Shortest Bounded Curvature Trajectory Via A Moving Circle: Theory and Applications

This paper presents a characterization of the time-optimal Dubins trajectory from an initial configuration (heading and orientation) to a final configuration via a moving circle. The circle can be moving on any arbitrary trajectory as long as its trajectory satisfies some regularity constraints. These paths are essential for applications in surveillance, collision avoidance, routing problem for delivery systems, etc. By Pontryagin’s maximum principle, the fundamental segments of the optimal trajectory are established. Thereafter, from the necessary conditions for the state inequality constraints, the analytical relations and geometric properties dictating the concatenation of the segments are proposed. Utilizing the proposed properties, a finite set of candidate optimal trajectory types is established. Numerical results are presented to validate the properties and highlight the application of these paths.