A trajectory tracking control method for a distributed drive vehicle considering energy consumption

Abstract

The application belongs to the technical field of intelligent driving, and discloses a distributed driving vehicle trajectory tracking control method considering energy consumption factors, which comprises the following steps: obtaining a reference trajectory to be tracked, and constructing a trajectory tracking control model according to the reference trajectory; obtaining a front wheel steering angle calculation formula and a rear wheel steering angle calculation formula according to the trajectory tracking control model; δ f = K p1 ·e1+K d1 ·e2; δ r = K p2 ·e1+K d2 ·e2+1.5·u 2b ; δ f is the front wheel steering angle, δ r is the rear wheel steering angle, K p1 is a front wheel displacement error coefficient, K d1 is a front wheel speed error coefficient, K p2 is a rear wheel displacement error coefficient, and K d2 is a rear wheel speed error speed, e1 is a lateral displacement error, e2 is a lateral speed error, and u 2b is a feedback quantity of the rear wheel steering angle; a target function is established, the minimum of the target function is taken as an optimization target, an array composed of the front wheel displacement error coefficient, the front wheel speed error coefficient, the rear wheel displacement error coefficient and the rear wheel speed error speed is optimized, and an optimal array is obtained; and optimal front wheel steering angles and optimal rear wheel steering angles are calculated according to the optimal array.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent driving, and particularly relates to a distributed driving vehicle trajectory tracking control method considering energy consumption factors. BACKGROUND

[0002] The trajectory tracking problem is an important challenge for the rapid development of the intelligent driving industry. Vehicle trajectory tracking control, as a core component of intelligent driving technology, its control strategy not only concerns the accuracy and comfort of driving, but also directly affects the energy utilization efficiency of the vehicle. Therefore, studying the vehicle trajectory tracking control strategy considering energy consumption has important significance for improving the energy-saving performance of the automobile and promoting the sustainable development of transportation.

[0003] Most of the existing trajectory tracking control technologies take stability as the control target and cannot well consider the energy consumption factor. SUMMARY

[0004] The purpose of the application is to provide a distributed driving vehicle trajectory tracking control method considering energy consumption factors, which combines energy-saving design while tracking control, and can reduce energy consumption while maintaining high accuracy of trajectory tracking.

[0005] The technical scheme provided by the application is as follows:

[0006] A distributed driving vehicle trajectory tracking control method considering energy consumption factors, comprising the following steps:

[0007] Step 1, obtaining a reference trajectory to be tracked, and constructing a trajectory tracking control model according to the reference trajectory;

[0008] Step 2, obtaining a front wheel steering angle calculation formula and a rear wheel steering angle calculation formula according to the trajectory tracking control model;

[0009] δ f =K p1 ·e1+K d1 ·e2;

[0010] δ r =K p2 ·e1+K d2 ·e2+1.5·u 2b ;

[0011] Wherein, δ f is the front wheel steering angle, δ r is the rear wheel steering angle, K p1 is the front wheel displacement error coefficient, K d1 is the front wheel speed error coefficient, K p2 is the rear wheel displacement error coefficient, and K d2is the rear wheel speed error velocity, e1 is the lateral displacement error, e2 is the lateral velocity error, u 2b is the feedback of the rear wheel steering angle;

[0012] Step three, establishing a target function, and taking the minimum of the target function as the optimization goal, optimizing the array composed of the front wheel displacement error coefficient, the front wheel speed error coefficient, the rear wheel displacement error coefficient, and the rear wheel speed error velocity to obtain an optimal array;

[0013] Step four, calculating the optimal front wheel steering angle and the optimal rear wheel steering angle according to the optimal array.

[0014] Preferably, the trajectory tracking control model is:

[0015]

[0016] wherein, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, C pf is the front wheel cornering stiffness under the single-track model, C pr is the rear wheel cornering stiffness under the single-track model, C lf is the front wheel longitudinal stiffness under the single-track model, C lr is the rear wheel longitudinal stiffness under the single-track model, s f is the front wheel slip ratio under the single-track model, s r is the rear wheel slip ratio under the single-track model, m is the mass of the vehicle, I z is the moment of inertia of the vehicle around the z-axis, is the longitudinal velocity under the global coordinate system, is the lateral velocity under the global coordinate system, v y is the lateral velocity, v x is the longitudinal velocity, is the yaw angle, δ f is the front wheel steering angle, δ r is the rear wheel steering angle, is the longitudinal acceleration, is the yaw rate, is the lateral acceleration, is the yaw angular acceleration.

