Optimization-free trajectory planning method for autonomous vehicle in highly dynamic environment

Abstract

The invention provides an optimization-free trajectory planning method for an autonomous vehicle in a highly dynamic environment. The optimization-free trajectory planning method comprises the following steps: performing path planning by using a Bezier curve; generating a plurality of smooth candidate paths without static obstacle collision through the Bezier curve; speed planning based on backstepping control: aiming at each selected candidate path, adopting a backstepping method based on a barrier Lyapunov function to carry out controller design so as to construct an accelerated speed and a distance constraint condition of the target vehicle; and optimal trajectory selection: proposing a comprehensive cost function, considering multiple evaluation indexes for evaluating the quality of the candidate paths, and selecting the optimal trajectory of the target vehicle. Compared with the prior art, the automatic driving track obtained in the scheme does not need to be subjected to complex nonlinear optimization, the calculation load is reduced, and meanwhile, the safety and the constraint satisfaction capability of the track are guaranteed through the obstacle Lyapunov function and the backstepping control.

Description

Technical Field

[0001] The present invention relates to the field of autonomous driving technology, and in particular to an optimization-free trajectory planning method for autonomous driving vehicles in highly dynamic environments. Background Art

[0002] Intelligent driving, a key component of smart cars, is seen as an effective way to alleviate congestion and improve travel efficiency and safety. Trajectory planning in intelligent driving is crucial for achieving safe and efficient driving. Currently, trajectory planning relies on real-time fusion of multi-sensor environmental perception data and vehicle dynamics models, employing methods such as optimal control or sampling search to generate feasible trajectories that conform to vehicle dynamics constraints. In complex real-world scenarios, dynamic obstacles such as fast-moving vehicles and pedestrians place even higher demands on trajectory planning's real-time responsiveness.

[0003] Traditional trajectory planning methods typically rely on optimization-based approaches. These methods construct a cost function that incorporates parameters such as path length, obstacle risk, smoothness, and driving efficiency, and then minimize it using techniques such as convex optimization. While optimization-based algorithms can generate highly accurate feasible trajectories that strictly meet safety and dynamic constraints, they consume significant computational resources and struggle to meet real-time requirements in highly dynamic environments. Prior research has explored various optimization-free trajectory planning methods that avoid the complex nonlinear optimization problem by employing structured heuristic rules and efficient computational strategies. While these optimization-free methods avoid the computational complexity of solving nonlinear problems, they also have significant limitations. Graph search and sampling-based methods are efficient in low-dimensional spaces but struggle to meet complex constraints and are susceptible to the curse of dimensionality. Interpolation curve-based methods are computationally simple but lack the flexibility to handle changing driving scenarios. Many heuristic methods fail to effectively update trajectories and may produce suboptimal or even infeasible paths. Summary of the Invention

[0004] In view of the shortcomings of the prior art described above, the object of the present invention is to provide an optimization-free trajectory planning method for autonomous driving vehicles in highly dynamic environments, so as to solve the problems of limitations and lack of flexibility in trajectory planning for intelligent driving in the prior art.

[0005] To achieve the above and other related objectives, the present invention provides an optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment, comprising the following steps:

[0006] Use Bezier curves for path planning: Generate several candidate paths that are smooth and free of static obstacle collisions through Bezier curves;

[0007] Speed ​​planning based on backstepping control: For each candidate path selected, a controller is designed using a backstepping method based on the obstacle Lyapunov function to construct acceleration and distance constraints for the target vehicle;

[0008] Optimal trajectory selection: A comprehensive cost function is proposed, which considers multiple evaluation indicators to evaluate the quality of the candidate paths and select the optimal trajectory of the target vehicle.

[0009] Optionally, after the optimal trajectory is selected, the following steps are further included:

[0010] Trajectory tracking: An iterative linear quadratic regulator controller is used to accurately track the selected optimal trajectory, ensuring safety and stability during lane changes.

[0011] Optionally, the properties of the Bezier curve are determined by the coordinates of the control points, and the candidate paths of different driving styles are generated by defining multiple control points; the parametric equation of the third-order Bezier curve is:

[0012] B(t)=(1-t) 3 P0+3(1-t) 2 tP1+3(1-t)t 2 P2+t 3 P3#(1)

[0013] Among them, P is the four position points of the target vehicle, P0 is the initial position, P1 is the position moved in the direction of P0, P3 is the target position, P2 is the position moved in the direction of P3, and t∈[0,1].

