overshoot obtained by this method is also better than that obtained by using α ω_fixed In particular, when following the straight path at 0°, 45° and 90°, α ω_change The overshoot produced by the method is less than 0.04 meters. Figure 6 It is also shown in the . Overall, α ω_change This method enables the robot to move faster toward a desired straight path.

[0212] Table 2 uses α ω_fixed and α ω_change Performance comparison of two methods for linear path following

[0213]

[0214] Example 3:

[0215] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, a path following control method for a ground adaptive wheeled mobile robot as described in any embodiment of the present invention is implemented.

[0216] Example 4:

[0217] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a path following control method for a ground adaptive wheeled mobile robot according to any embodiment of the present invention.

[0218] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A ground adaptive mobile robot control method based on Lyapunov stability and backstepping method, characterized in that: The specific steps include: A mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is established, and error prediction parameters of the mobile robot are constructed. The error prediction parameters include the virtual distance error e d and heading angle error e θ ; According to the virtual distance error e d and heading angle error e θ Construct an error kinematics model of a mobile robot; Based on the virtual distance error e d and heading angle error e θ Design a Lyapunov function V1(x) containing a saturation function and derive the expected control rate ω of the mobile robot d , and then combined with the error motion model to verify the stability of the mobile robot motion; The first-order approximate model of steering dynamics and the auxiliary control input v are introduced, and the steering rate error e of the mobile robot is calculated according to the auxiliary control input v. ω , and then build the steering dynamics model of the mobile robot in combination with the error kinematics model of the mobile robot; Based on the steering rate error e ω , virtual distance error e d and heading angle error e θ Design a Lyapunov function V2(x1) containing a saturation function, derive and calculate the auxiliary control input v of the mobile robot using the backstepping method, and then verify the stability of the mobile robot's motion by combining it with the steering dynamics model; In a mixed road environment, the adaptive variation coefficient of the first-order approximate model of steering dynamics is identified and adjusted by a controlled experiment method, and then combined with the expected control rate ω of the mobile robot d The real-time steering speed instruction ω of the mobile robot is calculated by the auxiliary control input v c .

2. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 1, characterized in that: The establishment of a mobile robot motion model including a mobile coordinate system and a fixed reference coordinate system is specifically as follows: Define a fixed reference coordinate system XOY, and establish a mobile coordinate system xoy with the center of mass of the mobile robot as the origin; The calculation formulas for the mobile robot's moving speed V and rotation speed ω are as follows: Where, ω l is the rotation speed of the left wheel of the mobile robot, ω r The rotation speed of the right wheel of the mobile robot; R is the wheel radius, 2f is the distance between the left and right wheels; The kinematic model of the mobile robot is established based on the mobile coordinate system xoy: Where x and y are the coordinates of the center of mass of the mobile robot in the fixed reference coordinate system XOY, θ is the heading of the mobile robot in the two-dimensional coordinate system, ω is the rotation speed of the mobile robot, and l is the distance between the rotation center and the center of mass of the mobile robot; When the distance between the rotation center and the center of mass of the mobile robot is less than a preset threshold, the above formula is simplified to: The simplified formula is used as the final kinematic model of the mobile robot.

3. The ground adaptive mobile robot control method based on Lyapunov stability and backstepping method according to claim 2 is characterized in that: The virtual distance error e d and heading angle error e θ The calculation formula is as follows: Define the virtual distance error e d The calculation formula is as follows: e d =f(x,y); Where f(x,y) is a continuous quadratically differentiable function; Virtual distance error e d Taking the derivative, the calculation formula is as follows: Where, f x and f y are the first-order partial derivatives of the function f(x,y) with respect to the variables x and y, V is the moving speed of the mobile robot, θ is the actual heading of the mobile robot, is the gradient modulus of the function f(x,u); Among them, the gradient mode The calculation formula is as follows: Preset heading angle error e θ The calculation formula is as follows: e θ =θ-θ d ; Where θ is the actual heading of the mobile robot, θ d is the desired heading of the mobile robot; the desired heading of the mobile robot is calculated according to the first-order partial derivatives of the desired trajectory function with respect to the variables x and y.

4. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 3, characterized in that: The virtual distance error e d and heading angle error e θ The specific steps to construct the error kinematics model of the mobile robot are: Virtual distance error e d and heading angle error e θ The derivatives of together constitute the error kinematics model of the mobile robot, and the function formula is as follows:

5. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 3, characterized in that: The virtual distance error e d and heading angle error e θ The specific steps for designing the Lyapunov function V1(x) including the saturation function are: Define the set D1 = {(e d ,e θ )||e d ≤e d0 ,|e θ |<π}, where e d0 is a fixed positive number; let x=(e d ,e θ ) T , construct the Lyapunov function V1(x) containing the saturation function, the function formula is as follows: In the formula, k1 is a fixed positive number, f sat (y) is the saturation function; x is the virtual distance error e d and heading angle error e θ The variable point constructed together, x=(e d ,e θ ) T , T is the transposition mark; Among them, the saturation function f sat The definition formula of (y) is as follows: Where the parameter y0 is a given positive constant.

6. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 5, characterized in that: Derivation and calculation of the expected control rate ω of the mobile robot d The specific steps are: The derivative of the Lyapunov function V1(x) containing the saturation function with respect to time is obtained. The specific formula is as follows: according to Non-positive definite selection of expected control rate ω d , the specific selection formula is as follows: Where k2 is a known positive constant.

7. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 1, characterized in that: The steps of introducing the first-order approximate model of steering dynamics and the auxiliary control input v, and constructing the steering dynamics model of the mobile robot according to the auxiliary control input v and the error kinematics model of the mobile robot are as follows: The first-order dynamic approximation model is specifically: Where, ω c is the speed command, α ω Adaptive change coefficient according to the change of road conditions; ω is the rotation speed of the mobile robot; The calculation formula of the preset auxiliary control input v is specifically: At the same time, the steering rate error e is preset ω The calculation formula is: e ω =oh-oh d ; The steering rate error e ω Take the derivative: Combined with the error kinematics model of the mobile robot, the steering dynamics model of the mobile robot can be obtained. The specific function formula is as follows:

8. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 1, characterized in that: The steering rate error e ω , virtual distance error e d and heading angle error e θ The specific steps for designing the Lyapunov function V2(x1) including the saturation function are: Definition D2 = {(e d ,e θ ,e ω )||e d |≤e d1 ,|e θ |<π,|e ω |≤e ω1 }, where e ω1 is a normal quantity; preset x1=(e d ,e θ ,e ω ) T , construct the Lyapunov function V2(x1) containing the saturation function, the function formula is as follows:

9. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 8, characterized in that: The steps of deriving and calculating the auxiliary control input v of the mobile robot according to the backstepping method are specifically as follows: The derivative of the Lyapunov function V2(x1) containing the saturation function with respect to time is obtained. The specific formula is as follows: The desired control rate ω is selected d Substituting into the derivative, we get: Based on The auxiliary control input v is selected as non-positive definite. The specific selection formula is as follows: Where k ω is a known normal quantity.

10. The method for controlling a ground adaptive mobile robot based on Lyapunov stability and backstepping according to claim 9, characterized in that: The real-time steering speed instruction ω of the mobile robot c The specific calculation formula is: Where ω is the real-time steering speed of the mobile robot.

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