Optimal Path for a Car-like Robot to Reach a Given Straight Line
Chao Chen · 2018
This paper presents a closed form solution for the optimal path for a car to reach a given straight line with a specified direction, i.e., the shortest distance between an arbitrary pose (x, y,θ0) and a target line ( d, θ) with the constraint of a maximum curvature of the path. This shortest path metric does not consider collision with obstacles. The result can serve as a heuristic to solve path planning problems for autonomous vehicles, especially for parking and pull-out scenarios, where a vehicle needs to drive from a reference line to a given final pose or vice versa. The distance metric is verified with the shortest path obtained from an exhaustive sampling along the target line. The comparison shows that the explicit metric function provides the optimal path length in an instant time frame. As a result, the distance metric can be used in online planning applications.