Racing car racing speed control method based on Gaussian process regression enhancement model predictive control

Abstract

The invention discloses a racing car racing control method based on Gaussian process regression enhancement model predictive control, and belongs to the field of unmanned driving system trajectory planning and tracking control. The method mainly comprises the following steps: firstly, constructing a racing car racing random optimal control problem model comprising a state equation, a measurement equation and probability constraints, and secondly, respectively modeling system uncertainty and measurement links by adopting a Gaussian process regression model; the method comprises the following steps: firstly, designing prudent model predictive control of racing car racing and an extended Kalman filter GP-EKF based on Gaussian process regression to realize high-precision state estimation, finally, fusing the GP-EKF and the prudent model predictive control, constructing learning model predictive control GP-EKF-LMPC based on GP-EKF enhancement, and feeding back posterior state estimation to an optimization problem, so as to realize high-precision state estimation. And solving an optimal control instruction of racing car racing in real time. Experiments show that the method can significantly improve the control precision and robustness in a complex scene.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned driving system trajectory planning and tracking control, and in particular relates to a racing car speed control method based on Gaussian process regression enhanced model predictive control. Background Art

[0002] With the advancement of science and technology, driverless technology has become a hot topic in the current automotive field. Among them, driverless racing, that is, autonomous driving racing technology, integrates artificial intelligence, sensors and automatic control technology to enable the car to drive autonomously without a human driver. This technology not only improves the performance and safety of the car, but also greatly reduces human errors. Driverless racing is gradually becoming a new trend in racing sports, which not only promotes the innovation of racing technology, but also brings a new viewing experience and competitive mode to racing sports.

[0003] Thanks to the increasing computing power, Model Predictive Control (MPC) can be used for path tracking and racing of autonomous vehicles. MPC is based on a mathematical model to optimize the motion control of the vehicle within a limited time range. On the one hand, this model should fully represent the vehicle properties and dynamics, and on the other hand, it should be suitable for online optimization frameworks. Especially in autonomous racing, the vehicle operates at its performance limit, which is a challenging trade-off. Among the published control methods, there is a mean estimate of Gaussian Process Regression (GPR) as the dynamic model required for MPC. However, the system state (such as speed and position) is often not directly available or can only be obtained with noise, which may lead to potential uncertainty, thus affecting the actual control performance. Although some public literature also uses Extended Kalman Filter (EKF) to obtain state estimation, it requires that the measurement model of the unmanned racing car can be obtained in advance and is continuously differentiable. In view of the above problems, the present invention proposes a reinforcement learning model predictive control method combining Gaussian process regression with a filter to improve the control performance of the unmanned racing car under extreme conditions. Summary of the invention

[0004] The purpose of the present invention is to provide a racing car speed control method based on Gaussian process regression enhanced model predictive control, so as to solve the problem that the existing model predictive control MPC in racing car speed may lead to control failure due to model deviation, inaccurate state estimation and discontinuity of measurement model, thereby improving the control quality, stability and efficiency.

[0005] To achieve the above object, the technical solution adopted by the present invention is: The racing speed control method of a car based on Gaussian process regression enhanced model predictive control includes the following steps: S1. Construct a random optimal control problem for a racing car, establish the state equation and measurement equation of the racing car discrete time system, the state equation includes a nominal model and an uncertainty model including a state-related residual model and an independent and identically distributed process noise, and obtain a random optimal control problem model with the goal of minimizing the expected cost and satisfying the system state and control input probability constraints; S2. Use Gaussian process regression model to model system uncertainty and measurement link respectively, and obtain system uncertainty GPR model and measurement link GPR model, wherein the system uncertainty GPR model takes state-control tuple as input and uncertainty as output, and the measurement link GPR model takes system state as input and measurement output as output; S3, designing a prudent model predictive control for racing cars, compensating the nominal model by using the Gaussian process regression model to predict the mean and variance of uncertainty, and constructing a probabilistic reachable set based on the variance of the predicted uncertainty to convert the probabilistic constraint into a tightened deterministic constraint, adjusting the tightening amplitude of the probabilistic constraint in real time, and then constructing the stochastic optimal control problem model described in step S1 into an approximate deterministic optimal control problem model; S4. Design an extended Kalman filter GP-EKF based on Gaussian process regression, and iteratively update the system state estimation in the non-continuous differentiable scenario through prediction steps and correction steps. The prediction step predicts the state mean and variance based on the nominal model and the system uncertainty GPR model. The correction step calculates the Kalman gain after linearizing the measurement link GPR model and updates the posterior state mean and variance. S5. Integrate the GP-EKF and prudent model predictive control to construct the GP-EKF-LMPC based on GP-EKF enhancement learning model predictive control. The posterior state estimation of step S4 is used as input and fed back to the approximate deterministic optimal control problem model of step S3 to generate optimal control instructions in real time to complete the racing task.

