An explicit control law design method for autonomous vehicles

Abstract

The application relates to the technical field of intelligent driving of an automobile, in particular to a design method of an explicit control law of an automatic driving automobile, and the method comprises the following steps: constructing a vehicle dynamics model with an affine structure; based on the vehicle dynamics affine model, converting a target function and a constraint condition of a tracking obstacle avoidance constraint type optimal control problem into a control Lyapunov function and a control barrier function; performing weighted addition on the control Lyapunov function and the control barrier function to construct a control Lyapunov-barrier function; and using the gradient of the control Lyapunov-barrier function, a state transition matrix of the dynamics model and a control input transition matrix to design the explicit control law of the automatic driving automobile. Therefore, the problem that, in the related art, the constraint type optimal control problem in obstacle avoidance tracking control needs to be solved through large-scale iterative calculation, the calculation complexity increases sharply when facing multiple obstacles, and the real-time performance and safety of the vehicle-mounted controller cannot meet the millisecond level are solved.

Description

Technical Field

[0001] This application relates to the field of intelligent driving technology for automobiles, and in particular to a method for designing explicit control laws for autonomous vehicles. Background Technology

[0002] Currently, with the development of intelligent vehicles, autonomous driving, as a core component of a new round of technological revolution, is becoming a strategic competition focus for major industrial powers around the world. Ensuring that vehicles can quickly track trajectories and actively avoid obstacles safely in complex traffic environments is a basic requirement for high-level autonomous vehicles and has become an urgent problem to be solved in the field of autonomous driving.

[0003] In most cases, obstacle avoidance and tracking control is carried out through model predictive control. The obstacle avoidance and tracking scenario is constructed as a constrained optimal control problem, that is, the optimal control input that satisfies the KKT (Karush-Kuhn-Tucker) constraint optimal conditions is found through iterative methods to control the vehicle.

[0004] However, the related technologies rely excessively on large-scale iterative calculations. When a car faces multiple obstacles, the computational complexity increases sharply, which cannot meet the millisecond-level real-time requirements of the vehicle controller, nor can it meet the safety requirements. Improvements are urgently needed. Summary of the Invention

[0005] This application provides an explicit control law design method for autonomous vehicles to solve the problem in related technologies where the computational complexity increases sharply when facing multiple obstacles due to the need for large-scale iterative calculations to solve the constrained optimal control problem in obstacle avoidance and tracking control, which cannot meet the millisecond-level real-time performance and safety requirements of the on-board controller.

[0006] This application provides a method for designing explicit control laws for autonomous vehicles, characterized by the following steps: constructing a vehicle dynamics model with an affine structure; based on the vehicle dynamics affine model, converting the objective function and constraints of the tracking and obstacle avoidance constraint-type optimal control problem into a control Lyapunov function and a control obstacle function; weighting the control Lyapunov function and the control obstacle function to construct a control Lyapunov-obstacle function; and using the gradient of the control Lyapunov-obstacle function, the state transition matrix of the dynamics model, and the control input transition matrix to design an explicit control law for the autonomous vehicle.

[0007] Optionally, in one embodiment of this application, the expression for the vehicle dynamics model with an affine structure can be:

[0008]

[0009] Where X is the vehicle state vector; Let X be the time derivative of X; U be the control input vector; f(·) be the vehicle state transition matrix; g(·) be the control input transition matrix; v x v is the longitudinal velocity of the vehicle. y The vehicle's lateral speed; ω is the vehicle's heading angle; k is the vehicle's yaw rate; f For front wheel stiffness; k r For rear wheel stiffness; l f The distance from the vehicle's center to the front axle; l r denoted as denoted as , where is the distance from the vehicle center to the rear axle; m is the vehicle mass; Iz is the yaw moment of inertia; a is the acceleration; and δ is the front wheel steering angle.

[0010] Optionally, in one embodiment of this application, the expression for controlling the Lyapunov function can be:

[0011] V RD1 =P1(v x -v x，Ref ) 2 +P2(v y -v y，Ref ) 2 +P3(ω-ω Ref ) 2

[0012]

[0013] Among them, V RD1为 The control Lyapunov function relative to the first-order tracking target; v x v is the longitudinal velocity of the vehicle. x，Ref For reference longitudinal velocity; v y v is the lateral velocity of the vehicle. y，Ref ω is the reference lateral velocity; ω is the vehicle's yaw rate; ω Ref For reference yaw rate; V RD2 p is the control Lyapunov function for the relative second-order tracking target; x p represents the longitudinal position of the vehicle. x，Ref For reference longitudinal position; p y p represents the lateral position of the vehicle. y，Ref For reference horizontal position; Vehicle heading angle; The reference orientation angle is P1 to P6, which are the weights assigned to the squared terms of the state error.

