Local path planning scheme for car-like robots’ shortest turning motion using geometric analysis

This work presents the curvature-continuous path planning of a car-like robot for its turning motion around an obstacle. For the smoothness of the path, we adopt a cubic parabola whose curvature increases proportional to the location of the robot from its initial pose. We define multi-stage path planning problems. In the base stage, we assume a fixed initial and a fixed target configuration of a robot in an SE(2) state space and present an analytic formula for the curvature-continuous path and its deterministic way of checking a collision with a polygonal obstacle. In the inductive stage, we move our focus to the closed-form expression of a distance-optimal, collision-free path under flexible target orientation. In both stages, we provide in-depth performance analysis and validations with various case studies. The resulting paths in the base stage comply curvature-continuity constraint (less than 0.2 rad/m curvature changes) with 5.5 ms computation time, which is suitable for real-time applications. Regarding the inductive stage, the distance-optimal paths formed by our method satisfy the curvature-continuity constraint (0.2 rad/m maximum curvature) and consume less time (maximum 2.34 ms) while still showing similar path lengths (average 23.8 m), compared to those by an existing method (∞ rad/m maximum curvature, 110.7 ms maximum computation time, and 24.6 m average path length).