[0014] Alternatively, in a Cartesian coordinate system, the vehicle position (x, y) is expressed as a function of parameter t, and a third-order Bezier curve can be expressed as:

[0015]

[0016] Alternatively, P1 can be defined on the tangent line of P0 and moved a certain distance along that direction, with the following relationship:

[0017]

[0018] Among them, γ i is the heading angle of the target vehicle in motion.

[0019] Optionally, the barrier Lyapunov function V1 is designed as follows:

[0020]

[0021] Among them, z1 is the distance error, through the formula z1=p1-p 1dCalculated, p1 is the distance of the target vehicle along the planned path, p 1d is the expected distance of the target vehicle along the planned path; g is a custom variable, when z1≥0, g=1; when z1<0, g=0; k b and k c is the boundary value of the barrier Lyapunov function.

[0022] Optionally, an additional barrier Lyapunov function is constructed to limit the acceleration while constraining the distance error to meet the comfort requirements of the passengers in the target vehicle.

[0023] Optionally, a backstepping controller based on the obstacle Lyapunov function is applied to each candidate path to generate a planned distance, speed, and acceleration relative to the target vehicle, wherein the backstepping controller limits the acceleration to [-4, 4] m / s 2 within the range.

[0024] Optionally, the evaluation indicators include path length, obstacle risk, path smoothness and driving efficiency, and weights are set for the evaluation indicators to adapt to various application scenarios, and the evaluation criteria for the optimal path are normalized.

[0025] Optionally, the cost function is as follows:

[0026] cost total =w s cost s +w e cost e +w sf cost sf +w en cost en +w l cost l (18)

[0027] Among them, cost s Represents the path smoothness cost, cost e Represents the driving efficiency cost, cost sf Represents the safety cost of the target vehicle, cost en Represents the energy cost of the target vehicle, cost l Represents the path length cost. w s 、w e 、w sf 、w en 、w l is the weight of each item.

[0028] In the solution implemented by the above-mentioned optimization-free trajectory planning method for autonomous vehicles in highly dynamic environments, the use of Bezier curve-based path planning can achieve high-frequency trajectory updates, ensuring trajectory smoothness and collision safety; by combining backstepping control with the obstacle Lyapunov function (BLF), this method imposes multiple constraints on the speed and acceleration of the target vehicle, effectively improving trajectory safety and driving comfort. The optimization-free method significantly reduces computational costs while also achieving high-frequency trajectory updates; a comprehensive cost function is used to evaluate multiple indicators such as path length, obstacle risk, path smoothness, and driving efficiency to ensure optimal path selection in complex environments. Compared with existing technologies, the autonomous driving trajectory obtained in this solution does not require complex nonlinear optimization, reducing the computational load, while ensuring trajectory safety and constraint satisfaction through BLF and backstepping control. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 The diagram shows a path planning diagram obtained through step S10 in a lane change scenario;

[0030] Figure 2 The three candidate paths generated by step S10 in the lane change scenario are shown;

[0031] Figure 3 Shown is a schematic diagram of the distance obtained by speed planning in step S20 in a lane change scenario;

[0032] Figure 4 The display is a speed diagram obtained by performing speed planning in step S20 in a lane change scenario;

[0033] Figure 5 Shown is a schematic diagram of acceleration obtained through speed planning in step S20 in a lane change scenario;

[0034] Figure 6 The figure shows a schematic diagram of the speed planning obtained in step S40 in the lane change scenario;

[0035] Figure 7 A schematic diagram of the path planning obtained through step S10 in the left turn scenario is shown;

[0036] Figure 8 The three candidate paths generated by step S10 in the left-turn scenario are shown;

[0037] Figure 9 The diagram shows the distance obtained by speed planning in step S20 in the left turn scenario;

[0038] Figure 10 The diagram shows the speed obtained by performing speed planning in step S20 in the left-turn scenario;

[0039] Figure 11 Shown is a schematic diagram of the acceleration obtained by performing speed planning in step S20 in a left turn scenario;

[0040] Figure 12 The diagram shows a speed planning diagram obtained in step S40 in a lane change scenario. DETAILED DESCRIPTION

[0041] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0042] The following describes the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art will readily appreciate the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the various details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are intended only to illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0043] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0044] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the embodiments of the present invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring the embodiments of the present invention.