[0017] Preferably, the feedback of the rear wheel steering angle is calculated by the following formula:

[0018]

[0019] wherein, is the derivative of the speed error with a feedback link, is the derivative of the yaw rate error with a feedback link; c1, c2 are constants, g = 9.8 m / s2 is the gravity acceleration.

[0020] Preferably, the objective function is:

[0021]

[0022] wherein e1 is the lateral displacement error, e2 is the lateral velocity error, e3 is the yaw angle error, e4 is the yaw angle velocity error, q1, q2, q3, q4 are weight coefficients of each error quantity, q e is the economic weight coefficient, τ is the time, T ∞ is the final state time, n is the motor speed, T is the motor torque, η T is the motor efficiency.

[0023] Preferably, the relationship between the lateral displacement error, the lateral velocity error, the yaw angle error and the yaw angle velocity error and the front wheel displacement error coefficient, the front wheel velocity error coefficient, the rear wheel displacement error coefficient and the rear wheel velocity error coefficient is:

[0024]

[0025] wherein y r is the reference lateral displacement, is the reference lateral velocity, is the reference lateral acceleration, is the reference yaw angle, is the reference yaw angle velocity, is the reference yaw angle acceleration, A is the first error coefficient matrix, B is the second error coefficient matrix, are the derivatives of e1, e2, e3, e4 respectively.

[0026] Preferably, in the step three, the black hawk optimization algorithm is used to optimize the array composed of the front wheel displacement error coefficient K p1 , the front wheel velocity error coefficient K d1 , the rear wheel displacement error coefficient K p2 and the rear wheel velocity error coefficient K d2 , including the following steps:

[0027] Step 1, taking the array of parameters to be optimized {K p1 K d1 K p2 K d2} as individuals in the population to be optimized, and initializing the population to be optimized to obtain the initialized population;

[0028] wherein the number of individuals in the initial population is n;

[0029] Step 2, taking the objective function as the fitness function; updating the individuals in the population by using the black eagle optimization algorithm, outputting n individuals with smaller fitness as the optimal solution set after each round of update, as the next generation population;

[0030] Step 3, repeating step 2 to iteratively update the individuals in the population until a set number of iterations is reached;

[0031] Step 4, selecting an individual with the smallest fitness from the optimal solution set obtained in the last iteration as the optimization result.

[0032] Preferably, in the step 4, if the optimal solution set obtained in the last iteration has multiple individuals with the same fitness and equal to the minimum fitness, the economic term J e of the objective function corresponding to these individuals is calculated, and the individual with the minimum J e is selected as the optimization result.

[0033] Wherein:

[0034] The present application has the following beneficial effects:

[0035] The distributed drive vehicle trajectory tracking control method considering energy consumption factors provided by the present application can reduce energy consumption while maintaining high accuracy of trajectory tracking through optimization algorithm and system architecture. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The figure is a schematic diagram of the trajectory tracking control model.

[0037] Figure 2 The figure is a flowchart of the optimization of the array composed of the front wheel displacement error coefficient, the front wheel speed error coefficient, the rear wheel displacement error coefficient and the rear wheel speed error coefficient.

[0038] Figure 3 The figure is a flowchart of the black eagle optimization algorithm. DETAILED DESCRIPTION

[0039] The present application will be further described in detail below with reference to the accompanying drawings, so that those skilled in the art can implement it according to the description.

[0040] As shown in the figure, the present application provides a distributed drive vehicle trajectory tracking control method considering energy consumption factors, and the specific implementation process is as follows. Figures 1-3

[0041] According to the working condition and the target reference trajectory (the reference trajectory to be tracked), the current parameters of the vehicle are calculated and obtained by using the following formula:​

[0042]

[0043] wherein, denotes the longitudinal velocity in the global coordinate system, denotes the lateral velocity in the global coordinate system, y denotes the lateral displacement, v y denotes the lateral velocity, v x denotes the longitudinal velocity, denotes the yaw angle, τ denotes time.

