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 acubic parabolawhose curvature increases proportional to the location of therobot from its initial pose. We define multi-stage path planning problems. In the base stage, we assume a fixed initial anda fixed target configuration of a robot in anSE(2)state space and present an analytic formula for the curvature-continuouspath and its deterministic way of checking a collision with a polygonal obstacle. In the inductive stage, we move our focusto the closed-form expression of a distance-optimal, collision-free path under flexible target orientation. In both stages, weprovide in-depth performance analysis and validations with various case studies. The resulting paths in the base stage complycurvature-continuity constraint (less than 0.2 rad/m curvature changes) with 5.5 ms computation time, which is suitable forreal-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 similarpath lengths (average 23.8 m), compared to those by an existing method (infinity rad/m maximum curvature, 110.7 ms maximumcomputation time, and 24.6 m average path length).