Vertical parking path planning based on Reeds–Shepp curve and an improved particle swarm optimization algorithm

Abstract Current geometric-based path-planning methods for vertical parking in automated parking systems face issues such as stringent initial position requirements, insufficient clearance from garage boundaries, and discontinuous curvature. To address these problems, this paper proposes a parking path-planning method that integrates the Reeds–Shepp curve with an improved particle swarm optimization (PSO) algorithm. The parking process is decomposed into forward and backward segments, each generated using the Reeds–Shepp curve to enhance flexibility. The shift point, defined as the transition between the two segments, serves as the decision variable in the PSO framework. The fitness function jointly considers path length and deviation between the target pose and garage entry. A quadratic Bézier curve and a nonlinear adaptation mechanism are incorporated into the PSO to determine the optimal shift point, mitigating the risk of proximity to garage boundaries. The initial path is then generated using the Reeds–Shepp curve based on the initial pose, shift point, and target pose. After discretization, the path points are optimized via a nonlinear optimization formulation to eliminate curvature discontinuities at segment junctions. Experimental results demonstrate that the proposed method generates feasible, continuous-curvature parking paths across a variety of initial poses, outperforming conventional approaches in terms of flexibility and clearance.