Parking path planning method, system and equipment based on low-dimensional optimization and medium

Abstract

The invention provides a parking path planning method, system and device based on low-dimensional optimization, and a medium, and the method comprises the steps: determining a vehicle kinematic constraint based on the initial pose of a vehicle through employing a vehicle kinematic model; based on the initial pose and the target pose, utilizing geometric characteristics of the shortest parallel parking path to carry out multi-stage curvature segmentation modeling on the parking path to obtain an entering section, a transition section and an adjusting section; introducing constraints in each path stage to construct a low-dimensional nonlinear optimization objective function; the optimization variables are geometric parameters of each path stage, and the geometric parameters of the transition section comprise coefficients of a quintic polynomial; and based on the initial pose and the vehicle kinematics constraint, solving the low-dimensional nonlinear optimization objective function to obtain a parking path planning result from the vehicle to the target parking space. By analyzing the geometric characteristics of the shortest parallel parking path, the parking path is subjected to multi-stage curvature segmentation modeling, the variable dimension can be reduced and optimized, the calculation consumption is reduced, and the calculation efficiency and the real-time performance are improved.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving technology, and in particular to a parking path planning method, system, device, and medium based on low-dimensional optimization. Background Technology

[0002] With the increasing rate of private car ownership in society, the dynamic vehicle density per unit area in built-up areas has significantly increased, leading to a shortage of parking spaces. Therefore, how to achieve efficient parallel parking within limited parking spaces has become a problem to be solved in the field of automated parking.

[0003] Traditional automated parking path planning methods are mainly based on geometric curves (such as Dubins curves, Klossoyd curves, and Bezier curves) for path generation. These methods perform well in terms of computational efficiency, but usually require a large parking space and cannot achieve accurate parking in small parking spaces.

[0004] To overcome these problems, in recent years, an increasing number of studies have begun to adopt methods based on Optimal Control Theory (OCP) to consider vehicle kinematics and make full use of limited parking space. For example, Zips et al. proposed minimizing parking time by optimizing the length of the parking path. However, since the optimization problem involves nonlinear vehicle models and non-convex obstacle avoidance constraints, a large number of discretization points are required during the calculation, resulting in excessively long computation time. Summary of the Invention

[0005] This invention provides a parking path planning method, system, device, and medium based on low-dimensional optimization to solve existing problems.

[0006] This invention provides a parking path planning method based on low-dimensional optimization, comprising: Obtain the initial pose of the vehicle and the target pose of the target parking space; Based on the initial pose, the vehicle kinematic constraints are determined using a pre-built vehicle kinematic model. Based on the initial pose and the target pose, the parking path is modeled in multiple stages of curvature segmentation using the geometric characteristics of the shortest parallel parking path, resulting in multiple path stages. The multiple path stages include an entry segment, a transition segment, and an adjustment segment. The transition segment is obtained by parametrically modeling the curvature using a fifth-order polynomial. Pre-constructed curvature constraints and smoothness constraints are introduced in each of the path stages to construct a low-dimensional nonlinear optimization objective function; the optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each of the path stages, and the geometric parameters of the transition segment include the coefficients of the fifth-degree polynomial. Based on the initial pose and the vehicle kinematic constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0007] Furthermore, based on the initial pose and the target pose, and utilizing the geometric characteristics of the shortest parallel parking path, the parking path is modeled using multi-stage curvature segmentation to obtain multiple path stages, including: Based on the initial pose and the target pose, the parking path is divided into an entry segment, a transition segment and an adjustment segment connected in sequence; A constant curvature circular arc is used to model the entry section, which is used to improve the vehicle's approach speed to the target parking space. The adjustment segment is modeled using a hybrid path of straight lines and circular arcs, ensuring that the heading angle of the vehicle when it arrives at the target parking space remains consistent with the direction of the parking space. Based on the entry segment and the adjustment segment, a fifth-order polynomial with respect to the path length is used to model the curvature transformation of the transition segment, which is used to connect the entry segment and the adjustment segment and ensure the continuity of the first derivative of the path curvature. The transition segment satisfies the following formula:

[0008] Where, k s The curvature at arc length parameter s reflects the degree of steering aggression of the vehicle at that point. s is the arc length parameter along the path, indicating the position from the start of the transition segment. The coefficients a0, a1, a2, a3, a4, and a5 are all geometric parameters to be optimized.

[0009] Furthermore, the curvature constraint includes the absolute value of the curvature of the entry segment and the adjustment segment being equal to the minimum turning curvature of the vehicle; The smoothness constraints include the curvature at the start of the transition segment being equal to the curvature of the entry segment, the curvature at the end of the transition segment being equal to the curvature of the adjustment segment, and the first derivative of the curvature at the start of the transition segment being zero, and the first derivative of the curvature at the end of the transition segment being zero.

[0010] Further, the step of solving the low-dimensional nonlinear optimization objective function based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space includes: The dynamic steering constraint coefficient is determined based on the minimum turning radius, vehicle speed, and angular velocity in the initial pose. Based on the vehicle kinematic constraints and dynamic steering constraint coefficients, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space. The dynamic steering constraint coefficient satisfies the following formula:

[0011] in, This is the dynamic steering constraint coefficient. To minimize the bending rate, For adjustment coefficients, For vehicle speed, ω is the angular velocity.

