1. Introduction
Path planning as an essential part of the autonomous driving has been widely researched in recent years. The path planning layer of autonomous vehicles (AVs) can be classified into the global and local path planners according to the planning horizon [
1,
2]. The global path planners are mainly focused on the navigation with the optimal economic, the least congestion and the highest average speed by considering the entire configurable space from the start point to the target point [
3]. Different from the global path planners, local path planners usually pay more attention to the improvements on the driving safety and the vehicle stability in the process of dynamic obstacle avoidance by considering the constraints of kinematics and dynamics, during autonomous driving [
4].
Many planning algorithms of AVs are inherited from wheeled-robotics principles because of their similarities in structure and control. In the wheeled robotics community, path planning methodologies can be classified into four groups, including graph search-based, sampling-based, interpolation-based and numerical optimization-based [
5]. The idea behind graph search-based methods is to construct a configurable state-space based on graph theory and then use different search strategies (e.g., Voronoi diagrams [
6], the Dijkstras algorithm [
7], the A
algorithm [
8] or the State Lattice algorithm [
9]) to generate a discrete route with grid or lattice occupancy. Being different from graph search-based methods, sampling-based methods can be further categorized into stochastic sampling and deterministic sampling depending on the sampling space used. Deterministic sampling-based methods [
10] require less computation cost than the stochastic sampling-based methods [
11], as they sample in a semistructured space instead of an entire configuration action-space or state-space. There are some common features between graph-based and sampling-based methods. For example, the paths generated from both methods are connected by a series of discrete waypoints [
12], and these paths need further smoothing for practical application in AVs or wheeled-robotics. Since continuous curvature is a necessary requirement of drivable paths, interpolation-based path planning methods have been developed to generate smooth and continuous-curvature routes based on different curve models, such as spline curves model [
13], clothoid curve model [
14], etc.
The feasible solutions of satisfying the smooth and drivable constraints are usually not unique. Thus, numerical optimization-based path planning methods are developed to obtain the optimal route based on designing an objective function [
15], e.g., the shortest-distance, the highest-efficiency, the shortest-time, etc. A potential field-based path planning method (PFBM), as a typical numerical optimization approach, was proposed by establishing the attractive potential field (PF) around a target point and the repulsive potential fields around obstacles to realize the obstacle avoidance of a robot in [
16]. A composite PF is established with the constructed repulsive and attractive PFs, to automatically guide a robot to the destination by searching the gradient descent direction. Up to now, the PFBM has been applied both in structured [
17,
18] and unstructured [
19] environments for AV path planning. Traditional PFBMs are usually based on a known target point and span the entire discrete space, which makes them reasonable and efficient for robotics control in indoor or simple environments. However, these requirements are difficult to accurately determine for autonomous driving in practical road environments. Furthermore, there is no qualitative assessment of the reasonability of the paths generated using PFBM, especially in driving scenarios with multiple obstacles. Besides, the planned paths are very sensitive to the configuration of the parameters [
16]. For example, if the parameters of the PF functions are inappropriately configured or the obstacles are located with short distances, the route generated using PFBM is likely to fall into local minima, resulting in rough and unexpected routes.
To address the above mentioned problems, in this paper we propose a hybrid potential field sigmoid curve method (HPFSM) as shown in
Figure 1, which aims to optimize the planned path of PFBM and to achieve an expected collision-free trajectory to improve the performance of autonomous driving. Firstly, the PF functions are designed based on the geometric shape, relative position and distance, etc. Then, the potential fields are established for the obstacles, the target lane and the road boundaries according to the defined PF functions, respectively. A collision-free route with the minimum PF can be achieved by fusing the established PFs. A constrained nonlinear optimization problem is constructed based on the collision-free path and the sigmoid curves. Finally, an optimal path of satisfying the constraints of collision avoidance and vehicle dynamics can be achieved by solving with the interior point algorithm. The main contributions of this study include:
- (1)
A novel hybrid path planning method is proposed to get better collision-free path for improvements on vehicle stability and ride comfort during autonomous driving by combining potential field with sigmoid curve.
- (2)
Based on the distribution function of two-dimensional joint probability density, an improved potential field of the obstacle is designed to mimic more realistic distribution of collision risk by decoupling the PF in longitudinal and lateral directions.
- (3)
With the designed objective of the shortest path generation, the trajectory is optimized to improve the vehicle stability and the ride comfort during autonomous driving by considering the constraints of collision avoidance and vehicle dynamics.
This paper is organized as follows:
Section 2 designs a potential field-based path planning and shows how PFBM can generate unexpected paths.
Section 3 introduces the proposed HPFSM.
Section 4 presents the validation and evaluation results by comparing the proposed method with PFBM both in the static and dynamic driving scenarios. Finally,
Section 5 presents our conclusions.