[0014] Optionally, in one embodiment of this application, the expression of the control barrier function in the form of a Softplus function can be:

[0015]

[0016]

[0017] Among them, H RD1 H is the control barrier function corresponding to the relative first-order constraint variable; RD2 c is the control barrier function corresponding to the relative second-order constraint variable; i The adjustment parameter for controlling the gradient of the barrier function; x min This represents the lower bound of the corresponding constraint variable; x max v is the upper limit of the corresponding constraint variable; x v is the longitudinal velocity of the vehicle. y ω is the lateral velocity of the vehicle; p is the yaw rate of the vehicle; ω is the yaw rate of the vehicle; x p represents the longitudinal position of the vehicle. y The vehicle's lateral position; This refers to the vehicle's heading angle.

[0018] Optionally, in one embodiment of this application, the expression of the Gaussian distribution form of the control barrier function can be:

[0019]

[0020] Where C is a parameter that adjusts the size of the function according to the size of the obstacle; p x p represents the longitudinal position of the vehicle. x，obs p represents the longitudinal position of the obstacle. y p represents the lateral position of the vehicle. y，obs The lateral position of the obstacle; The variance is the longitudinal positional variance. This represents the lateral positional variance.

[0021] Optionally, in one embodiment of this application, the expression for the control Lyapunov-barrier function can be:

[0022]

[0023] Where B is the control Lyapunov-barrier function; w RD1 The weights for the relative first-order control Lyapunov; V RD1 For relative first-order control Lyapunov functions; w RD1，i H represents the weight corresponding to the barrier function for the i-th relative first-order constraint variable; RD1，i w is the control barrier function relative to the i-th first-order constraint variable; RD2 The weights of the derivatives of the Lyapunov function are controlled relative to the second-order tracking target; The derivative of the Lyapunov function controlling the relative second-order tracking target; w RD2，iThe weights of the derivative of the barrier function are used to control the i-th relative first-order constraint variable; N is the derivative of the control barrier function for the i-th relative second-order constraint variable; RD1 N represents the number of relative first-order constraints. RD2 The number of relative second-order constraints.

[0024] Optionally, in one embodiment of this application, the expression of the explicit control law can be:

[0025]

[0026]

[0027] Where U is the control input vector; X is the vehicle state vector; α is the Lie derivative of B with respect to f(X); β is the Lie derivative of B with respect to g(X); and γ is a parameter for adjusting the convergence of the function B.

[0028] This application's embodiments can transform the objective function and constraints of a constrained optimal control problem into a control Lyapunov function and a control obstacle function. These two functions are then weighted and summed to construct a control Lyapunov-obstacle function. The gradient of the control Lyapunov-obstacle function, the state transition matrix of the dynamic model, and the control input transition matrix can then be used to design an explicit control law for autonomous vehicles, achieving millisecond-level high real-time control and ensuring the real-time performance and safety of vehicle control. This solves the problem in related technologies where large-scale iterative calculations are required to solve constrained optimal control problems in obstacle avoidance and tracking control, leading to a sharp increase in computational complexity when dealing with multiple obstacles, thus failing to meet the millisecond-level real-time performance and safety requirements of onboard controllers.

[0029] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0030] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0031] Figure 1 This is a flowchart of an explicit control law design method for an autonomous vehicle according to an embodiment of this application. Detailed Implementation