[0012] Furthermore, when dynamic obstacles exist, the low-dimensional nonlinear optimization objective function is solved based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space, including: Obtain the current position and velocity variable with direction of motion of the dynamic obstacle; Based on the position and velocity variables, a pre-trained obstacle motion prediction model is used to predict the motion trajectory of the dynamic obstacle within a future planning time window. Based on the predicted trajectory, a safe buffer zone surrounding the obstacle is constructed in the spatiotemporal domain as an obstacle avoidance constraint. Based on the initial pose, the vehicle kinematic constraints, and the obstacle avoidance constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0013] Furthermore, the motion trajectory satisfies the following formula:

[0014] in, Let the center position of the j-th obstacle be at time t+Δt. Let Δt be the center position of the j-th obstacle at time t, and Δt be the time interval. For velocity variables; The obstacle avoidance constraint satisfies the following formula:

[0015] Where d() is the Euclidean distance function, Let be the position coordinates of the vehicle at the arc length parameter s. Let [the trajectory of the j-th obstacle] be the motion trajectory within the time window [t, t+Δt]. This is the preset safe distance threshold.

[0016] Furthermore, the low-dimensional nonlinear optimization objective function satisfies the following formula:

[0017] in, Let be the radius of curvature of the k-th path stage. , Let be the heading angles for the (k+1)th path stage and the kth path stage. Let be the path length between the k-th path stage and the (k+1)-th path stage. Indicates the smoothness of the parking process. It is the curvature fitting error corresponding to the transition segment, which corresponds to a fifth-order polynomial transition segment, and N is the total number of path stages.

[0018] This invention also provides a parking path planning system based on low-dimensional optimization, comprising: The acquisition module is used to acquire the initial pose of the vehicle and the target pose of the target parking space; The model building module is used to determine vehicle kinematic constraints based on the initial pose and using a pre-built vehicle kinematic model; based on the initial pose and the target pose, and using the geometric characteristics of the shortest parallel parking path, to perform multi-stage curvature segmentation modeling on the parking path, resulting in multiple path stages; the multiple path stages include an entry segment, a transition segment, and an adjustment segment, wherein the transition segment is obtained by parametric modeling the curvature using a fifth-order polynomial; pre-built curvature constraints and smoothness constraints are introduced into each of the path stages to construct a low-dimensional nonlinear optimization objective function; the optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each of the path stages, and the geometric parameters of the transition segment include the coefficients of the fifth-order polynomial; The parking path planning module is used to solve the low-dimensional nonlinear optimization objective function based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space.

[0019] Furthermore, the model building module is specifically used for: Based on the initial pose and the target pose, the parking path is divided into an entry segment, a transition segment and an adjustment segment connected in sequence; A constant curvature circular arc is used to model the entry section, which is used to improve the vehicle's approach speed to the target parking space. The adjustment segment is modeled using a hybrid path of straight lines and circular arcs, ensuring that the heading angle of the vehicle when it arrives at the target parking space remains consistent with the direction of the parking space. Based on the entry segment and the adjustment segment, a fifth-order polynomial with respect to the path length is used to model the curvature transformation of the transition segment, which is used to connect the entry segment and the adjustment segment and ensure the continuity of the first derivative of the path curvature. The transition segment satisfies the following formula:

[0020] Where, k s The curvature at arc length parameter s reflects the degree of steering aggression of the vehicle at that point. s is the arc length parameter along the path, indicating the position from the start of the transition segment. The coefficients a0, a1, a2, a3, a4, and a5 are all geometric parameters to be optimized.

[0021] Furthermore, the curvature constraint includes the absolute value of the curvature of the entry segment and the adjustment segment being equal to the minimum turning curvature of the vehicle; The smoothness constraints include the curvature at the start of the transition segment being equal to the curvature of the entry segment, the curvature at the end of the transition segment being equal to the curvature of the adjustment segment, and the first derivative of the curvature at the start of the transition segment being zero, and the first derivative of the curvature at the end of the transition segment being zero.

[0022] Furthermore, the parking path planning module is specifically used for: The dynamic steering constraint coefficient is determined based on the minimum turning radius, vehicle speed, and angular velocity in the initial pose. Based on the vehicle kinematic constraints and dynamic steering constraint coefficients, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space. The dynamic steering constraint coefficient satisfies the following formula:

[0023] in, This is the dynamic steering constraint coefficient. To minimize the bending rate, For adjustment coefficients, For vehicle speed, ω is the angular velocity.

[0024] Furthermore, the parking path planning module is specifically used for: When a dynamic obstacle exists, obtain the current position and velocity variable with direction of motion of the dynamic obstacle; Based on the position and velocity variables, a pre-trained obstacle motion prediction model is used to predict the motion trajectory of the dynamic obstacle within a future planning time window. Based on the predicted trajectory, a safe buffer zone surrounding the obstacle is constructed in the spatiotemporal domain as an obstacle avoidance constraint. Based on the initial pose, the vehicle kinematic constraints, and the obstacle avoidance constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0025] The trajectory of motion satisfies the following formula:

[0026] in, Let the center position of the j-th obstacle be at time t+Δt. Let Δt be the center position of the j-th obstacle at time t, and Δt be the time interval. For velocity variables; The obstacle avoidance constraint satisfies the following formula:

[0027] Where d() is the Euclidean distance function, Let be the position coordinates of the vehicle at the arc length parameter s. Let [the trajectory of the j-th obstacle] be the motion trajectory within the time window [t, t+Δt]. This is the preset safe distance threshold.