[0006] Furthermore, in step S1, the stochastic optimal control problem model is as follows: In the formula, E represents the expected value, , , are the system state, control input and measurement output at time k, represents the system state at time k and control input The corresponding cost function is, Indicates the system status of the terminal at the moment N The cost function is is the nominal model, is the state-dependent residual model, is independent and identically distributed process noise, , is the measurement function, To measure noise, , represents the control strategy, Represents probability.

[0007] Furthermore, in step S2, in the uncertain GPR model, the state control tuple is the input, and the corresponding uncertainty The uncertainty at time k is calculated as follows: In the formula, represents the uncertainty at time k, is the pseudo-inverse matrix.

[0008] Furthermore, the specific implementation process of step S2 includes: combining the similarity between the test data points and the observed data points, the covariance relationship between the observed data points and the observed uncertainty, calculating the mean of the posterior distribution of the test data points, and thus predicting the measured output value of the test data points.

[0009] Furthermore, the specific implementation process of step S3 includes: (1) The design control strategy is linear state feedback. The control strategy formula is as follows: In the formula, is the predicted state mean, is the predicted control input mean, is the system state at time k, is the feedback gain; Define the state deviation and control input deviation as: In the formula, is the state deviation, To control input deviation; (2) Using the first-order Taylor approximation of the nominal model and the mean function of the system uncertainty GPR model, the system state mean and system state variance are obtained: In the formula, represents the mean value of the system state at time k+1, represents the nominal model, represents the mean function of uncertainty at time k obtained based on the Gaussian process regression model, , They represent the variance of the system state at time k+1 and time k respectively, , is the covariance function of uncertainty at time k obtained based on the Gaussian process regression model, and T represents the transpose; Combining the control strategy formula, the control input variance is obtained as: , where Indicates the control input variance at time k.

[0010] Furthermore, in step S3, converting the probabilistic constraint into a tightened deterministic constraint includes: (1) Based on the system state variance and control input variance, the constructed probability is The k-step probability reachable set of state deviations and the k-step probability reachable set of input deviations ,get: (2) With the help of probabilistic reachable sets, the probabilistic constraints of the system state and control input at step k are converted into tightened deterministic constraints, as follows: In the formula, , They represent the system state after k-step transformation and the deterministic constraint set of control input, respectively. , They represent the original system state and the probability constraint set of the control input respectively. Represents the Minkowski difference operation.

[0011] Furthermore, in step S3, the expected cost function is approximated by the mean of the predicted state and the mean of the predicted control input to obtain an approximate deterministic optimal control problem model: In the formula, express Satisfy the system state deterministic constraints set , express Satisfy the set of control input deterministic constraints, Indicates that the initial state is , Indicates that the initial state covariance is 0.

[0012] Further, in step S4, the prediction model of the prediction step is: In the formula, Indicates the mean , the covariance is Gaussian distribution of Performing a first-order Taylor expansion on the prediction model at time t-1, the mean and variance of the prior state of the first step prediction at that time are as follows: In the formula, , They represent the prior state mean and variance of the first step prediction at time t-1, , They represent the mean and variance of the posterior state at time t-1 respectively, represents the control input at time t-1, .

[0013] Further, in step S4, the correction step specifically includes: The measurement link GPR model is linearized at the mean through the first-order Taylor expansion to obtain the measurement matrix , the Kalman gain is: In the formula, represents the Kalman gain at time t, represents the measurement matrix, Indicates that the mean value of the given prior state The covariance of the measurement noise; Then the mean and variance of the posterior state are updated as follows: In the formula, , They represent the mean and variance of the updated posterior state at time t, respectively. is the actual measured value of the system at time t, represents the predicted measurement mean based on the prior state mean, and I is the identity matrix.