[0032] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0033] The following describes an explicit control law design method for an autonomous vehicle according to embodiments of this application, with reference to the accompanying drawings. Addressing the issue mentioned in the background art where the computational complexity increases dramatically in multi-obstacle scenarios due to the need for large-scale iterative calculations to solve constrained optimal control problems in obstacle avoidance and tracking control, failing to meet the millisecond-level real-time performance and safety requirements of onboard controllers, this application provides an explicit control law design method for an autonomous vehicle. In this method, the objective function and constraints of the constrained optimal control problem can be transformed into a control Lyapunov function and a control obstacle function. These two functions are then weighted and summed to construct a control Lyapunov-obstacle function. The gradient of the control Lyapunov-obstacle function, the state transition matrix of the dynamic model, and the control input transition matrix can then be used to design the explicit control law for the autonomous vehicle, achieving millisecond-level high real-time control and ensuring the real-time performance and safety of vehicle control. This solves the problem in related technologies where the computational complexity increases dramatically in multi-obstacle scenarios due to the need for large-scale iterative calculations to solve constrained optimal control problems in obstacle avoidance and tracking control, failing to meet the millisecond-level real-time performance and safety requirements of onboard controllers.

[0034] Specifically, Figure 1 This is a flowchart of an explicit control law design method for an autonomous vehicle according to an embodiment of this application.

[0035] like Figure 1 As shown, the explicit control law design method for this autonomous vehicle includes the following steps:

[0036] In step S101, a vehicle dynamics model with an affine structure is constructed, wherein the expression of the vehicle dynamics model with an affine structure can be:

[0037]

[0038] Where X is the vehicle state vector; Let X be the time derivative of X; U be the control input vector; f(·) be the vehicle state transition matrix; g(·) be the control input transition matrix; v x v is the longitudinal velocity of the vehicle. y The vehicle's lateral speed; ω is the vehicle's heading angle; k is the vehicle's yaw rate; f For front wheel stiffness; k rFor rear wheel stiffness; l f The distance from the vehicle's center to the front axle; l r denoted as denoted as , where is the distance from the vehicle center to the rear axle; m is the vehicle mass; Iz is the yaw moment of inertia; a is the acceleration; and δ is the front wheel steering angle.

[0039] It is understood that any vehicle dynamics model can be used as the vehicle dynamics model for autonomous driving control, including but not limited to: bicycle models, kinematic models, etc., and this application does not impose specific restrictions. Judging from the input end, it can be further divided into: non-affine structure models and radial structure models.

[0040] As one possible approach, embodiments of this application can approximate a non-affine dynamics model into a vehicle dynamics model with an affine structure through some transformations and conversions, thereby enabling the design of explicit control laws for autonomous vehicles.

[0041] For example, this application uses a bicycle model as an example. The expression for the bicycle model can be:

[0042]

[0043]

[0044] Where X is the vehicle state vector; Let X be the derivative of X with respect to time; U be the control input vector; f(·) be the transition matrix between the vehicle state and the control input; p x p represents the longitudinal position of the vehicle. y The vehicle's lateral position; v is the vehicle's heading angle; x v is the longitudinal velocity of the vehicle. y ω is the vehicle's lateral velocity; a is the vehicle's yaw rate; δ is the acceleration; k is the front wheel steering angle; f For front wheel stiffness; k r For rear wheel stiffness; l f The distance from the center of the vehicle to the front axle; r is the distance from the center of the vehicle to the rear axle; m is the vehicle mass; I z This is the moment of inertia of yaw rotation.

[0045] In order to transform the bicycle model into a vehicle dynamics model with an affine structure, the embodiments of this application can ignore the longitudinal resistance caused by steering. And the variable δ is approximated. This can be understood as the embodiments of this application being able to... Approximating sinδ and cosδ to δ and 1 respectively, we obtain a vehicle dynamics model with an affine structure. The expression for this model can be:

[0046]

[0047] Where X is the vehicle state vector; Let X be the time derivative of X; U be the control input vector; f(·) be the vehicle state transition matrix; g(·) be the control input transition matrix; v x v is the longitudinal velocity of the vehicle. y The vehicle's lateral speed; ω is the vehicle's heading angle; k is the vehicle's yaw rate; f For front wheel stiffness; k r For rear wheel stiffness; l f The distance from the vehicle's center to the front axle; l r is the distance from the vehicle center to the rear axle; m is the vehicle mass; I z δ is the yaw moment of inertia; a is the acceleration; δ is the front wheel rotation angle.