[0044] As shown in the following equation, the trajectory tracking coordinate model is calculated according to the vehicle specific parameters and the current parameters: Figure 1

[0045]

[0046] wherein, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, C pf is the front wheel cornering stiffness under the single track model, C pr is the rear wheel cornering stiffness under the single track model, C lf is the front wheel longitudinal stiffness under the single track model, C lr is the rear wheel longitudinal stiffness under the single track model, s f is the front wheel slip ratio under the single track model, s r is the rear wheel slip ratio under the single track model, m is the mass of the vehicle, I z is the moment of inertia of the vehicle around the z axis; the above are the vehicle specific parameters.

[0047] the front wheel steering angle δ f , the rear wheel steering angle δ r , the longitudinal acceleration the yaw rate the lateral acceleration and the yaw angular acceleration are the current parameters when the vehicle is running.

[0048] According to the trajectory tracking coordinate model, δ f , δ r are calculated:

[0049]

[0050] e rr = [e1 e2 e3 e4] T

[0051] wherein, y is the lateral displacement, is the lateral velocity, is the yaw angle,​ is the yaw rate, y r is the reference lateral displacement, is the reference lateral velocity, is the reference yaw angle, is the reference yaw rate, e1 is the lateral displacement error, e2 is the lateral velocity error, e3 is the yaw angle error, e4 is the yaw rate error, e rr is the error matrix composed of e1, e2, e3, e4.

[0052]

[0053] wherein s1 is the velocity error with feedback link, s2 is the yaw rate error with feedback link; c1, c2 are constants.

[0054]

[0055] wherein λ1, λ2, λ3, λ4 are respectively the approaching rate functions; ψ, ξ are constants

[0056] The derivative of the feedback error is calculated by the formula:

[0057]

[0058] wherein κ1, κ2, κ3, κ4 are respectively the feedback parameters; is the derivative of the velocity error with feedback link, is the derivative of the yaw rate error with feedback link.

[0059] According to the trajectory tracking model formula, the intermediate variables u 1f , u 2f , f, g are derived:

[0060]

[0061] The feedback amount u 2b of the rear wheel turning angle is calculated by the formula:

[0062]

[0063] The front and rear wheel turning angle formula is obtained:

[0064] δ f = K p1 ·e1 + K d1 ·e2

[0065] δ r = K p2 ·e1 + K d2 ·e2 + 1.5·u 2b

[0066] wherein, K p1 is a front wheel displacement error coefficient, K d1 is a front wheel speed error coefficient, K p2 is a rear wheel displacement error coefficient, K d2 is a rear wheel speed error speed

[0067] According to trajectory tracking coordinate model simplification, we get:

[0068]

[0069] The above state space equation can be expressed as follows:

[0070]

[0071] That is:

[0072]

[0073] Taking the accuracy of trajectory tracking as the optimization objective, K p1 , K d1 , K p2 , K d2 are iteratively optimized, and the performance index is expressed as:

[0074]

[0075] wherein, A is a first error coefficient matrix, B is a second error coefficient matrix, q1, q2, q3, q4 are weight coefficients of each error quantity, since most working conditions are in high-speed working conditions, the lateral speed and yaw angular speed are set to higher order quantities to ensure the stability in high-speed working conditions. e q is an economic weight coefficient, τ is time, T ∞ is the final state time, n is the motor speed, obtained by the sensor, T is the motor torque, obtained by the sensor, η T is the motor efficiency, obtained by the motor map.

[0076] To achieve the purpose of adjusting the control quantity U = [δ p1 δ d1 ] p2 , K d2 , K f , K r , K T , thereby changing the state quantity and further achieving the purpose of adjusting the error matrix e rr = [e1 e2 e3 e4] T .

[0077] In this embodiment, for the performance index J, the BEO algorithm is used to calculate K p1 , K d1 , K p2 , K d2 Perform iterative optimization to find the optimal solution in a large range of iteration space. The specific process is as follows.