[0028] The low-dimensional nonlinear optimization objective function satisfies the following formula:

[0029] in, Let be the radius of curvature of the k-th path stage. , Let be the heading angles for the (k+1)th path stage and the kth path stage. Let be the path length between the k-th path stage and the (k+1)-th path stage. Indicates the smoothness of the parking process. It is the curvature fitting error corresponding to the transition segment, which corresponds to a fifth-order polynomial transition segment, and N is the total number of path stages.

[0030] This application also provides an electronic device, which includes at least a processor and a memory, wherein the processor is configured to execute a computer program stored in the memory to implement the steps of the parking path planning method based on low-dimensional optimization as described above.

[0031] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the parking path planning method based on low-dimensional optimization as described above.

[0032] This application also provides a computer program product, which includes: computer program code, and when the computer program code is run on a computer, causing the computer to perform the steps of any of the parking path planning methods based on low-dimensional optimization described above.

[0033] In this embodiment of the invention, the initial pose of the vehicle and the target pose of the target parking space are obtained. Based on the initial pose, a pre-built vehicle kinematics model is used to determine the vehicle kinematic constraints. Based on the initial pose and the target pose, the geometric characteristics of the shortest parallel parking path are used to perform multi-stage curvature segmentation modeling of the parking path, resulting in multiple path stages. These multiple path stages include an entry segment, a transition segment, and an adjustment segment. The transition segment is obtained by parametrically modeling the curvature using a fifth-order polynomial. Pre-built curvature constraints and smoothness constraints are introduced into each path stage to construct a low-dimensional nonlinear optimization objective function. The optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each path stage, and the geometric parameters of the transition segment include the coefficients of the fifth-order polynomial. Based on the initial pose and vehicle kinematic constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space. By analyzing the geometric characteristics of the shortest parallel parking path and performing multi-stage curvature segmentation modeling of the parking path, the dimensionality of optimization variables can be reduced, computational consumption can be reduced, and computational efficiency and real-time performance can be improved. Attached Figure Description

[0034] The accompanying drawings, which form part of this specification, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart illustrating a parking path planning method based on low-dimensional optimization provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a typical parking scenario provided by an embodiment of the present invention; Figure 3 A schematic diagram of the relationship between curvature and path provided in an embodiment of the present invention; Figure 4 A comparative chart of experimental results provided for an embodiment of the present invention; Figure 5 A schematic diagram of a parking path planning system based on low-dimensional optimization provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0036] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this invention is for describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0037] Example 1: Figure 1 A flowchart illustrating a parking path planning method based on low-dimensional optimization provided in this embodiment of the invention includes the following steps: S101: Obtain the initial pose of the vehicle and the target pose of the target parking space.

[0038] S102: Based on the initial pose, determine the vehicle kinematic constraints using a pre-built vehicle kinematic model.

[0039] S103: Based on the initial pose and target pose, the geometric characteristics of the shortest parallel parking path are used to perform multi-stage curvature segmentation modeling of the parking path, resulting in multiple path stages; the multiple path stages include an entry segment, a transition segment, and an adjustment segment. The transition segment is obtained by parametrically modeling the curvature using a fifth-order polynomial.

[0040] S104: Introduce pre-constructed curvature constraints and smoothness constraints at each path stage to construct a low-dimensional nonlinear optimization objective function; the optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each path stage, and the geometric parameters of the transition segment include the coefficients of a fifth-degree polynomial.

[0041] S105: Based on the initial pose and vehicle kinematic constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0042] In this embodiment of the invention, by analyzing the geometric characteristics of the shortest parallel parking path and performing multi-stage curvature segmentation modeling of the parking path, the dimensionality of optimization variables can be reduced, computational costs can be lowered, and computational efficiency and real-time performance can be improved. Furthermore, in narrow parking spaces and complex parking scenarios, the success rate of parking is increased, making the entire parking process safer and more reliable.

[0043] The parking path planning method based on low-dimensional optimization provided in this embodiment of the invention is applied to a vehicle equipped with an automatic parking system.

[0044] Pose includes position ( , ) and heading angle In S101 above, the initial pose of the vehicle is the pose information at the initial moment when the vehicle is tracing its parking path, and the target pose of the target parking space is the pose information at the corresponding moment when the vehicle enters the target parking space. In this embodiment of the invention, an optimal parking path curve is first established, which is applicable to different parking scenarios. Figure 2 This illustrates a typical parking scenario where the vehicle's length L is 4.5 meters (m) and width W is 1.8 meters, the parking space's length Ls is 6.3 meters, and the parking space's width Ws is 2.2 meters. The initial pose of the vehicle in this scenario is... That is, the vehicle's starting position is (8.3m, 4.1m), the heading angle is 0°, and the target pose of the target parking space is... The target position is (2.5m, 1.1m), and the heading angle is 0°. The vehicle's wheelbase... The maximum front wheel steering angle is 2.65m. At an angle of 37°, in this scenario, the maneuverable longitudinal distance D for the vehicle to park in the parking space is... l It is 7.5m.

[0045] In this embodiment of the invention, a vehicle kinematics model is pre-established: with the rear axle center as the reference point, the vehicle state is defined as ( , ),in , These represent the horizontal and vertical position coordinates, respectively. This represents the heading angle. In S102 above, the vehicle kinematic constraints satisfy the following formula:

[0046] Where g represents the direction of vehicle movement. Indicates moving forward or backward. For the front wheel steering angle, Here, we will explain one implementation of S102 above, using this formula: In the parking path planning method proposed in this embodiment of the invention, the vehicle's motion behavior is determined by its kinematic model. The vehicle kinematic model can be modeled based on the vehicle's geometric parameters and steering characteristics, where g is the reciprocal of the path curvature k, which is the normalized form of the radius of curvature. In this implementation, the entire parking path is represented as a curvature function k(s) with respect to the arc length parameter s. L represents the total path length. According to the vehicle kinematics model, the position increment and heading angle increment along the path are determined by the curvature k(s). This formula can be obtained by inversely deducing the path differential relationship using the curvature. This formula indicates that the vehicle's position at each arc length parameter s can be obtained by integrating along the path, and the steering angle at each arc length parameter s can be calculated through integration, ensuring that the heading angle is continuous and conforms to the vehicle's motion laws.