[0048] In step S102, based on the affine model of vehicle dynamics, the objective function and constraints of the tracking and obstacle avoidance constrained optimal control problem are transformed into a control Lyapunov function and a control obstacle function. The expression for the control Lyapunov function can be:

[0049] V RD1 =P1(v x -v x，Ref ) 2 +P2(v y -v y，Ref ) 2 +P3(ω-ω Ref ) 2

[0050]

[0051] Among them, V RD1 The control Lyapunov function relative to the first-order tracking target; v x v is the longitudinal velocity of the vehicle. x，Ref For reference longitudinal velocity; v y v is the lateral velocity of the vehicle. y，Ref ω is the reference lateral velocity; ω is the vehicle's yaw rate; ω Ref For reference yaw rate; V RD2 p is the control Lyapunov function for the relative second-order tracking target; x p represents the longitudinal position of the vehicle. x，Ref For reference longitudinal position; p y p represents the lateral position of the vehicle. y，Ref For reference horizontal position; Vehicle heading angle; The reference orientation angle is P1 to P6, which are the weights assigned to the squared terms of the state error.

[0052] It is understood that the purpose of this application's embodiments is to design explicit control laws for controlling autonomous vehicles to track and avoid obstacles. Specifically, for explicit control laws, this application's embodiments carefully consider the interrelationships between the control input and each state variable constituting the function to ensure that the accurate control inputs required to construct the functions of each state variable are obtained. Therefore, when designing the function, this application's embodiments can separately consider constraints and optimization objectives with different relative orders in the control system. That is, the objective function and constraints of the constrained optimal control problem can be transformed into a control Lyapunov function and a control obstacle function.

[0053] In actual implementation, the embodiments of this application can transform the objective function of the constrained optimal control problem into a control Lyapunov function based on a vehicle dynamics model with an affine structure, thereby controlling the vehicle to stably track the trajectory by designing an explicit control law for autonomous vehicles.

[0054] For example, this application embodiment uses the vehicle dynamics model with an affine structure obtained in step S101 as an example, p x py and It is a relative second-order state variable, while v x v y ω and ω are relative first-order state variables.

[0055] Specifically, in constrained optimal control problems, the objective function consists of the tracking error of the reference trajectory and the square of the input signal. To ensure convergence of the tracking target, embodiments of this application can introduce a control Lyapunov function, setting the reference state as the equilibrium point of the control Lyapunov function. The control Lyapunov function can be viewed as a function whose value increases with distance from the equilibrium point, exhibiting a gradually increasing gradient, such as a function with convex properties.

[0056] In other words, the embodiments of this application can consider the control Lyapunov functions of relative first order and relative second order according to the relative order of each optimization objective. The expression for the control Lyapunov function can be:

[0057] V RD1 =P1(v x -v x，Ref ) 2 +P2(v y -v y，Ref ) 2 +P3(ω-ω Ref ) 2

[0058]

[0059] Among them, V RD1 The control Lyapunov function relative to the first-order tracking target; v x v is the longitudinal velocity of the vehicle. x，Ref For reference longitudinal velocity; v y v is the lateral velocity of the vehicle. y，Ref ω is the reference lateral velocity; ω is the vehicle's yaw rate; ω Ref For reference yaw rate; V RD2 p is the control Lyapunov function for the relative second-order tracking target; x p represents the longitudinal position of the vehicle. x，Ref For reference longitudinal position; p y p represents the lateral position of the vehicle. y，Ref For reference horizontal position; Vehicle heading angle; The reference orientation angle is P1 to P6, which are the weights assigned to the squared terms of the state error.

[0060] Optionally, in one embodiment of this application, the expression of the control barrier function in the form of a Softplus function can be:

[0061]

[0062]

[0063] Among them, H RD1 H is the control barrier function corresponding to the relative first-order constraint variable; RD2 c is the control barrier function corresponding to the relative second-order constraint variable; i The adjustment parameter for controlling the gradient of the barrier function; x min This represents the lower bound of the corresponding constraint variable; x max v is the upper limit of the corresponding constraint variable; x v is the longitudinal velocity of the vehicle. y ω is the lateral velocity of the vehicle; p is the yaw rate of the vehicle; ω is the yaw rate of the vehicle; x py represents the vehicle's longitudinal position; py represents the vehicle's lateral position. This refers to the vehicle's heading angle.

[0064] As one possible implementation method, in actual execution, the embodiments of this application can be based on a vehicle dynamics model with an affine structure to transform the constraints of the constrained optimal control problem into a control obstacle function, thereby designing an explicit control law for autonomous vehicles to control the vehicle to follow safety constraints and ensure driving safety.

