A Unified and Quality-Guaranteed Approach for Dubins Vehicle Path Planning With Obstacle Avoidance and Curvature Constraint

Robotic technologies and applications have recently witnessed remarkable advancements. A major challenge is the shortest-path planning problem of a curvature-bounded vehicle from the known starting configuration to visit a target point and finally return to the starting configuration in an obstacle environment. Spurred by this significant issue in robotic surveillance and patrolling applications, this paper proposed the Two-trip Obstacle-environment Relaxed Dubins Problem (TORDP). In TORDP, the vehicle’s target-visiting heading is a critical variable. Analytical approaches have existed for simpler scenarios than TORDP. However, these approaches are unavailable when solving the complex TORDP simultaneously with bounded curvature, variable target heading and unified ability to tackle with- or without- obstacle cases. Hence, we develop the mixed-integer piecewise-linear program (MIPWLP) approach, making the otherwise intractable complex scenario unifiedly solved with guaranteed good quality. Extensive experiments demonstrate that the proposed approach demonstrates effective performance. Furthermore, the objective approximation error in some cases was analyzed to achieve a length near the optimal length within $h^{2}/(2\sqrt {2})$ tolerance where h is the approximation piece length. The proposed MIPWLP approach could also offer a generalizable optimization framework for broader robotic path-planning applications in constrained environments.