[0078] The BEO algorithm is inspired by the behavior of black hawks, whose primary biological behaviors include hunting, migration, and reproduction. Predatory behaviors can be broken down into stalking, circling, capturing, snatching, and warning; reproductive behaviors include courtship and incubation.

[0079] The following will construct a mathematical model of the BEO algorithm from the aspects of the black hawk's tracking, circling, capturing, snatching, warning, migration, courtship and hatching behaviors.

[0080] initialization

[0081] First, set the number of individuals in the population to n, the dimension of the variable to be optimized to d = 4, and use K to represent the black hawk population matrix. i=1,2,...,n represents different black hawk individuals to be optimized:

[0082] K j =lb+rand·(ub-lb),j=1,2,...,n;

[0083] Where lb and ub are the upper and lower bounds of the optimization variable respectively; rand is a column vector with a dimension of 4, whose elements are random values ​​from 0 to 1. The fitness value of the individual is expressed as f K In this case, f K =J.

[0084] After initialization, the "tracking" step is performed.

[0085] The tracking process uses the following formula to update the individual:

[0086]

[0087] Among them, K r is a random position in the search space, K k is the position of a random individual, K best is the current best solution set; D is K best The farthest distance from the search boundary, t represents the number of iterations; r1 is a random number between 0 and 1, and t1 is a random number between 0 and 1 generated by tent_map. is the auxiliary tracking population matrix of the t+1th time, K t+1 is the tracking population matrix of the t+1th time, α is the tracking update auxiliary function, The tth random individual position, The optimal solution of the tth iteration.

[0088] The candidate solution and its corresponding fitness value f are calculated by the formula st , and temporarily recorded as the minimum fitness value f best .

[0089] Where tent_map is as follows:

[0090]

[0091] Where x and a are two independent variables of tent_map.

[0092] Determine whether K best has reached the search boundary. If yes, execute the "warning" step to generate a new candidate solution to replace the solution beyond the boundary, and then continue to execute the "hover", "capture", and "rob" steps for updating. If not, directly execute the "hover", "capture", and "rob" steps for updating.

[0093] The formula for the warning process update is:

[0094]

[0095] Where, ζ = -10d sni + 15, d si is the distance between the i-th dimensional space and the center of the search space, d smin and d smax are the minimum and maximum d si , is K t rearranged in order of proximity to the center of the search space. ζ is the boundary auxiliary function, θ n is the sine auxiliary function, is the t+1th warning update auxiliary matrix, (i,j) represents the i-th row and j-th column, and P(j) is the probability density function of the Poisson distribution.

[0096] The candidate solution and fitness value f are calculated by the warning process update formula w , and the smaller fitness value is used to replace f best , and the candidate solution set is recorded.

[0097] The warning process update formula uses the Poisson distribution to guide the movement of particles, generating a new K t+1 to replace the solution beyond the search boundary.

[0098] The circling process uses the following formula to update individuals:

[0099]

[0100] in, M is a 4-dimensional convolution matrix, a = r2·2π, a is the convolution angle; r2 is a random number between 0 and 1.

[0101] The candidate solution and fitness value f are calculated by the circling process update formula ho , and replace f with the smaller fitness value best And record the candidate solution set.

[0102] The function of the circling operation is to perform a rotation search to further improve the range of the global optimal position. The circling strategy performs a rotation search within the range of the global optimal position initially determined by the tracking strategy.

[0103] The capture process uses the following formula to update individuals:

[0104]

[0105] in, D1 is the first position adjustment factor, D2 is the second position adjustment factor, s0 is a column vector with a dimension of 4, and the elements are between 0.5 and 1; K * Represents the capture update auxiliary matrix.

[0106] Similarly, the capture process update formula is used to calculate the candidate solution and fitness value f c , and replace f with the smaller fitness value best And record the candidate solution set.

[0107] The snatching process uses the following formula to update individuals:

[0108]

[0109] Where r3 is a random vector of dimension d, and the values ​​of the elements in each dimension follow a normal distribution.

[0110] Use the snatch process update formula to calculate the candidate solution and fitness value f sn , and replace f with the smaller fitness value best And record the candidate solution set.