[0065] For example, this application embodiment uses the vehicle dynamics model with an affine structure obtained in step S101 as an example, px p y and It is a relative second-order state variable, while v x v y ω and ω are relative first-order state variables.

[0066] Specifically, in constrained optimal control problems, constraints have different characteristics and forms. To meet the needs of these different characteristics, this application embodiment can divide constraints into two types: upper and lower bound constraints related to the physical characteristics of the system itself; and constraints related to surrounding obstacles. To ensure that the vehicle does not violate the constraints and to guarantee safety, this application embodiment can introduce a control obstacle function. The control obstacle function can be viewed as a function whose gradient is closer to zero the farther away from the constraint boundary, and whose function value and gradient gradually increase the closer to the constraint boundary, such as a concave function for dangerous areas. This application embodiment can construct a control obstacle function suitable for upper and lower bound constraints using the Softplus activation function.

[0067] In other words, for constraints related to upper and lower limits, this application embodiment can utilize the Softplus activation function to describe them, ensuring vehicle behavior safety near the constraint boundaries and reducing the impact of constraints on overall control performance. In this case, the original constraints can be converted into an exponential function. Specifically, as the vehicle approaches the constraint boundary, the Softplus function value gradually increases, and the gradient also gradually increases, thus gradually returning to a safe region far from the constraint boundary. When the vehicle is far from the constraint boundary, the Softplus function has no gradient, thus not affecting the vehicle's trajectory tracking.

[0068] Furthermore, it can be understood that the embodiments of this application can consider control barrier functions of relative first order and relative second order based on the relative order of each constraint condition. The expressions for the control barrier functions of relative first order and relative second order can be:

[0069]

[0070]

[0071] Among them, H RD1 H is the control barrier function corresponding to the relative first-order constraint variable; RD2 c is the control barrier function corresponding to the relative second-order constraint variable; i The adjustment parameter for controlling the gradient of the barrier function; x min This represents the lower bound of the corresponding constraint variable; x max v is the upper limit of the corresponding constraint variable; x v is the longitudinal velocity of the vehicle.y ω is the lateral velocity of the vehicle; p is the yaw rate of the vehicle; ω is the yaw rate of the vehicle; x py represents the vehicle's longitudinal position; py represents the vehicle's lateral position. This refers to the vehicle's heading angle.

[0072] Optionally, in one embodiment of this application, the expression for the Gaussian distribution of the control barrier function can be:

[0073]

[0074] Where C is a parameter that adjusts the size of the function according to the size of the obstacle; p x p represents the longitudinal position of the vehicle. x，obs p represents the longitudinal position of the obstacle. y p represents the lateral position of the vehicle. y，obs The lateral position of the obstacle; The variance is the longitudinal positional variance. This represents the lateral positional variance.

[0075] In some embodiments, a constraint control function applicable to surrounding obstacles can be constructed using a Gaussian distribution function. Specifically, in this application embodiment, the constraints related to surrounding obstacles can be described using a Gaussian distribution function. In this case, the state of the surrounding obstacles can be used as a variable of the exponent of the Gaussian distribution function. As the vehicle approaches the constraint boundary, the Gaussian distribution function gradually increases, and the gradient also gradually increases, thereby gradually returning to a safe region away from the constraint boundary. When the vehicle is far from the constraint boundary, the Gaussian distribution function has no gradient, thus not affecting the vehicle's trajectory tracking.

[0076] Furthermore, since the constraints related to obstacles are position-dependent, embodiments of this application can consider a relative second-order control obstacle function. The expression for the relative second-order control obstacle function can be:

[0077]

[0078] Where C is a parameter that adjusts the size of the function according to the size of the obstacle; p x p represents the longitudinal position of the vehicle. x，obs p represents the longitudinal position of the obstacle. y p represents the lateral position of the vehicle. y，obs The lateral position of the obstacle; The variance is the longitudinal positional variance. This represents the lateral positional variance.