[0014] Furthermore, the control instructions in step S5 include acceleration and steering angle, and the goal is to minimize the lap time while satisfying the track boundary safety constraints.

[0015] The beneficial effects of the above scheme are: The present invention solves the problems that the system state is difficult to directly observe in the racing scene and the control effect of the traditional model predictive control technology is not ideal due to the inaccurate model by designing a Gaussian process regression filter reinforcement learning model predictive control method. By adjusting the control instructions in real time, this method can cope with various complex situations such as track changes and vehicle dynamics, thereby ensuring that the car completes the race in the safest state and the shortest time. Compared with the traditional model predictive control technology, the present invention shows significant advantages in control quality and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The driving trajectory and speed diagram of the racing car using the traditional MPC control method; Figure 2 The driving trajectory and speed diagram of the racing car using the learning MPC control method; Figure 3 The driving trajectory and speed diagram of the car using the cautious MPC control method; Figure 4 The driving trajectory and speed diagram of the racing car using the GP-EKF-LMPC control method of the present invention. DETAILED DESCRIPTION

[0017] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] It should be noted that unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0019] In order to solve the problem that the system state cannot be directly obtained during racing and the existing measurement model is not continuous and differentiable, the present invention designs a learning based Model Predictive Control (LMPC) that integrates the system nominal model and the residual uncertainty Gaussian process regression model. It estimates the future position and speed of the car in real time according to the road conditions and the car state, and gives the optimal acceleration and steering control instructions.

[0020] A racing speed control method based on Gaussian process regression enhanced model predictive control includes the following steps: S1. Construct a random optimal control problem for a racing car, establish the state equation and measurement equation of the racing car discrete time system, the state equation includes a nominal model and an uncertainty model including a state-related residual model and an independent and identically distributed process noise, and obtain a random optimal control problem model with the goal of minimizing the expected cost and satisfying the system state and control input probability constraints; S2. Use Gaussian process regression model to model system uncertainty and measurement link respectively, and obtain system uncertainty GPR model and measurement link GPR model, wherein the system uncertainty GPR model takes state-control tuple as input and uncertainty as output, and the measurement link GPR model takes system state as input and measurement output as output; S3, designing a prudent model predictive control for racing cars, compensating the nominal model by using the Gaussian process regression model to predict the mean and variance of uncertainty, and constructing a probabilistic reachable set based on the variance of the predicted uncertainty to convert the probabilistic constraint into a tightened deterministic constraint, adjusting the tightening amplitude of the probabilistic constraint in real time, and then constructing the stochastic optimal control problem model described in step S1 into an approximate deterministic optimal control problem model; S4. Design an extended Kalman filter GP-EKF based on Gaussian process regression, and iteratively update the system state estimation in the non-continuous differentiable scenario through prediction steps and correction steps. The prediction step predicts the state mean and variance based on the nominal model and the system uncertainty GPR model. The correction step calculates the Kalman gain after linearizing the measurement link GPR model and updates the posterior state mean and variance. S5. Integrate the GP-EKF and prudent model predictive control to construct the GP-EKF-LMPC based on GP-EKF enhancement learning model predictive control. The posterior state estimation of step S4 is used as input and fed back to the approximate deterministic optimal control problem model of step S3 to generate optimal control instructions in real time to complete the racing task.

[0021] Each step of the present invention is described in detail below: Step S1, constructing a car racing stochastic optimal control problem model.

[0022] For a racing car discrete time system, its state equation and measurement equation are: (1a) (1b) in, , , are the system state, control input and measurement output at time k respectively. is the known part of the dynamic model, which is the nominal model. The unknown part of the system is called uncertainty and is expressed as , including the state-dependent residual model and independent and identically distributed process noise , , is the measurement function, To measure noise, f and g are continuous differentiable functions. In addition, the state and input are subject to probability constraints, and the probability of constraint violation is no greater than The stochastic optimal control problem model of car racing is obtained: (2a) (2b) (2c) (2d) (2e) (2f) In the formula, E represents the expected value, represents the system state at time k and control input The corresponding cost function is, Indicates the system status of the terminal at the moment N The cost function is represents the control strategy, Represents probability.

