Path tracking control method for mobile robot based on improved dung beetle optimization algorithm

Abstract

A mobile robot path tracking control method based on an improved dung beetle optimization algorithm includes the following steps: 1. Perform kinematic analysis on the mobile robot and establish a control system state equation; 2. Based on the control system state equation, design a PID controller based on the dung beetle optimization algorithm; 3. Improve the dung beetle optimization algorithm to obtain an improved robot path tracking controller; 4. According to the controller designed in step 3, perform real-time path tracking control on the robot. In order to achieve accurate tracking of the mobile robot path, a PID controller based on an improved dung beetle optimization algorithm is proposed. The PID controller is optimized by the improved dung beetle optimization algorithm to quickly adjust the PID parameters; Piecewise chaotic mapping, random walk strategy, adaptive factor, etc. are introduced into the dung beetle optimization algorithm to improve its performance. Through the improved dung beetle optimization algorithm, better trajectory tracking control performance is obtained.

Description

Technical Field

[0001] The present invention belongs to the field of tracking control technology, and specifically relates to a mobile robot motion control technology, and more specifically to a mobile robot path tracking control method based on an improved dung beetle optimization algorithm. Background Art

[0002] Wheeled mobile robots have been widely used in many applications such as industrial automation, hazardous areas, and personal applications in different services. Path following control of mobile robots is an important part of modern robots, whose main task is to move on a specific path. Therefore, achieving autonomous and accurate path following control of robots has become the focus of current research.

[0003] PID control has a simple structure, strong adaptability, and reliable operation, so PID control is still the most widely used strategy today. Traditional PID control has large overshoot, slow response, and requires a trial-and-error approach, which makes it difficult to meet the real-time requirements of industrial control. The fundamental problem of PID control is to solve its parameter optimization problem and select appropriate parameters to enable the PID controller to achieve small error control for the path tracking of the mobile robot. Summary of the invention

[0004] The object of the present invention is to provide a mobile robot path tracking control method based on an improved dung beetle optimization algorithm, which can use advanced control technology to adjust PID controller parameters online to perform mobile robot path tracking control.

[0005] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0006] The mobile robot path tracking control method based on the improved dung beetle optimization algorithm includes the following steps:

[0007] Step 1: Perform kinematic analysis on the mobile robot and establish the control system state equation;

[0008] Step 2: Based on the control system state equation, design a PID controller based on the dung beetle optimization algorithm;

[0009] Step 3, improving the dung beetle optimization algorithm to obtain an improved robot path tracking controller;

[0010] Step 4: Based on the controller designed in step 3, perform real-time path tracking control on the robot.

[0011] As a further solution of the present invention, in step 1, a two-wheel differential mobile robot is taken as a structural model, and a kinematic analysis is first performed on the mobile robot to obtain a distance deviation d e and the angle deviation θ e

[0012]

[0013] where v l is the left wheel speed, v r is the right wheel speed, L is the distance between the two wheels, s is the Laplace transform variable; the transfer function of the drive motor is

[0014]

[0015] The left wheel speed is n l , the control voltage is U l , the constant k related to the back EMF l , T m is the electrical time constant, and similarly, n is set for the right wheel r , U r , k r ; Let x 1 =ΔV,x 2 =θ e (s),x 3 =d e (s), △V is the change in robot motion speed, ΔU=U ι -U r , the state equation of the mobile robot control system is obtained as

[0016]

[0017] in In the actual system, the position deviation is used as the output of the system, and the output equation is:

[0018]

[0019] Where C=

[001] , D=0.

[0020] As a further solution of the present invention, in step 2, the three parameters k in the PID controller are optimized by the dung beetle optimization algorithm. p , k i , k d To optimize the parameters, the PID controller expression is as follows

[0021]

[0022] Where e(t) is the position error, K p is the scale parameter, K i is the integration parameter, K d is the differential parameter.