[0079] In step S103, the control Lyapunov function and the control barrier function are weighted and added together to construct the control Lyapunov-barrier function. The expressions for the control Lyapunov function and the control barrier function can be:

[0080]

[0081] Where B is the control Lyapunov-barrier function; w RD1 The weights for the relative first-order control Lyapunov; V RD1 For relative first-order control Lyapunov functions; w RD1，i H represents the weight corresponding to the barrier function for the i-th relative first-order constraint variable; RD1，i w is the control barrier function relative to the i-th first-order constraint variable; RD2 The weights of the derivatives of the Lyapunov function are controlled relative to the second-order tracking target; The derivative of the Lyapunov function controlling the relative second-order tracking target; w RD2，i The weights of the derivative of the barrier function are used to control the i-th relative first-order constraint variable; N is the derivative of the control barrier function for the i-th relative second-order constraint variable; RD1 N represents the number of relative first-order constraints. RD2 The number of relative second-order constraints.

[0082] As one possible implementation, embodiments of this application can construct a control Lyapunov-obstacle function by weighted summing of the control Lyapunov function and the control obstacle function. The constructed function can comprehensively consider the optimization objective and constraints of the system. Furthermore, based on this function, explicit control laws for controlling autonomous vehicles can be designed, thereby significantly reducing computational complexity and computation time, and improving the efficiency and practicality of the control process.

[0083] For example, the control Lyapunov function and the control barrier function in step S102 are fused with appropriate weights to construct a control Lyapunov-barrier function. When the state of the constructed function is of higher order, the differential term of the function can be added. When the state of the constructed function is relatively first order, it can be added directly. The expression of the control Lyapunov-barrier function can be:

[0084]

[0085] Where B is the control Lyapunov-barrier function; w RD1 The weights for the relative first-order control Lyapunov; V RD1 For relative first-order control Lyapunov functions; w RD1，i H represents the weight corresponding to the barrier function for the i-th relative first-order constraint variable;RD1，i w is the control barrier function relative to the i-th first-order constraint variable; RD2 The weights of the derivatives of the Lyapunov function are controlled relative to the second-order tracking target; The derivative of the Lyapunov function controlling the relative second-order tracking target; w RD2，i The weights of the derivative of the barrier function are used to control the i-th relative first-order constraint variable; N is the derivative of the control barrier function for the i-th relative second-order constraint variable; RD1 N represents the number of relative first-order constraints. RD 2 represents the number of relative second-order constraints.

[0086] In step S104, the explicit control law for the autonomous vehicle is designed using the gradient of the control Lyapunov-barrier function, the state transition matrix of the dynamic model, and the control input transition matrix. The expression for the explicit control law can be:

[0087]

[0088]

[0089] Where U is the control input vector; X is the vehicle state vector; α is the Lie derivative of B with respect to f(X); β is the Lie derivative of B with respect to g(X); and γ is a parameter for adjusting the convergence of the function B.

[0090] As one possible approach, embodiments of this application can utilize the gradient of the control Lyapunov-barrier function, the state transition matrix of the dynamic model, and the control input transition matrix to design an explicit control law for controlling an autonomous vehicle.

[0091] Specifically, in the embodiments of this application, the explicit control law can make the control Lyapunov-barrier function B monotonically converge to 0 over time, thereby ensuring the stability and safety of the system.

[0092] For example, in this embodiment, the stable region can be described as a convex function with a lower bound and an equilibrium point of 0, and the dangerous region as a concave function greater than a certain specific value. The property that the control Lyapunov-barrier function B, obtained by adding these two functions, converges to 0 indicates that the system will avoid entering the dangerous region greater than the specific value and tend towards the equilibrium point 0. Therefore, in this embodiment, the expression of the designed explicit control law can be:

[0093]

[0094]

[0095] Where U is the control input vector; X is the vehicle state vector; α is the Lie derivative of B with respect to f(X); β is the Lie derivative of B with respect to g(X); and γ is a parameter for adjusting the convergence of the function B.

[0096] The embodiments of this application can use the design method of explicit control laws to solve the problems of poor real-time performance and poor safety in related technologies that solve the obstacle avoidance and tracking optimal control problem by iterative method. This significantly reduces the computational complexity and computation time, and improves the efficiency and practicality of the control process.