[0047] For example, in an embodiment of the present invention, the following optimal control problem (OCP) can be established with the goal of minimizing the total travel path length of the vehicle:

[0048] in( , () indicates the vehicle's location. Here are the lateral coordinates of the vehicle. Here are the longitudinal position coordinates of the vehicle. The yaw angle represents the vehicle's heading, which can be used to indicate the vehicle's orientation. g represents the direction of the vehicle's movement. Indicates moving forward or backward. This refers to the front wheel steering angle, which is the steering angle of the vehicle's front wheels relative to the longitudinal axis. The arc length parameter represents the planned path of the vehicle (representing the path length from the initial position). Indicates the initial arc length parameter. This represents the target arc length parameter.

[0049] In one implementation, step S103 above may include the following steps: Based on the initial pose and the target pose, the parking path is divided into an entry segment, a transition segment and an adjustment segment connected in sequence; A constant curvature circular arc is used to model the entry section, which is used to improve the vehicle's approach speed to the target parking space, so that the vehicle can quickly approach the entrance of the target parking space. A hybrid path of straight lines and circular arcs is used to model the adjustment segment, ensuring that the heading angle of the vehicle when it arrives at the target parking space is consistent with the direction of the parking space. Based on the entry segment and the adjustment segment, a fifth-order polynomial with respect to the path length is used to model the curvature transformation of the transition segment, which is used to connect the entry segment and the adjustment segment and ensure the continuity of the first derivative of the path curvature. In this implementation, one way to represent the geometric characteristics of the shortest parallel parking path can be seen in the optimization objective of minimizing the total driving path length of the vehicles in the example above.

[0050] This implementation introduces multi-stage curvature segmentation modeling to ensure the smoothness of curvature and curvature derivative, thereby reducing steering wheel vibration.

[0051] Figure 3 This diagram illustrates the piecewise functional relationship between curvature k and path length s in a parking path, serving as a visual representation of the three parts of the parking path: "entry segment," "transition segment," and "adjustment segment." The horizontal axis represents the path length s (in meters), and the vertical axis represents the curvature k (in meters). -1 ): (1) Entry Section: A constant curvature circular arc is used to allow vehicles to quickly approach the parking space entrance, such as... Figure 3 In segment AB (solid blue line), the constant negative curvature k is -0.3, indicating that the vehicle enters the parking space along the left-turn arc. Figure 2 The parking scenario shown corresponds to the initial reversing phase of the vehicle. (2) Transition section: A fifth-order polynomial curve is used to fit the curvature change to ensure the continuity of the first derivative of the curvature, such as Figure 3 In the segment from BC to DE (red dashed line), the curvature k smoothly increases from -0.3 to 0.3, then smoothly decreases back to -0.3, representing the transition segment. Figure 2 In the parking scenario shown, a fifth-order polynomial fitting is used to achieve continuous curvature variation; for example, the transition segment satisfies the following formula:

[0052] Where, k s Let be the curvature at arc length s, reflecting the degree of steering aggression of the vehicle at that point. s is the arc length along the path, representing the starting position from the transition section's origin. Coefficients a0, a1, a2, a3, a4, and a5 are geometric parameters to be optimized, their values ​​determined by boundary conditions. a0 represents the initial curvature at the transition section's starting point; this value is equal to the curvature of the entry section, ensuring curvature continuity at the connection point. a1 represents the linear trend affecting curvature change with the path, determining the slope of curvature change in the initial stage. a2 is a quadratic term controlling curvature change, affecting the curve's bending shape and used to adjust acceleration or deceleration characteristics during the transition process. a3 is a cubic term controlling curvature change, a core parameter for achieving a smooth transition, responsible for generating S-shaped or inverse S-shaped curve trends. a4 is a quartic term controlling curvature change, further fine-tuning the intermediate shape of the transition section and enhancing path smoothness. a5 is a quintic term controlling curvature change, mainly affecting the rate of change near the endpoint, ensuring the first derivative of curvature approaches zero at the endpoint. The boundary conditions satisfied by this fifth-order polynomial are described in the curvature and smoothness constraints below. This can avoid numerical instability problems caused by higher-order polynomials. Furthermore, the coefficients a0, a1, a2, a3, a4, and a5, as low-dimensional optimization variables, can significantly reduce computational complexity and are suitable for real-time online path planning scenarios.

[0053] (3) Adjustment section: A mixed path of straight lines and arcs is used to align the vehicle's posture with the direction of the target parking space, such as... Figure 3 In segment EF (blue solid line), the constant negative curvature k is -0.3, indicating the adjustment segment ( Figure 2 The parking scenario shown allows the vehicle to align with the parking space, achieving precise parking.

[0054] The curvature functions of each segment together constitute a complete path curvature profile. k ( sAs the core variable in low-dimensional optimization problems, its geometric parameters (such as segment lengths, curvature values, and polynomial coefficients) will be optimized to generate the optimal parking path that satisfies kinematic constraints, obstacle avoidance requirements, and smoothness.