[0023] As a further solution of the present invention, the movement formula of the dung beetle in space in the dung beetle optimization algorithm (DBO) in step 2 is as follows:

[0024] x i (t+1)=x i (t)+c 1 (x i (t)-Lb)+c 2 (x i (t)-Ub) Equation 6

[0025] where x i (t) represents the position information of the i-th dung beetle in the t-th iteration, c 1 Random numbers that follow a normal distribution, c 2 represents a random vector belonging to (0, 1), Lb and Ub represent the upper and lower boundaries of the dung beetle's movement, and are updated by the following formula:

[0026]

[0027] Where R is the control parameter, which increases linearly from 1 to infinity with the number of iterations, that is, R = 1 / (1-t / T max ), t is the number of iterations, T max represents the maximum number of iterations, Xb is the current local optimal position, and is updated by the following formula:

[0028] Xb=x i (t), (f(x i (t))>f(Xb)) Equation 8

[0029] As the dung beetle moves, its foraging range continues to approach the global optimal point, and eventually it finds the global optimal point.

[0030] As a further solution of the present invention, the steps of optimizing the parameters of the PID controller by using the dung beetle optimization algorithm in step 2 are as follows:

[0031] S01: Initialize dung beetle population parameters;

[0032] S02: Calculate the fitness function of dung beetles;

[0033] S03: Calculate the corresponding parameters of each dung beetle and determine the initial population extreme value;

[0034] S04: Update population boundaries and dung beetle locations;

[0035] S05: Calculate the fitness function of the dung beetle;

[0036] S06: Update population extreme value;

[0037] S07: Determine whether the iteration termination condition is met. If so, output the optimal solution. If not, return to S03 and repeat S04 to S06.

[0038] As a further solution of the present invention, in step 3, the Piecewise chaotic mapping is used to initialize the dung beetle population to increase the ergodicity of the initial population. The Piecewise chaotic mapping formula is as follows:

[0039]

[0040] Among them, p∈(0,1) is the control parameter.

[0041] As a further solution of the present invention, in step 3, a random walk strategy is used to disturb the dung beetle's ball rolling behavior, enhance its search performance, and improve the local search performance of the optimal position. The formula of the random walk strategy is as follows:

[0042] X(t) = {0, c ussum [2r(t 1 )-1]c ussum [2r(t 2 )-1],…,c ussum [2r(t n )-1]} Formula 10

[0043] Take a random function r(t) such as

[0044]

[0045] In order to ensure that the algorithm moves within a certain range, it needs to be normalized, as shown in the following formula:

[0046]

[0047] Where: is the position of the i-th dung beetle in the t-th iteration; a i and b i are the minimum and maximum values ​​of the random walk variable of the i-th dimension respectively; c i and d i are the minimum and maximum values ​​of the random walk variable of the i-th dimension at the t-th iteration, respectively.

[0048] As a further solution of the present invention, the adaptive factors k and c are introduced in step 3 to balance the global and local search capabilities and prevent falling into the local optimal solution. Its expression is

[0049]

[0050] Where rand is a random number between (0,1).

[0051] The improved formula for the movement of dung beetles in space is as follows:

[0052] x i(t+1)=exp(c·k)·cos(2π·c)x i (t)+c 1 ×(x i (t)-L b )+c 2 ×(x i (t)-U b ) Formula 14

[0053] As a further solution of the present invention, the fitness function in the controller in step 4 is set

[0054] The calculation is as follows:

[0055]

[0056] Where: e(t) is the error between input and output, u(t) is added to avoid excessive control amplitude, w 1

[0057] and w 2 is the weight, take w 1 =0.999,w 2 =0.001, w 3 =2,w 4 =1000.