[0097] The explicit control law design method for autonomous vehicles proposed in this application transforms the objective function and constraints of a constrained optimal control problem into a control Lyapunov function and a control obstacle function. These two functions are then weighted and summed to construct a control Lyapunov-obstacle function. The gradient of the control Lyapunov-obstacle function, the state transition matrix of the dynamic model, and the control input transition matrix can then be used to design the explicit control law for the autonomous vehicle, achieving millisecond-level high real-time control and ensuring the real-time performance and safety of vehicle control. This solves the problem in related technologies where large-scale iterative calculations are required to solve constrained optimal control problems in obstacle avoidance and tracking control, leading to a sharp increase in computational complexity when dealing with multiple obstacles, thus failing to meet the millisecond-level real-time performance and safety requirements of onboard controllers.

Claims

1. A method for designing explicit control laws for autonomous vehicles, characterized in that, Includes the following steps: Construct a vehicle dynamics model with an affine structure; Based on the aforementioned affine model of vehicle dynamics, the objective function and constraints of the tracking and obstacle avoidance constrained optimal control problem are transformed into a control Lyapunov function and a control obstacle function. The control Lyapunov function and the control barrier function are weighted and added together to construct the control Lyapunov-barrier function; The explicit control law for controlling an autonomous vehicle is designed using the gradient of the control Lyapunov-barrier function, the state transition matrix of the dynamic model, and the control input transition matrix. The expression for the explicit control law is as follows: in, To control the input vector; This is the vehicle state vector; for right Li's derivative; for right Li's derivative; For adjustment function Convergence parameters; To control the Lyapunov-barrier function; This is the transition matrix for the vehicle's state; The transition matrix is ​​used to control the input.

2. The method according to claim 1, characterized in that, The expression for the vehicle dynamics model with an affine structure is: in, This is the vehicle state vector; for A guide about time; To control the input vector; This is the transition matrix for the vehicle's state; The transition matrix is ​​used to control the input; The longitudinal speed of the vehicle; The vehicle's lateral speed; Vehicle heading angle; The vehicle's yaw rate; For front wheel stiffness; For rear wheel stiffness; This is the distance from the center of the vehicle to the front axle. This is the distance from the center of the vehicle to the rear axle. For vehicle quality; This is the moment of inertia of yaw rotation; For acceleration; This refers to the steering angle of the front wheels.

3. The method according to claim 2, characterized in that, The expression for the control Lyapunov function is: in, For the control Lyapunov function relative to the first-order tracking target; The longitudinal speed of the vehicle; For reference longitudinal velocity; The vehicle's lateral speed; For reference lateral velocity; The vehicle's yaw rate; For reference yaw rate; For the control Lyapunov function relative to the second-order tracking target; The longitudinal position of the vehicle; For reference, the vertical position; The vehicle's lateral position; For reference horizontal position; Vehicle heading angle; For reference orientation angle; arrive To assign weights to the squared terms of each state error.

4. The method according to claim 3, characterized in that, The expression of the control barrier function in Softplus form is: in, This is the control barrier function corresponding to the relative first-order constraint variable; This is the control barrier function corresponding to the relative second-order constraint variable; The adjustment parameters are used to control the gradient of the barrier function; This represents the lower limit of the corresponding constraint variable; This represents the upper limit of the corresponding constraint variable; The longitudinal speed of the vehicle; The vehicle's lateral speed; The vehicle's yaw rate; The longitudinal position of the vehicle; The vehicle's lateral position; This refers to the vehicle's heading angle.

5. The method according to claim 3, characterized in that, The expression for the Gaussian distribution form of the control barrier function is: in, The parameters for adjusting the function size according to the size of the obstacle; The longitudinal position of the vehicle; The longitudinal position of the obstacle; The vehicle's lateral position; The lateral position of the obstacle; The variance is the longitudinal positional variance. This represents the lateral positional variance.

6. The method according to claim 1, characterized in that, The expression for the control Lyapunov-barrier function is: in, To control the Lyapunov-barrier function; The weights are relative to the first-order control Lyapunov. It is a relative first-order control Lyapunov function; For the first Each relative first-order constraint variable controls the weights corresponding to the barrier function; For the first A control barrier function for a relative first-order constraint variable; The weights of the derivatives of the Lyapunov function are controlled relative to the second-order tracking target; The derivative of the Lyapunov function controlling the relative second-order tracking target; For the first The weights of the derivative of the barrier function are controlled by a relative first-order constraint variable; For the first The derivative of the barrier function controlled by a relative second-order constraint variable; The number of relative first-order constraints; The number of relative second-order constraints.

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