[0055] In this implementation, a multi-stage curvature modeling strategy is introduced in S103. The transition segment uses a fifth-order polynomial for curvature fitting. This model not only reduces the dimensionality of the optimization variables and ensures the continuity of the curvature function, but also ensures the continuity of its first derivative, avoiding excessively rapid changes in steering angle and significantly improving the smoothness of steering wheel input. At the same time, the transition segment is seamlessly connected with the arc segment and the straight segment, ensuring the geometric consistency of the entire path and improving driving comfort and vehicle control stability.

[0056] The curvature constraints pre-built in S104 above may include the absolute value of the curvature of the entry segment and the adjustment segment being equal to the minimum turning curvature of the vehicle.

[0057] The pre-built smoothness constraints can include the curvature at the start of the transition segment being equal to the curvature of the entry segment, the curvature at the end of the transition segment being equal to the curvature of the adjustment segment, and the first derivative of the curvature at the start of the transition segment being zero, and the first derivative of the curvature at the end of the transition segment being zero.

[0058] In one implementation, a dynamic steering constraint coefficient can be introduced on top of the optimal control constraints. This dynamic steering constraint coefficient serves as an adaptive minimum turning radius constraint mechanism, dynamically adjusting the lower limit of the turning radius by incorporating the vehicle's longitudinal and angular velocity parameters in real time. Thus, when the vehicle is at high speed or large angular velocity, the system can automatically relax the steering constraints to ensure safety and stability; when the vehicle is at low speed or making small angle adjustments, the turning radius can be reduced, making the path more compact and continuous. This effectively avoids path abrupt changes and redundant adjustment actions caused by rigid radius constraints in traditional planning, thereby improving path continuity and smoothness.

[0059] For example, S105 above may include the following steps: The dynamic steering constraint coefficients are determined based on the minimum turning radius, vehicle speed, and angular velocity in the initial pose. Based on vehicle kinematic constraints and dynamic steering constraint coefficients, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0060] For example, the dynamic steering constraint coefficient satisfies the following formula:

[0061] in, This is the dynamic steering constraint coefficient, which is the radius of curvature of the path at the arc length parameter s. To minimize the bending rate, This is an adjustment coefficient; the specific value of the adjustment coefficient is not restricted here. For vehicle speed With angular velocity The function, For vehicle speed, ω is the angular velocity.

[0062] In a possible parking scenario, dynamic obstacles exist along the parking path. This application's embodiment introduces a dynamic obstacle prediction model to predict these obstacles. By modeling the obstacle's position and velocity, its future position distribution is calculated, and a minimum safe distance constraint is applied during the planning process. This allows the movement trend of obstacles to be considered in advance during path generation, effectively avoiding potential collision risks. Compared to static modeling, this significantly improves the robustness and adaptability of the planning algorithm in real-world scenarios, while also increasing optimization efficiency.

[0063] For example, when a dynamic obstacle is present, the above S104 may include the following steps: Obtain the current position and velocity variable with direction of motion of the dynamic obstacle; Based on position and velocity variables, a pre-trained obstacle motion prediction model is used to predict the motion trajectory of dynamic obstacles within a future planning time window. Based on the predicted trajectory, a safe buffer zone around the obstacle is constructed in the spatiotemporal domain as an obstacle avoidance constraint; Based on the initial pose, vehicle kinematic constraints, and obstacle avoidance constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0064] For example, in a dynamic obstacle prediction model, the prediction time window, i.e., the future planning time window, is [t, t+Δt]. The motion trajectory obtained by predicting the obstacle state satisfies the following formula:

[0065] in, Let the center position of the j-th obstacle be at time t+Δt. Let Δt be the center position of the j-th obstacle at time t, and Δt be the time interval. The velocity variable is used; this formula predicts the obstacle's motion in the short time domain by linear extrapolating the current state and motion trend of the dynamic obstacle. Optionally, to improve the prediction accuracy of the obstacle, Dynamic updates can be achieved through methods such as Kalman filtering or neural network models.

[0066] The obstacle avoidance constraints introduced during the planning process satisfy the following formula:

[0067] Where d() is the Euclidean distance function, Let be the position coordinates of the vehicle at the arc length parameter s. Let [the trajectory of the j-th obstacle] be the motion trajectory within the time window [t, t+Δt]. The preset safe distance threshold is used. Obstacle avoidance constraints ensure that the vehicle maintains a safe distance from surrounding dynamic obstacles at any time on the planned path. This formula combines vehicle position with time, creating a spatiotemporally coupled obstacle avoidance constraint. Compared to traditional static obstacle avoidance, which only considers the current position of the obstacle and cannot handle dynamic scenarios such as pedestrians crossing or vehicles approaching from behind, the introduction of prediction-based spatiotemporal obstacle avoidance constraints enables advance avoidance of future conflicts, significantly improving the robustness and safety of the automatic parking system.

[0068] The parking path planning results obtained in this scenario, thanks to collision detection and optimization, not only maximize the use of parking space but also ensure that the path completely avoids collisions. The simplification of obstacle avoidance constraints allows for faster path optimization, thereby improving real-time performance and ensuring that the final parking path is both safe and efficient.

[0069] In one implementation, the low-dimensional nonlinear optimization objective function involved in the above steps satisfies the following formula:

[0070] in, Let be the radius of curvature of the k-th path stage. , Let be the heading angles for the (k+1)th path stage and the kth path stage. Let be the path length between the k-th path stage and the (k+1)-th path stage, corresponding to the target model OCP. This is because in a circular path, the path length = radius of curvature × angle. Indicates the smoothness of the parking process. It is the curvature fitting error corresponding to the transition segment, which corresponds to a fifth-order polynomial transition segment, and N is the total number of path stages.