[0058] Beneficial effects of the present invention:

[0059] 1. In order to achieve accurate tracking of the mobile robot path, a PID controller based on the improved dung beetle optimization algorithm is proposed. The PID controller is optimized by the improved dung beetle optimization algorithm, and the PID parameters are quickly adjusted;

[0060] 2. Piecewise chaotic mapping, random walk strategy, adaptive factor, etc. are introduced into the dung beetle optimization algorithm to improve its performance. Through the improved dung beetle optimization algorithm, better trajectory tracking control performance is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a structural diagram of the control method of the present invention;

[0062] Figure 2 It is a PID controller flow chart of the improved dung beetle optimization algorithm of the present invention;

[0063] Figure 3 The figure is a fitness function curve diagram before and after the improvement of the dung beetle optimization algorithm of the present invention;

[0064] Figure 4 This is a straight line tracking trajectory effect diagram of the present invention. DETAILED DESCRIPTION

[0065] Example 1

[0066] Reference Figure 1-4 , as an embodiment of the present invention, provides a mobile robot path tracking control method based on an improved dung beetle optimization algorithm, comprising the following steps:

[0067] Step 1: Perform kinematic analysis on the mobile robot and establish the control system state equation;

[0068] Step 2: Based on the control system state equation, design a PID controller based on the dung beetle optimization algorithm;

[0069] Step 3, improving the dung beetle optimization algorithm to obtain an improved robot path tracking controller;

[0070] Step 4: Based on the designed controller, perform real-time path tracking control on the robot.

[0071] In this embodiment, the robot is first subjected to kinematic analysis to obtain the distance deviation d e and the angle deviation θ e

[0072]

[0073] where v l is the left wheel speed, v r is the right wheel speed, L is the distance between the two wheels, s is the Laplace transform variable; the transfer function of the drive motor is

[0074]

[0075] The left wheel speed is n l , the control voltage is U l , the constant k related to the back EMF l , T m is the electrical time constant, and similarly, n is set for the right wheel r , U r , k r ; Let x 1 =ΔV,x 2 =θ e (s),x 3 =d e (s), △V is the change in robot motion speed, ΔU=U ι -U r , the state equation of the mobile robot control system is obtained as

[0076]

[0077] in In the actual system, the position deviation is used as the output of the system, and the output equation is:

[0078]

[0079] Where C=

[001] , D=0.

[0080] The left and right wheels of the mobile robot are driven by motors. When the robot moves in a straight line, the voltages of the left and right wheel drive motors are equal. When the mobile robot deviates from the path, a correction value ±ΔU / 2 is added to the input voltage of the left and right wheels of the mobile robot. The position deviation is used as the output of the system, and the voltage difference between the two wheels is used as the input. Then, the three parameters k in the PID controller are optimized by the dung beetle optimization algorithm. p , k i , k d Optimize the parameters to obtain the optimal control parameters to reduce the tracking error. The PID controller expression is as follows:

[0081]

[0082] Where e(t) is the position error, K p is the scale parameter, K i is the integration parameter, K d is the differential parameter.

[0083] The movement formula of dung beetles in space in the dung beetle optimization algorithm is as follows:

[0084] x i (t+1)=x i (t)+c 1 (x i (t)-Lb)+c 2 (x i (t)-Ub) Equation 6

[0085] where x i (t) represents the position information of the i-th dung beetle in the t-th iteration, c 1 Random numbers that follow a normal distribution, c 2 represents a random vector belonging to (0, 1), Lb and Ub represent the upper and lower boundaries of the dung beetle's movement, and are updated by the following formula:

[0086]

[0087] Where R is the control parameter, which increases linearly from 1 to infinity with the number of iterations, that is, R = 1 / (1-t / T max ), t is the number of iterations, T max represents the maximum number of iterations, Xb is the current local optimal position, and is updated by the following formula:

[0088] Xb=x i (t), (f(x i(t))>f(xb)) Equation 8

[0089] As the dung beetle moves, its foraging range continues to approach the global optimal point, and eventually it finds the global optimal point.

[0090] The steps for optimizing the parameters of the PID controller using the dung beetle optimization algorithm are as follows:

[0091] S01: Initialize dung beetle population parameters;

[0092] S02: Calculate the fitness function of dung beetles;

[0093] S03: Calculate the corresponding parameters of each dung beetle and determine the initial population extreme value;

[0094] S04: Update population boundaries and dung beetle locations;

[0095] S05: Calculate the fitness function of the dung beetle;

[0096] S06: Update population extreme value;

[0097] S07: Determine whether the iteration termination condition is met. If so, output the optimal solution. If not, return to S03 and repeat S04 to S06.