[0023] Step S2: designing a Gaussian process regression model for uncertainty and measurement of a racing car system.

[0024] GPR is used to model the uncertainty of the racing system in (1a) and the measurement link in (1b). In the uncertain GPR model, the state control tuple is the input, and the corresponding uncertainty is the output. The uncertainty at time k is: (3) In the formula, represents the uncertainty at time k, is the pseudo-inverse matrix.

[0025] The set of M observation data is denoted as . Given a test data point Based on this data set, The posterior distribution of is still Gaussian: (4) The mean and variance of the posterior distribution of the test data points are: (5a) (5b) Here yes The covariance matrix of .

[0026] In addition, since the traditional measurement model of the racing system is not continuous and differentiable, the present invention also uses GPR to model the observed dynamics. and measurement output As the input and output of the GPR model respectively. The data set composed of observation data is denoted as The GPR model for the measurement phase is trained based on the data set, and its mean and variance are similar to those of formulas (5a) and (5b).

[0027] It should be noted that the above observation data sets are all measured by system sensors. The present invention combines the similarity between the test data points and the observation data points, the covariance relationship between the observation data points, and the observed uncertainty to calculate the mean of the posterior distribution of the test data points, thereby predicting the measured output value of the test data points.

[0028] Step S3: designing a prudent model predictive control for racing.

[0029] Assuming that the state can be fully measured, a prudent model predictive control for racing cars is designed. The mean and variance of the GPR model prediction uncertainty are used to compensate for the inaccurate nominal model, and the tightening amplitude of the probability constraint is adjusted in real time according to the variance of the prediction uncertainty to achieve prudent control.

[0030] (1) Design control strategy as linear state feedback: (6) In the formula, is the predicted state mean, is the predicted control input mean, is the system state at time k, is the feedback gain.

[0031] In order to improve the computational efficiency, the feedback gain The state deviation and control input deviation are defined as: (7a) (7b) (2) Using the first-order Taylor approximation of the nominal model f and the mean function of the uncertain GPR model, the system state mean and system state variance are obtained: (8a) (8b) In the formula, represents the mean value of the system state at time k+1, represents the nominal model, represents the mean function of uncertainty at time k obtained based on the Gaussian process regression model, , They represent the variance of the system state at time k+1 and time k respectively, , is the covariance function of uncertainty at time k obtained based on the Gaussian process regression model, and T represents the transpose; Combining the control strategy formula (6), the control input variance is obtained as: , where Indicates the control input variance at time k.

[0032] (3) Define the n-step probabilistic reachable set: For variable x, the initial value is ,if , n is an integer greater than 0, then the set is the n-step probabilistically reachable set (n-step PRS) of x.

[0033] Based on the system state variance and control input variance , the construction probability is The k-step probability reachable set of state deviations and the k-step probability reachable set of input deviations , from the definition we know: (9a) (9b) Then, the probabilistic constraints of the system state and control input at step k are transformed into tightened deterministic constraints with the help of PRS, as follows: (10a) (10b) In the formula, , They represent the system state after k-step transformation and the deterministic constraint set of control input, respectively. , They represent the original system state and the probability constraint set of the control input respectively. Represents the Minkowski difference operation.

[0034] Then it can be guaranteed that the state probability constraint in formula (2e) and the control input probability constraint in formula (2f) are satisfied. That is, if ,but ; like ,but .

[0035] In order to reduce the computational complexity, the expected cost function is approximated by the mean of the predicted state and the mean of the predicted control input. Therefore, when the state is completely measurable, the stochastic optimal control problem model is constructed as an approximate deterministic optimal control problem model, as follows: (11) In the formula, express Satisfy the system state deterministic constraints set , express Satisfy the set of control input deterministic constraints, Indicates that the initial state is , Indicates that the initial state covariance is 0. is the nominal input sequence.

[0036] Step S4: design an extended Kalman filter GP-EKF based on Gaussian process regression.

[0037] When the system state cannot be directly or completely measured, the state estimation method must be used to ensure the control performance. Considering that the measurement model of the racing system is discontinuous and differentiable, the present invention designs an extended Kalman filter GP-EKF based on Gaussian process regression and integrates the above cautious model predictive control to solve the stochastic optimal control problem of racing.