[0071] This formula is used to generate smooth, efficient, and easy-to-execute parking paths while satisfying vehicle kinematic constraints and obstacle avoidance requirements. This represents the heading angle change penalty term. By adjusting the sensitivity of different path stages to heading changes, it aims to minimize the abrupt changes in heading angle between adjacent path points, thereby ensuring the directional continuity and smoothness of the path. The term representing the curvature smoothness penalty encourages smaller curvature fluctuations in the path by balancing the priorities of path length and smoothness, thereby improving driving comfort and control stability. Compared to traditional methods that only optimize path length or use fixed spline interpolation, this invention achieves a balance between global optimality and local smoothness in a low-dimensional space by introducing the aforementioned composite objective function. This makes it particularly suitable for real-time online planning requirements in automated parking scenarios.

[0072] When solving this low-dimensional nonlinear optimization objective function, an improved Sequential Quadratic Programming (SQP) algorithm can be used. The optimized path is transformed into a sequence of steering angles that the vehicle can execute, and then proportional-integral-derivative (PID) control or model predictive control (MPC) controllers are used for real-time tracking, thereby enabling online parking.

[0073] Traditional automated parking path planning methods primarily rely on geometric curve models, such as Dubins curves, Klossoyd curves, Bézier curves, and polynomial curves. These methods theoretically generate smooth and continuous paths with high computational efficiency. However, they typically require large parking spaces, and in practical applications, they may fail to achieve efficient parallel parking in confined spaces due to the lack of consideration for the geometric constraints of specific parking locations. Therefore, to address the limitations of geometric curve models, sampling-based path planning methods and optimization control theory-based path planning methods have been proposed.

[0074] Sampling-based path planning methods can effectively overcome the problem of excessive parking space requirements in geometric curve models. They primarily rely on sampling methods such as Rapidly-exploring Random Tree (RRT) or Probabilistic Roadmap (PRM) to plan parking paths by randomly generating sample points within the parking lot and connecting these points. While sampling methods can adapt to complex parking lot geometries, their inherent random sampling results in poor path continuity and accuracy, and also incurs significant computational costs.

[0075] Path planning methods based on Optimal Control Theory (OCP) transform the parking task into an optimization problem, allowing researchers to generate optimal paths while considering vehicle dynamics. These methods typically require solving nonlinear programming (NLP) problems to obtain the optimal path. Although this approach can generate accurate parking paths and fully consider vehicle kinematic constraints, it is computationally expensive due to the involvement of nonlinear vehicle models and complex obstacle avoidance constraints. Most importantly, the discretization of points during the computation process can lead to the failure of collision avoidance constraints, further increasing the complexity of path planning. Therefore, while existing OCP-based methods can provide accurate path planning, their heavy reliance on discretization points and complex obstacle avoidance constraints results in high computational costs, poor real-time performance, and the potential for collisions between discrete points.

[0076] Compared to traditional methods, this invention analyzes the geometric characteristics of the optimal parking path curve to establish an optimal parking path curve, which can then be applied to different parking scenarios, including automated parallel parking systems. This method accelerates the numerical calculation process by reducing optimization variables and incorporating dynamic obstacle prediction, thereby improving computational efficiency and solving the problem of high computational load in traditional optimization-based path planning methods. To demonstrate the effectiveness of this invention, the proposed low-dimensional optimization path planning method is validated under different parallel parking scenarios, both static and dynamic. Simulations are performed using MATLAB. Comparison methods include Optimal Control Program (OCP) and Sampling Program (SBP). Evaluation metrics include path length, curvature continuity, computation time, obstacle avoidance success rate, and final parking accuracy. Experimental results are available in [link to experimental results]. Figure 4As shown, in static parking scenario a (Path in parallel parking scenario), the method provided by this embodiment of the invention has an average computation time of 0.12s, which is only 18% of the OCP method. The path length and parking accuracy are basically consistent with OCP. In dynamic obstacle simulation scenarios c and d, the method provided by this embodiment of the invention can achieve an obstacle avoidance success rate of 94%, while OCP and SBP are only 70% and 65%, respectively. In addition, regarding the continuity of steering angle b, the method provided by this embodiment of the invention reduces the maximum angle change rate by 36%, effectively improving driving smoothness. The experimental results show that the method provided by this embodiment of the invention can not only consider the vehicle's kinematic characteristics, but also make full use of limited parking space, reduce redundant parking operations by optimizing the parking path, and thus improve the computational efficiency and real-time performance of the automatic parking system.

[0077] Example 2: Based on the same concept, Figure 5 A schematic diagram of a parking path planning system based on low-dimensional optimization provided in an embodiment of the present invention includes: The acquisition module is used to acquire the initial pose of the vehicle and the target pose of the target parking space; The model building module is used to determine vehicle kinematic constraints based on the initial pose and using a pre-built vehicle kinematic model. Based on the initial and target poses, it performs multi-stage curvature segmentation modeling of the parking path using the geometric characteristics of the shortest parallel parking path, resulting in multiple path stages. These multiple path stages include an entry segment, a transition segment, and an adjustment segment. The transition segment is obtained by parametrically modeling the curvature using a fifth-order polynomial. Pre-built curvature constraints and smoothness constraints are introduced into each path stage to construct a low-dimensional nonlinear optimization objective function. The optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each path stage, and the geometric parameters of the transition segment include the coefficients of the fifth-order polynomial. The parking path planning module is used to solve a low-dimensional nonlinear optimization objective function based on the initial pose and vehicle kinematic constraints, and obtain the parking path planning result from the vehicle to the target parking space.