[0098] In order to further optimize the controller performance, the dung beetle optimization algorithm is improved. The improved controller structure diagram and the flowchart of the improved dung beetle optimization algorithm are shown in Figure 2. Figure 1 and Figure 2 shown.

[0099] The Piecewise chaotic mapping is used to initialize the dung beetle population to increase the ergodicity of the initial population. The Piecewise chaotic mapping formula is as follows:

[0100]

[0101] Among them, p∈(0,1) is the control parameter.

[0102] The random walk strategy is used to disturb the dung beetle's ball rolling behavior, enhance its search performance, and improve the local search of the optimal position. The formula of the random walk strategy is as follows:

[0103] X(t) = {0, c usum [2r(t 1 )-1],c ussum [2r(t 2 )-1],…,c ussum [2r(t n )-1]} Formula 10

[0104] Take a random function r(t) such as

[0105]

[0106] In order to ensure that the algorithm moves within a certain range, it needs to be normalized, as shown in the following formula:

[0107]

[0108] Where: is the position of the i-th dung beetle in the t-th iteration; a i and b i are the minimum and maximum values ​​of the random walk variable of the i-th dimension respectively; c i and d i are the minimum and maximum values ​​of the random walk variable of the i-th dimension at the t-th iteration, respectively.

[0109] At the same time, adaptive factors k and c are introduced to balance the global and local search capabilities and prevent falling into the local optimal solution. Its expression is

[0110]

[0111] Where rand is a random number between (0,1).

[0112] The improved formula for the movement of dung beetles in space is as follows:

[0113] x i (t+1)=exp(c·k)·cos(2π·C)·x i (t))+c 1 ×(x i (t)-L b )+c 2 ×(x i (t)-U b ) Formula 14

[0114] The fitness function in the controller is designed as follows:

[0115]

[0116] Where: e(t) is the error between input and output, u(t) is added to avoid excessive control amplitude, w 1 and w 2 is the weight, take w 1 =0.999,w 2 =0.001, w 3 =2,w 4 =1000.

[0117] During the movement, after obtaining the optimal control parameters, the movement process of the car is continuously tracked, and the position deviation is corrected and compensated according to the input pressure difference to ensure that the car moves along a specific path and prevent the position deviation from being too large.

[0118] The fitness function curves of the improved dung beetle optimization algorithm and the original algorithm are as follows: Figure 3 As shown, it can be seen that the improved dung beetle optimization algorithm has a faster descent speed and convergence speed, and can find the optimal solution faster.

[0119] The improved dung beetle optimization algorithm and the original algorithm track the straight line trajectory. Figure 4 As shown, it can be seen that the improved dung beetle optimization algorithm has a shorter PID adjustment time and a smaller steady-state error, and has greater superiority, and can be used to solve the mobile robot path tracking task.

[0120] The present invention proposes a PID controller based on an improved dung beetle optimization algorithm to achieve accurate tracking of the path of a mobile robot. The improved dung beetle optimization algorithm is used to optimize the parameters of the PID controller and quickly adjust the PID parameters. Piecewise chaotic mapping, random walk strategy, adaptive factor and the like are introduced into the dung beetle optimization algorithm to improve its performance. Through the improved dung beetle optimization algorithm, better trajectory tracking control performance is obtained.