[0045] In an exemplary embodiment, the optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment includes at least steps S10 to S40, such as Figure 1 The detailed description is as follows:

[0046] Step S10: Use Bezier curves for path planning, and generate several candidate paths that are smooth and free of static obstacle collisions through the Bezier curves;

[0047] like Figure 1 As shown in the figure, taking the lane change scenario as an example, a third-order Bezier curve [P0, P1, P2, P3] is used as the path curve connecting points P0 and P3. The properties of the Bezier curve are determined by the coordinates of the control points. The parametric equation of the third-order Bezier curve is:

[0048] B(t)=(1-t) 3 P0+3(1-t) 2 tP1+3(1-t)t 2 P2+t 3 P3, t∈[0, 1]#(1)

[0049] In the Cartesian coordinate system, the vehicle position (x, y) is expressed as a function of the parameter t, and the third-order Bezier curve can be expressed as:

[0050]

[0051] Figure 1 The curvature k(t) of the curve can be interpreted as the heading angle γ of the moving vehicle i ,To ensure that the initial heading angle of the target vehicle remains unchanged during the high-frequency planning process, P1 can be defined on the tangent line of P0 and move a small distance along this direction, as follows:

[0052]

[0053] Similar to the above case, multiple target points can be defined to generate different candidate paths to increase the diversity of subsequent trajectory planning.

[0054] Step S20: Based on the speed planning of backstepping control, for each selected candidate path, a controller is designed using a backstepping method based on the obstacle Lyapunov function to construct the acceleration and distance constraints of the target vehicle;

[0055] Design of S21 backstepping controller

[0056] The controller design is carried out by backstepping method based on barrier Lyapunov function to construct acceleration and distance constraints. The barrier Lyapunov function (BLF) is a continuous and smooth function with continuous first-order partial derivatives at every point in its domain. When the independent variable z approaches the boundary value -k of the barrier Lyapunov function (BLF), the acceleration and distance constraints are obtained. b and k c When , the barrier Lyapunov function (BLF) V tends to infinity; based on the following state equation, speed planning based on backstepping control is performed:

[0057]

[0058] Where p1, p2, p3, and U represent the distance, velocity, acceleration, and jerk of the target vehicle along the planned path, respectively, and q is the system output.

[0059] The following are the steps to set up the backstepping controller:

[0060] (1) Based on the design principle of the backstepping controller, the distance error z1 is defined as:

[0061] z1=p1-p 1d #(5)

[0062] Among them, p1 is the distance of the target vehicle along the planned path, p 1d is the expected distance of the target vehicle along the planned path.

[0063] Since the target vehicle has different distance constraints to the following and preceding vehicles in the target lane, there are different constraints on z1. In order to constrain the output error z1, the obstacle Lyapunov function V1 is designed as follows:

[0064]

[0065] Among them, g is a custom variable. When z1≥0, g=1; when z1<0, g=0; -k b and k c is the boundary value of the barrier Lyapunov function (BLF).

[0066] In the process of vehicle trajectory planning, the obstacle Lyapunov function (BLF) parameter k b and k c The setting must be smaller than d2 and d1. d2 is the distance from the target vehicle to the obstacle in front after changing lanes, and d1 is the distance from the target vehicle to the obstacle behind after changing lanes.

[0067] The derivative of V1 is:

[0068]

[0069] α1 is the virtual control quantity, and the expression of the stability function α1 is:

[0070]

[0071] (2) The error z2 is between p2 and α1:

[0072] z2=p2-α1#(9)

[0073] At this time, the barrier Lyapunov function is:

[0074]

[0075] The derivative of V2 is:

[0076]

[0077] The stability function α2 is:

[0078]

[0079] (3) As above, the error z3 is between p3 and α2:

[0080] z3=p3-α2#(13)

[0081] While constraining the distance, an additional barrier Lyapunov function is constructed to limit the acceleration to meet the passenger comfort requirements. It is worth mentioning that the same constraints are applied to z3 and p3, which indicates that the assumed α2 is sufficiently small. Based on this assumption, the updated barrier Lyapunov function is as follows:

[0082]

[0083] In the above formula, k d Indicates the boundary value of acceleration error z3.