[0078] In one possible implementation, the model building module is specifically used for: Based on the initial pose and the target pose, the parking path is divided into an entry segment, a transition segment and an adjustment segment connected in sequence; A constant curvature circular arc is used to model the entry section, which is used to improve the entry speed of vehicles approaching the target parking space; A hybrid path of straight lines and circular arcs is used to model the adjustment segment, ensuring that the heading angle of the vehicle when it arrives at the target parking space is consistent with the direction of the parking space. Based on the entry segment and the adjustment segment, a fifth-order polynomial with respect to the path length is used to model the curvature transformation of the transition segment, which is used to connect the entry segment and the adjustment segment and ensure the continuity of the first derivative of the path curvature. The transition section satisfies the following formula:

[0079] Where, k s The curvature at arc length parameter s reflects the degree of steering aggression of the vehicle at that point. s is the arc length parameter along the path, indicating the position from the start of the transition segment. The coefficients a0, a1, a2, a3, a4, and a5 are all geometric parameters to be optimized.

[0080] In one possible implementation, the curvature constraint includes the absolute value of the curvature of the entry segment and the adjustment segment being equal to the minimum turning curvature of the vehicle. Smoothness constraints include the curvature at the start of the transition segment being equal to the curvature of the entry segment, the curvature at the end of the transition segment being equal to the curvature of the adjustment segment, and the first derivative of the curvature at the start of the transition segment being zero, and the first derivative of the curvature at the end of the transition segment being zero.

[0081] Furthermore, the parking path planning module is specifically used for: The dynamic steering constraint coefficients are determined based on the minimum turning radius, vehicle speed, and angular velocity in the initial pose. Based on vehicle kinematic constraints and dynamic steering constraint coefficients, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space. The dynamic steering constraint coefficient satisfies the following formula:

[0082] in, This is the dynamic steering constraint coefficient. To minimize the bending rate, For adjustment coefficients, For vehicle speed, ω is the angular velocity.

[0083] In one possible implementation, the parking path planning module is specifically used for: When dynamic obstacles exist, obtain the position and velocity variable with the direction of motion of the dynamic obstacles at the current moment; Based on position and velocity variables, a pre-trained obstacle motion prediction model is used to predict the motion trajectory of dynamic obstacles within a future planning time window. Based on the predicted trajectory, a safe buffer zone around the obstacle is constructed in the spatiotemporal domain as an obstacle avoidance constraint; Based on the initial pose, vehicle kinematic constraints, and obstacle avoidance constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

[0084] In one possible implementation, the motion trajectory satisfies the following formula:

[0085] in, Let the center position of the j-th obstacle be at time t+Δt. Let Δt be the center position of the j-th obstacle at time t, and Δt be the time interval. For velocity variables; Obstacle avoidance constraints satisfy the following formula:

[0086] Where d() is the Euclidean distance function, Let be the position coordinates of the vehicle at the arc length parameter s. Let [the trajectory of the j-th obstacle] be the motion trajectory within the time window [t, t+Δt]. This is the preset safe distance threshold.

[0087] In one possible implementation, the low-dimensional nonlinear optimization objective function satisfies the following formula:

[0088] in, Let be the radius of curvature of the k-th path stage. , Let be the heading angles for the (k+1)th path stage and the kth path stage. Let be the path length between the k-th path stage and the (k+1)-th path stage. Indicates the smoothness of the parking process. It is the curvature fitting error corresponding to the transition segment, which corresponds to a fifth-order polynomial transition segment, and N is the total number of path stages.

[0089] Example 3: Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Based on the above embodiments, this embodiment of the present invention also provides an electronic device, including a processor 601, a communication interface 602, a memory 603 and a communication bus 604, wherein the processor 601, the communication interface 602 and the memory 603 communicate with each other through the communication bus 604. The memory 603 stores a computer program, which, when executed by the processor 601, causes the processor 601 to perform the steps in the parking path planning method based on low-dimensional optimization shown in the above embodiment.

[0090] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0091] The communication interface 602 is used for communication between the above-mentioned electronic device and other devices.

[0092] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0093] The processors mentioned above can be general-purpose processors, including central processing units, network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits, field-programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0094] Example 4: Based on the above embodiments, this invention also provides a computer-readable storage medium storing a computer program, which is processed by the above-described parking path planning method based on low-dimensional optimization.

[0095] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative in all respects and are not the only ones. All modifications within the scope of this invention or its equivalents are included in this invention.

[0096] The embodiments described in this invention are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or apparatuses.