[0121] Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

Claims

1. A mobile robot path tracking control method based on an improved dung beetle optimization algorithm is characterized by: The following steps are involved: Step 1: Perform kinematic analysis on the mobile robot and establish the control system state equation. In this step, a two-wheel differential mobile robot is taken as the structural model. First, perform kinematic analysis on the mobile robot to obtain the distance deviation d e and the angle deviation θ e where v l is the left wheel speed, v r is the right wheel speed, L is the distance between the two wheels, s is the Laplace transform variable; the transfer function of the drive motor is The left wheel speed is n l , the control voltage is U l , the constant k related to the back EMF l , T m is the electrical time constant, and similarly, n is set for the right wheel r , U r , k r ; Let x1 = ΔV, x2 = θ e (s),x3=d e (s), △V is the change in robot motion speed, ΔU=U ι -U r , the state equation of the mobile robot control system is obtained as in In the actual system, the position deviation is used as the output of the system, and the output equation is: Where C = [001], D = 0; Step 2: Based on the control system state equation, design a PID controller based on the dung beetle optimization algorithm. The three parameters k in the PID controller are adjusted by the dung beetle optimization algorithm. p , k i , k d To optimize the parameters, the steps for optimizing the parameters of the PID controller using the dung beetle optimization algorithm are as follows: S01: Initialize dung beetle population parameters; S02: Calculate the fitness function of dung beetles; S03: Calculate the corresponding parameters of each dung beetle and determine the initial population extreme value; S04: Update population boundaries and dung beetle locations; S05: Calculate the fitness function of the dung beetle; S06: Update population extreme value; S07: Determine whether the iteration termination condition is met. If so, output the optimal solution. If not, return to S03 and repeat S04 to S06. The PID controller expression is as follows Where e(t) is the position error, K p is the scale parameter, K i is the integration parameter, K d is a differential parameter. The movement formula of the dung beetle in space in the dung beetle optimization algorithm is as follows: x i (t + 1)=x i (t)+c1(x i (t)-Lb)+c2(x i (t)-Ub) Equation 6 where x i (t) represents the position information of the i-th dung beetle in the t-th iteration, c1 is a random number that follows a normal distribution, c2 represents a random vector belonging to (0, 1), Lb and Ub represent the upper and lower boundaries of the dung beetle's movement, and are updated by the following formula: Where R is the control parameter, which increases linearly from 1 to infinity with the number of iterations, that is, R = 1 / (1-t / T max ), t is the number of iterations, T max represents the maximum number of iterations, Xb is the current local optimal position, and is updated by the following formula: Xb = x i (t), (f(x i (t)) > f(Xb)) Equation 8 During the movement of the dung beetle, its foraging range keeps approaching the global optimal point, and finally it finds the global optimal point. Step 3: Improve the dung beetle optimization algorithm to obtain an improved robot path tracking controller. Use Piecewise chaotic mapping to initialize the dung beetle population and increase the ergodicity of the initial population. The Piecewise chaotic mapping formula is as follows: Among them, p∈(0,1) is the control parameter, The random walk strategy is used to disturb the dung beetle's ball rolling behavior, enhance its search performance, and improve the local search of the optimal position. The formula of the random walk strategy is as follows: X(t) = {0, c ussum [2r(t1) - 1], c ussum [2r(t2) - 1], …, c ussum [2r(t n ) - 1]} Equation 10 Take a random function r(t) such as In order to ensure that the algorithm moves within a certain range, it needs to be normalized, as shown in the following formula: Where: is the position of the i-th dung beetle in the t-th iteration; a i and b i are the minimum and maximum values ​​of the random walk variable of the i-th dimension respectively; and are the minimum and maximum values ​​of the random walk variable of the i-th dimension at the t-th iteration respectively; In this step, adaptive factors k and c are introduced to balance the global and local search capabilities and prevent falling into the local optimal solution. The expression is: In the formula, rand is a random number (0,1), The improved formula for the movement of dung beetles in space is as follows: x i (t + 1) = exp(c·k)·cos(2π·c)·x i (t) + c1×(x i (t) - L b ) + c2×(x i (t) - U b ) Equation 14 Step 4: Based on the controller designed in step 3, perform real-time path tracking control on the robot.

2. The mobile robot path tracking control method based on the improved dung beetle optimization algorithm as claimed in claim 1, characterized in that: The fitness function in the controller of step 4 is designed as follows: Where: e(t) is the error between input and output, u(t) is added to avoid excessive control amplitude, w1 and w2 are weights, w1=0.999, w2=0.001, w3=2, w4=1000.

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