[0084] The derivative of V3 is:

[0085]

[0086] The control quantity U of the backstepping controller is:

[0087]

[0088] (4) Closed-loop system:

[0089]

[0090] S22 system stability analysis

[0091] For the closed-loop system (17), the barrier Lyapunov function is constructed as V3(z) in Eq. (14), which is in the region Ω z :={-k b <z1<k c , -k d <z3<k d} is continuous and positive definite. When z1 approaches k c and -k b , |z2| and |z3| reach infinity and k respectively d When V3(z) approaches infinity, this indicates that the barrier Lyapunov function V3(z) is in the region Ω z The inner part is also radially unbounded.

[0092] In Ω zIn the same region of for The derivative is negative definite, so any equation starting from Ω z z will converge asymptotically to the origin.

[0093] Step S30: Optimal trajectory selection, proposing a comprehensive cost function, considering multiple evaluation indicators, for evaluating the quality of the candidate paths, and selecting the optimal trajectory.

[0094] A comprehensive cost function for evaluating trajectory quality is proposed. This function takes into account factors such as path length, obstacle risk, trajectory smoothness, and formal efficiency. The cost function provides a comprehensive evaluation, and its evaluation metrics can effectively optimize the practicality of trajectory selection. These metrics can be weighted to adapt to various application scenarios. The evaluation criteria of the reference trajectory are normalized so that they can be consistently evaluated and compared across different sampling instances. This ultimately helps to select the optimal trajectory at the current moment, and the cost function is described as follows:

[0095] cost total =w s cost s +w e cost e +w sf cost sf +w en cost en +w l cost l (18)

[0096] Among them, cost total Indicates the total cost, cost s 、cost e 、cost sf 、cost en 、cost l denote the normalized smoothness, efficiency, safety, energy and length cost respectively. s 、w e 、w sf 、w en 、w l Indicates the weights of these cost components.

[0097] The evaluation index of the candidate path is brought into the cost function for calculation. When the total cost of the candidate path is total When the value is the smallest, the candidate path can be selected as the optimal trajectory.

[0098] Step S40: trajectory tracking, using an iterative linear quadratic regulator controller to accurately track the selected optimal trajectory to ensure safety and stability during the lane change process.

[0099] To validate the effectiveness of the proposed method in various driving scenarios, two typical test cases were conducted: a lane change scenario and a left turn at an unsignaled intersection. First, the lane change experiment simulated a vehicle changing lanes to avoid a moving obstacle ahead. To further evaluate the algorithm's adaptability in complex traffic environments, a left turn experiment was conducted, simulating vehicle maneuvers at an urban intersection. These experiments were designed to evaluate the algorithm's performance under real-world driving conditions from multiple perspectives, ensuring its reliability across a wide range of driving scenarios.

[0100] 1. Lane change scenario

[0101] like Figure 2 As shown in the figure, to account for different driving styles, three reference paths for different driving styles are generated using Bezier curves: aggressive, moderate, and conservative. These paths are constructed by adjusting the curve's control points, which directly affect the lateral displacement and curvature of the lane change maneuver. The aggressive path has a shorter lane change distance and greater curvature, while the conservative path has a longer transition distance and smoother curvature. The moderate path falls between these two. This design generates a variety of candidate paths to accommodate the varying requirements for comfort and responsiveness in different driving scenarios.

[0102] like Figure 3-5 As shown in the figure, three reference trajectories with different driving styles are generated based on a specific path. A backstepping controller with an obstacle Lyapunov function is used to determine the planned distance, planned speed, and planned acceleration relative to the target vehicle. The desired distance is tracked by adjusting the relative distance, and the acceleration is controlled within the range of [-4, 4] to ensure passenger comfort.

[0103] like Figure 6 As shown in Figure 3, the iterative linear quadratic regulator (iLQR) controller that considers steering control and longitudinal velocity tracking can accurately track the planned trajectory and maintain system stability, ensuring that there is no collision with nearby obstacles.