[0111] The seizing process update formula simplifies the seizing behavior as a black hawk flying from one point curve to another point. Then the point jumping motion is used to simulate the seizing behavior of the black hawk. The seizing strategy is a jumping search method, which aims to jump search in the position adjusted by the previous strategy to improve the probability of finding the global optimal position.

[0112] The relationship between the current iteration number t, the maximum iteration number whether the relationship between the number of stopping updates H (the number of iterations eliminated in the iteration process) satisfies: If satisfied: perform the "migration" step for updating; if not satisfied: perform the "courtship" and "hatching" steps for updating and end the loop.

[0113] The migration process updates the individual using the following formula:

[0114]

[0115] wherein, f best is the current best fitness value, f(j) is the fitness value of the jth individual, s1 is the migration update auxiliary function, which is a column vector with a dimension of 4, and the elements are between -1 and 1, t2 is a random number from 0.4 to 1 formed by tent mapping, ε is a constant. z is the auxiliary migration function

[0116] The candidate solution and the fitness value f are calculated using the migration process update formula im , and the smaller fitness value among them is used to replace f best , and the candidate solution set is recorded.

[0117] The migration process update formula uses the fitness function value to represent the degree of adaptation of the black hawk to the environment, and constructs the migration function z(f) to further comprehensively simulate its migration rules: the lower the fitness, the farther the migration distance. The migration mechanism aims to migrate individuals with lower fitness to places far from the current best position, to reduce the possibility of falling into local optimum.

[0118] After performing the "migration" step for updating, it is judged whether: If satisfied: perform the "courtship" and "hatching" steps for updating and end the loop; if not satisfied: jump back to initialization and re-enter the loop.

[0119] The courtship process updates the individual using the following formula:

[0120]

[0121] wherein, Q is a step factor, and its functional expression comes from the deformation of the Sigmoid function; r4 and r6 are random numbers between 0 and 1, and r5 and r7 are column vectors with a dimension of 4, and the elements thereof conform to a normal distribution. j%2 represents the remainder of j divided by 2, for example: j%2 = 1 represents that the remainder of j divided by 2 is 1, that is, j is an odd number.

[0122] The candidate solution and the fitness value f are calculated by using the courtship process update formula c , and the smaller fitness value is used to replace f best , and the candidate solution set is recorded.

[0123] The courtship process update formula simulates the interaction behavior of male and female black eagles in the courtship process by using the similar wave and odd-even alternating mode between the sine functions.

[0124] The hatching process uses the following formula to update the individual:

[0125]

[0126] Wherein, R is a set of normally distributed arrays, K d is the group position matrix after rearranging the group position K from the nearest to the farthest from the nest

[0127] The candidate solution and the fitness value f are calculated by using the courtship process update formula ha , and the smaller fitness value is used to replace f best , and the candidate solution set is recorded.

[0128] The hatching process update formula simulates the case that male black eagles move more frequently near the nest and less frequently far away during the hatching period due to guarding the female black eagle hatching according to the normal distribution. The hatching strategy is a diffusion search method, which allows some individuals to continue to approach the current optimal value, while others diffuse outward, thereby preventing falling into a local optimal value.

[0129] When the iterative optimization is completed, the BEO optimization algorithm obtains the optimal solution, and if more than one group of optimal solution set is obtained by optimization, that is, the performance index is the minimum economic index , the solution is taken as the only optimal solution.

[0130] The distributed driving vehicle trajectory tracking control method considering energy consumption factors provided by the application successfully integrates energy-saving design while maintaining high accuracy of trajectory tracking, significantly reduces energy consumption through optimization algorithm and system architecture, and embodies the importance of energy efficient use and sustainable development, which has important significance for promoting the technological progress of related industries.

[0131] While embodiments of the application have been disclosed in connection with the above specification and drawings this description is not intended to limit the scope of the application and many modifications, enhancements, alternatives, and variations will become apparent to those skilled in the art from this disclosure. Accordingly, it is intended that the application not be limited to the described embodiments, but that it include all variations falling within the scope of the claims, and their equivalents.

