Shortest Bounded-Curvature Paths Via Circumferential Envelope of a Circle. Issue 2 (2020) - Jha, Bhargav; Chen, Zheng; Shima, Tal
Abstract: The paper characterizes the shortest bounded-curvature paths for a Dubins vehicle between two configurations with specified location and heading angle via the boundary of an intermediate circle. Only two distinct cases can arise in such engagements, first, when the shortest path is tangent to the circle at only one point, and second, when a segment of the shortest path overlaps a part of the circular boundary. Control command for both the cases are proposed, and some geometric properties for the first case are established by using necessary conditions for state inequality constraints and Pontryagin's maximum principle. Numerical examples are presented to illustrate the geometric properties of the shortest bounded-curvature paths. These geometric properties give insight about concatenation of different segments of the shortest path and allow us to state that the candidate shortest paths belong to a finite set.