[0097] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A parking path planning method based on low-dimensional optimization, characterized in that, The method includes: Obtain the initial pose of the vehicle and the target pose of the target parking space; Based on the initial pose, the vehicle kinematic constraints are determined using a pre-built vehicle kinematic model. Based on the initial pose and the target pose, the parking path is modeled in multiple stages of curvature segmentation using the geometric characteristics of the shortest parallel parking path, resulting in multiple path stages. The multiple path stages include an entry segment, a transition segment, and an adjustment segment. The transition segment is obtained by parametrically modeling the curvature using a fifth-order polynomial. Pre-constructed curvature constraints and smoothness constraints are introduced in each of the path stages to construct a low-dimensional nonlinear optimization objective function; the optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each of the path stages, and the geometric parameters of the transition segment include the coefficients of the fifth-degree polynomial. Based on the initial pose and the vehicle kinematic constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

2. The method as described in claim 1, characterized in that, Based on the initial pose and the target pose, and utilizing the geometric characteristics of the shortest parallel parking path, the parking path is modeled using multi-stage curvature segmentation to obtain multiple path stages, including: Based on the initial pose and the target pose, the parking path is divided into an entry segment, a transition segment and an adjustment segment connected in sequence; A constant curvature circular arc is used to model the entry section, which is used to improve the vehicle's approach speed to the target parking space. The adjustment segment is modeled using a hybrid path of straight lines and circular arcs, ensuring that the heading angle of the vehicle when it arrives at the target parking space remains consistent with the direction of the parking space. Based on the entry segment and the adjustment segment, a fifth-order polynomial with respect to the path length is used to model the curvature transformation of the transition segment, which is used to connect the entry segment and the adjustment segment and ensure the continuity of the first derivative of the path curvature. The transition segment satisfies the following formula: Where, k s The curvature at arc length parameter s reflects the degree of steering aggression of the vehicle at that point. s is the arc length parameter along the path, indicating the position from the start of the transition segment. The coefficients a0, a1, a2, a3, a4, and a5 are all geometric parameters to be optimized.

3. The method as described in claim 1 or 2, characterized in that, The curvature constraint includes the absolute value of the curvature of the entry segment and the adjustment segment being equal to the minimum turning curvature of the vehicle; The smoothness constraints include the curvature at the start of the transition segment being equal to the curvature of the entry segment, the curvature at the end of the transition segment being equal to the curvature of the adjustment segment, and the first derivative of the curvature at the start of the transition segment being zero, and the first derivative of the curvature at the end of the transition segment being zero.

4. The method as described in claim 1, characterized in that, The process involves solving the low-dimensional nonlinear optimization objective function based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space, including: The dynamic steering constraint coefficient is determined based on the minimum turning radius, vehicle speed, and angular velocity in the initial pose. Based on the vehicle kinematic constraints and dynamic steering constraint coefficients, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space. The dynamic steering constraint coefficient satisfies the following formula: in, This is the dynamic steering constraint coefficient. To minimize the bending rate, For adjustment coefficients, For vehicle speed, ω is the angular velocity.

5. The method as described in claim 1, characterized in that, When dynamic obstacles exist, the low-dimensional nonlinear optimization objective function is solved based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space, including: Obtain the current position and velocity variable with direction of motion of the dynamic obstacle; Based on the position and velocity variables, a pre-trained obstacle motion prediction model is used to predict the motion trajectory of the dynamic obstacle within a future planning time window. Based on the predicted trajectory, a safe buffer zone surrounding the obstacle is constructed in the spatiotemporal domain as an obstacle avoidance constraint. Based on the initial pose, the vehicle kinematic constraints, and the obstacle avoidance constraints, the low-dimensional nonlinear optimization objective function is solved to obtain the parking path planning result from the vehicle to the target parking space.

6. The method as described in claim 5, characterized in that, The trajectory of motion satisfies the following formula: in, Let the center position of the j-th obstacle be at time t+Δt. Let Δt be the center position of the j-th obstacle at time t, and Δt be the time interval. For velocity variables; The obstacle avoidance constraint satisfies the following formula: Where d() is the Euclidean distance function, Let be the position coordinates of the vehicle at the arc length parameter s. Let [the trajectory of the j-th obstacle] be the motion trajectory within the time window [t, t+Δt]. This is the preset safe distance threshold.

7. The method as described in claim 1, characterized in that, The low-dimensional nonlinear optimization objective function satisfies the following formula: in, Let be the radius of curvature of the k-th path stage. , Let be the heading angles for the (k+1)th path stage and the kth path stage. Let be the path length between the k-th path stage and the (k+1)-th path stage. Indicates the smoothness of the parking process. It is the curvature fitting error corresponding to the transition segment, which corresponds to a fifth-order polynomial transition segment, and N is the total number of path stages.

8. A parking path planning system based on low-dimensional optimization, characterized in that, include: The acquisition module is used to acquire the initial pose of the vehicle and the target pose of the target parking space; The model building module is used to determine vehicle kinematic constraints based on the initial pose and using a pre-built vehicle kinematic model; based on the initial pose and the target pose, and using the geometric characteristics of the shortest parallel parking path, to perform multi-stage curvature segmentation modeling on the parking path, resulting in multiple path stages; the multiple path stages include an entry segment, a transition segment, and an adjustment segment, wherein the transition segment is obtained by parametric modeling the curvature using a fifth-order polynomial; pre-built curvature constraints and smoothness constraints are introduced into each of the path stages to construct a low-dimensional nonlinear optimization objective function; the optimization variables of the low-dimensional nonlinear optimization objective function are the geometric parameters of each of the path stages, and the geometric parameters of the transition segment include the coefficients of the fifth-order polynomial; The parking path planning module is used to solve the low-dimensional nonlinear optimization objective function based on the initial pose and the vehicle kinematic constraints to obtain the parking path planning result from the vehicle to the target parking space.

9. An electronic device, characterized in that, The electronic device includes at least a processor and a memory, wherein the processor is used to execute a computer program stored in the memory to implement the steps of the parking path planning method based on low-dimensional optimization as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the steps of the parking path planning method based on low-dimensional optimization as described in any one of claims 1 to 7.

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