[0038] The GP-EKF process consists of two parts: prediction and correction. First, the prior state mean and variance are defined as and , and use and represents the posterior state mean and variance.

[0039] The prediction steps include: For the state equation (1a), its prediction model is expressed as: (12) In the formula, Indicates the mean , the covariance is Gaussian distribution.

[0040] The prediction model (12) includes the nominal model and the uncertainty modeled by GPR. The prediction model at time t-1 is approximated by the first-order Taylor expansion. The mean and variance of the prior state of the first step prediction at this time are as follows: (13a) (13b) In the formula, , They represent the prior state mean and variance of the first step prediction at time t-1, , They represent the mean and variance of the posterior state at time t-1 respectively, represents the control input at time t-1, .

[0041] The calibration steps specifically include: Based on the GPR model of the system measurement link, given the state ,but , whose mean and variance are similar to those of formulas (5a) and (5b). The GPR model of the measurement link is linearized at the mean through the first-order Taylor approximation to obtain the measurement matrix . Then the Kalman gain is: (14) In the formula, represents the Kalman gain at time t, represents the measurement matrix, Indicates that the mean value of the given prior state The covariance of the measurement noise.

[0042] Then the posterior state mean and variance are updated as follows: (15a) (15b) In the formula, , They represent the mean and variance of the updated posterior state at time t, respectively. is the actual measured value of the system at time t, represents the predicted measurement mean based on the prior state mean, and I is the identity matrix.

[0043] Step S5: construct a learning model predictive control GP-EKF-LMPC based on GP-EKF enhancement.

[0044] When the state cannot be directly or completely measured and the existing measurement model is not continuous and differentiable, the present invention combines GP-EKF with cautious model predictive control to obtain an approximate deterministic optimal control problem of the car racing stochastic optimal control problem model. The GP-EKF-LMPC model based on GP-EKF enhanced learning model predictive control is as follows: (16) In the formula, , , They represent the prior state means of the kth step, the first step and the Nth step prediction at time t, respectively. , They represent the prior state variances of the first step and the k+1 step predictions at time t, respectively. represents the actual control input at time t, represents the control input predicted at the kth step at time t, represents the updated posterior state mean at time t, , , represents a set of state deterministic constraints, Represents a set of deterministic constraints controlling the input.

[0045] In the process of solving the optimization problem, the posterior state mean and variance are updated according to formulas (15a) and (15b).

[0046] In order to intuitively demonstrate the effectiveness and superiority of the present invention, the traditional MPC, learning MPC, cautious MPC and the GP-EKF-LMPC designed by the present invention are used to control the speed of the racing car respectively. Figures 1 to 4 The driving trajectory and speed of the car under the control of the above four algorithms are shown respectively. Figures 1 to 4 In the figure, the track includes sharp turns, straights and curves. The boundaries are marked with solid black lines, the center line is marked with a dotted line in the middle, the black box on the driving trajectory represents the car, the circular / oval curve extending in front of the car represents the predicted trajectory, and other lines distributed inside and outside the track represent the actual trajectory of the car. Figure 1 Traditional MPC does not take system uncertainty into account. Figures 2 to 4 The model predictive control used takes into account system uncertainty, so the longer the prediction step, the greater the prediction deviation. The solid dots on the prediction trajectory represent the prediction mean, and the shadow represents the prediction variance. The rules of the competition require that the car complete 10 laps along the track at the fastest speed while driving safely (without running off the track).

[0047] Depend on Figures 1 to 4 It can be seen that: (1) Because the traditional MPC ignores the model deviation, the control quality is the worst, and it runs out of the track on the 6th lap and fails to finish the race, while the other three methods all complete the race. (2) Figure 2 It can be seen that learning MPC integrates the model uncertainty learned by GPR with the nominal dynamics, making the system model more accurate and thus achieving better performance. However, due to the high speed of the car, the car still frequently cuts the track boundary, especially in sharp turns. (3) Figure 3 The vehicle trajectory under cautious MPC control is described. To avoid boundary violations, the cautious MPC scheme tightens the constraints according to the predicted variance, resulting in a more cautious control output that maintains a safe distance from the boundary. (4) In addition, in the case of measurement uncertainty, the GP-EKF-LMPC learning model predictive control designed by the present invention makes the estimated state more accurate and weakens the impact of uncertainty online. Figure 3 and Figure 4 , the racing car's driving trajectory is more consistent than that of a vehicle that only uses cautious MPC control, improving driving safety and efficiency.