[0104] 2. Left turn at an intersection without a traffic light

[0105] By adjusting the control points of the Bezier curve, three reference paths for turning left at an intersection without traffic lights are obtained. The three paths correspond to aggressive, moderate, and conservative driving styles, respectively. They differ in turning radius and curvature to reflect different preferences for the intensity and comfort of turning actions. Figure 7 and Figure 8shown.

[0106] like Figure 9-11 As shown in the figure, in this scenario, the dynamic obstacle is moving faster than the vehicle, so a safe velocity trajectory must be planned to avoid collision with the vehicle behind. For each reference path, three reference velocity profiles are generated, ultimately resulting in nine candidate trajectories. After a specific period of time, the vehicle's velocity will converge to the velocity of the vehicle ahead, based on the characteristics of the obstacle's Lyapunov function.

[0107] The effect of trajectory tracking using iLQR is as follows Figure 12 As shown, accurate tracking can be achieved.

[0108] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. An optimization-free trajectory planning method for autonomous vehicles in highly dynamic environments, characterized by: The following steps are involved: Use Bezier curves for path planning: Generate several candidate paths that are smooth and free of static obstacle collisions through Bezier curves; Speed ​​planning based on backstepping control: For each candidate path selected, a controller is designed using a backstepping method based on the obstacle Lyapunov function to construct acceleration and distance constraints for the target vehicle; Optimal trajectory selection: A comprehensive cost function is proposed, which considers multiple evaluation indicators to evaluate the quality of the candidate paths and select the optimal trajectory of the target vehicle.

2. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 1, characterized in that: After the optimal trajectory is selected, the following steps are also included: Trajectory tracking: An iterative linear quadratic regulator controller is used to accurately track the selected optimal trajectory, ensuring safety and stability during lane changes.

3. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 1, characterized in that: The properties of the Bezier curve are determined by the coordinates of the control points. By defining multiple control points, the candidate paths for different driving styles are generated. The parametric equation of the third-order Bezier curve is: B(t)=(1-t) 3 P0+3(1-t) 2 tP1+3(1-t)t 2 P2+t 3 P3#(1) Among them, P is the four position points of the target vehicle, P0 is the initial position, P1 is the position moved in the direction of P0, P3 is the target position, P2 is the position moved in the direction of P3, and t∈[0,1].

4. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 3, characterized in that: In the Cartesian coordinate system, the vehicle position (x, y) is expressed as a function of the parameter t, and the third-order Bezier curve can be expressed as:

5. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 4, characterized in that: P1 can be defined on the tangent line of P0 and moved a certain distance along that direction, with the following relationship: Among them, γ i is the heading angle of the target vehicle in motion.

6. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 4, characterized in that: The barrier Lyapunov function V1 is designed as follows: Among them, z1 is the distance error, through the formula z1=p1-p 1d Calculated, p1 is the distance of the target vehicle along the planned path, p 1d is the expected distance of the target vehicle along the planned path; g is a custom variable, when z1≥0, g=1; when z1<0, g=0; k b and k c is the boundary value of the barrier Lyapunov function.

7. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 6, characterized in that: While constraining the distance error, an additional obstacle Lyapunov function is constructed to limit the acceleration to meet the comfort requirements of the passengers in the target vehicle.

8. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 7, characterized in that: Apply a backstepping controller based on the obstacle Lyapunov function to each candidate path to generate a planned distance, speed, and acceleration relative to the target vehicle. The backstepping controller limits the acceleration to [-4, 4] m / s. 2 within the range.

9. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 8, characterized in that: The evaluation indicators include path length, obstacle risk, path smoothness and driving efficiency. Weights are set for the evaluation indicators to adapt to various application scenarios, and the evaluation criteria for the optimal path are normalized.

10. The optimization-free trajectory planning method for an autonomous driving vehicle in a highly dynamic environment according to claim 9, characterized in that: The cost function is as follows: cost total =w s ·cost s +w e ·cost e +w sf ·cost sf +w en ·cost en +w l ·cost l (18) Among them, cost s Represents the path smoothness cost, cost e Represents the driving efficiency cost, cost sf Represents the safety cost of the target vehicle, cost en Represents the energy cost of the target vehicle, cost l Represents the path length cost. w s 、w e 、w sf 、w en 、w l is the weight of each item.

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