Claims

1. A trajectory tracking control method for a distributed drive vehicle considering energy consumption, characterized in that, The method comprises the following steps: Step 1: obtaining a reference trajectory to be tracked, and constructing a trajectory tracking control model according to the reference trajectory; The trajectory tracking control model is: wherein, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, C pf is the front wheel cornering stiffness under the single track model, C pr is the rear wheel cornering stiffness under the single track model, C lf is the front wheel longitudinal stiffness under the single track model, C lr is the rear wheel longitudinal stiffness under the single track model, s f is the front wheel slip ratio under the single track model, s r is the rear wheel slip ratio under the single track model, m is the mass of the vehicle, I z is the moment of inertia of the vehicle about the z axis, is the longitudinal velocity under the global coordinate system, is the lateral velocity under the global coordinate system, v y is the lateral velocity, v x is the longitudinal velocity, is the yaw angle, δ f is the front wheel steering angle, δ r is the rear wheel steering angle, is the longitudinal acceleration, is the yaw angular velocity, is the lateral acceleration, is the yaw angular acceleration; Step 2: obtaining a front wheel steering angle calculation formula and a rear wheel steering angle calculation formula according to the trajectory tracking control model; delta f = K p1 • e1 + K d1 • e2; delta r = K p2 * e1 + K d2 * e2 + 1.5 * u 2b ; wherein δ f is the front wheel steering angle, δ r is the rear wheel steering angle, K p1 is the front wheel displacement error coefficient, K d1 is the front wheel speed error coefficient, K p2 is the rear wheel displacement error coefficient, K d2 is the rear wheel speed error coefficient, e1 is the lateral displacement error, e2 is the lateral speed error, u 2b is the feedback of the rear wheel steering angle; The feedback quantity of the rear wheel steering angle is calculated by the following formula: wherein, is the derivative of the speed error with a feedback link, is the derivative of the yaw rate error with a feedback link; c1, c2 are constants; Step 3: establishing a target function, taking the minimum of the target function as an optimization objective, and optimizing an array composed of the front wheel displacement error coefficient, the front wheel speed error coefficient, the rear wheel displacement error coefficient and the rear wheel speed error coefficient to obtain an optimal array; The target function is: wherein e1 is a lateral displacement error, e2 is a lateral speed error, e3 is a yaw angle error, e4 is a yaw angle speed error, q1, q2, q3, q4 are weight coefficients of each error amount, q e is an economic weight coefficient, τ is time, T ∞ is a final state time, n is motor speed, T T is motor torque, η is motor efficiency; Step 4: calculating an optimal front wheel steering angle and an optimal rear wheel steering angle according to the optimal array.

2. The trajectory tracking control method for a distributed drive vehicle considering energy consumption according to claim 1, characterized in that, The relationship between the lateral displacement error, the lateral speed error, the yaw angle error and the yaw angle speed error and the front wheel displacement error coefficient, the front wheel speed error coefficient, the rear wheel displacement error coefficient and the rear wheel speed error coefficient is: where y r is a reference lateral displacement, is a reference lateral velocity, is a reference lateral acceleration, is a reference yaw angle, is a reference yaw rate, is a reference yaw acceleration, A is a first error coefficient matrix, B is a second error coefficient matrix, are derivatives of e1, e2, e3, e4, respectively.

3. The trajectory tracking control method for a distributed drive vehicle considering energy consumption according to claim 2, characterized by, In the third step, the Black-Hawk optimization algorithm is used to optimize the array consisting of the front wheel displacement error coefficient K p1 , the front wheel speed error coefficient K d1 , the rear wheel displacement error coefficient K p2 , and the rear wheel speed error coefficient K d2 , including the following steps: Step 1, taking the parameter array {K p1 K d1 K p2 K d2} to be optimized as an individual in the population to be optimized, and initializing the population to be optimized to obtain an initialized population; Wherein, the number of individuals in the initial population is n; Step 2: taking the target function as a fitness function; updating the individuals in the population by using the black eagle optimization algorithm, outputting n individuals with smaller fitness as the optimal solution set after each round of update, and taking the optimal solution set as the next generation population; Step 3: repeating step 2 to iteratively update the individuals in the population until a set number of iterations is reached; Step 4: selecting an individual with the smallest fitness from the optimal solution set obtained in the last iteration as the optimization result.

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