[0048] Therefore, the main advantages of the present invention are: (1) Effectively improve control accuracy and stability. By accurately estimating the system state through GP-EKF and combining it with the dynamic model optimization of LMPC, high-precision control instructions can still be generated in extreme scenarios such as sharp turns and straight-line acceleration in racing cars, thus avoiding control failure caused by model deviation in traditional MPC.

[0049] (2) Enhance the robustness of the system. The Gaussian process regression model is used to model the system uncertainty and measurement links respectively, so that the system can adapt to changes in track conditions and vehicle dynamic disturbances. The dynamic constraint adjustment mechanism of the probabilistic reachable set ensures that the system always meets the safety constraints within the allowable violation probability.

[0050] (3) Achieving a balance between efficiency and safety, GP-EKF-LMPC takes into account both safety and racing efficiency in the generation of control instructions. Experiments show that the time it takes to complete 10 laps is significantly shorter than that of the cautious MPC, and there is no track crossing ( Figure 4 ). By integrating state estimation and model prediction in real time, the system can still pass through sharp turns at a speed close to the limit, while traditional methods require slowing down to ensure safety.

[0051] (4) Reduce the dependence on the measurement model. The present invention does not require the measurement model to be continuously differentiable. Nonlinear observation dynamics can be constructed only through historical data, which solves the limitation of existing methods on strong assumptions about the measurement model and expands the application scenarios.

[0052] In summary, the present invention deeply integrates Gaussian process regression, state estimation and model predictive control through the GP-EKF-LMPC model, and realizes high-precision and high-robust autonomous control in the racing scene. On the one hand, it solves the bottlenecks of traditional methods in state estimation, model deviation and discontinuous differentiability of measurement model, and at the same time provides a safe and efficient racing control solution for unmanned racing cars, which can be extended to real-time optimization control of other nonlinear systems. Experimental results verify that this method has significant advantages in control quality, stability and efficiency.

[0053] Finally, it should be noted that the parts of the present invention that are not described in detail are all prior art. Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the aforementioned examples, those of ordinary skill in the art can still modify the technical solutions recorded in the aforementioned examples, or replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, etc. made within the spirit and principles of the invention should be included in the scope of protection of the invention.

Claims

1. A racing car speed control method based on Gaussian process regression enhanced model predictive control, characterized in that: The following steps are involved: S1. Construct a random optimal control problem for a racing car, establish the state equation and measurement equation of the racing car discrete time system, the state equation includes a nominal model and an uncertainty model including a state-related residual model and an independent and identically distributed process noise, and obtain a random optimal control problem model with the goal of minimizing the expected cost and satisfying the system state and control input probability constraints; S2. Use Gaussian process regression model to model system uncertainty and measurement link respectively, and obtain system uncertainty GPR model and measurement link GPR model, wherein the system uncertainty GPR model takes state-control tuple as input and uncertainty as output, and the measurement link GPR model takes system state as input and measurement output as output; S3, designing a prudent model predictive control for racing cars, compensating the nominal model by using the Gaussian process regression model to predict the mean and variance of uncertainty, and constructing a probabilistic reachable set based on the variance of the predicted uncertainty to convert the probabilistic constraint into a tightened deterministic constraint, adjusting the tightening amplitude of the probabilistic constraint in real time, and then constructing the stochastic optimal control problem model described in step S1 into an approximate deterministic optimal control problem model; S4. Design an extended Kalman filter GP-EKF based on Gaussian process regression, and iteratively update the system state estimation in the non-continuous differentiable scenario through prediction steps and correction steps. The prediction step predicts the state mean and variance based on the nominal model and the system uncertainty GPR model. The correction step calculates the Kalman gain after linearizing the measurement link GPR model and updates the posterior state mean and variance. S5. Integrate the GP-EKF and prudent model predictive control to construct the GP-EKF-LMPC based on GP-EKF enhancement learning model predictive control. The posterior state estimation of step S4 is used as input and fed back to the approximate deterministic optimal control problem model of step S3 to generate optimal control instructions in real time to complete the racing task.

2. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 1, characterized in that: In step S1, the stochastic optimal control problem model is as follows: In the formula, E represents the expected value, , , are the system state, control input and measurement output at time k, represents the system state at time k and control input The corresponding cost function is, Indicates the system status of the terminal at the moment N The cost function is is the nominal model, is the state-dependent residual model, is independent and identically distributed process noise, , is the measurement function, To measure noise, , represents the control strategy, Represents probability.

3. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 2 is characterized in that: In step S2, in the uncertain GPR model, the state control tuple is the input, and the corresponding uncertainty The uncertainty at time k is calculated as follows: In the formula, represents the uncertainty at time k, is the pseudo-inverse matrix.

4. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 3 is characterized in that: The specific implementation process of step S2 includes: combining the similarity between the test data points and the observed data points, the covariance relationship between the observed data points and the observed uncertainty, calculating the mean of the posterior distribution of the test data points, and thus predicting the measured output value of the test data points.

5. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 2, characterized in that: The specific implementation process of step S3 includes: (1) The design control strategy is linear state feedback. The control strategy formula is as follows: In the formula, is the predicted state mean, is the predicted control input mean, is the system state at time k, is the feedback gain; Define the state deviation and control input deviation as: In the formula, is the state deviation, To control input deviation; (2) Using the first-order Taylor approximation of the nominal model and the mean function of the system uncertainty GPR model, the system state mean and system state variance are obtained: In the formula, represents the mean value of the system state at time k+1, represents the nominal model, represents the mean function of uncertainty at time k obtained based on the Gaussian process regression model, , They represent the variance of the system state at time k+1 and time k respectively, , is the covariance function of uncertainty at time k obtained based on the Gaussian process regression model, and T represents the transpose; Combining the control strategy formula, the control input variance is obtained as: , where Indicates the control input variance at time k.

6. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 5, characterized in that: The conversion of the probabilistic constraints into tightened deterministic constraints in step S3 includes: (1) Based on the system state variance and control input variance, the constructed probability is The k-step probability reachable set of state deviations and the k-step probability reachable set of input deviations ,get: (2) With the help of probabilistic reachable sets, the probabilistic constraints of the system state and control input at step k are converted into tightened deterministic constraints, as follows: In the formula, , They represent the system state after k-step transformation and the deterministic constraint set of control input, respectively. , They represent the original system state and the probability constraint set of the control input respectively. Represents the Minkowski difference operation.

7. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 6, characterized in that: In step S3, the expected cost function is approximated by the mean of the predicted state and the mean of the predicted control input to obtain an approximate deterministic optimal control problem model: In the formula, express Satisfy the system state deterministic constraints set , express Satisfy the set of control input deterministic constraints, Indicates that the initial state is , Indicates that the initial state covariance is 0.

8. The racing car speed control method based on Gaussian process regression enhanced model predictive control according to claim 7, characterized in that: In step S4, the prediction model of the prediction step is: In the formula, Indicates the mean , the covariance is Gaussian distribution of Performing a first-order Taylor expansion on the prediction model at time t-1, the mean and variance of the prior state of the first step prediction at that time are as follows: In the formula, , They represent the prior state mean and variance of the first step prediction at time t-1, , They represent the mean and variance of the posterior state at time t-1 respectively, represents the control input at time t-1, .

9. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 7, characterized in that: In step S4, the correction step specifically includes: The measurement link GPR model is linearized at the mean through the first-order Taylor expansion to obtain the measurement matrix , the Kalman gain is: In the formula, represents the Kalman gain at time t, represents the measurement matrix, Indicates that the mean value of the given prior state The covariance of the measurement noise; Then the mean and variance of the posterior state are updated as follows: In the formula, , They represent the mean and variance of the updated posterior state at time t, respectively. is the actual measured value of the system at time t, represents the predicted measurement mean based on the prior state mean, and I is the identity matrix.

10. The racing speed control method based on Gaussian process regression enhanced model predictive control according to claim 1, characterized in that: The control instructions in step S5 include acceleration and steering angle, and the goal is to minimize the lap time while satisfying the track boundary safety constraints.

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