Shortest Dubins Path to a Moving Circle with Free Final Heading

In this paper the shortest time strategy of turn- constrained vehicle for reaching a circle moving on a straight line is posed and solved. The shortest curvature constrained path to a circle is comprised of a left or right turning arc of minimum turn radius (L/R) and straight-line segment (S). An analysis of each of the candidate Dubins modes, L, R, LS, and RS is provided. Under the condition that the agent’s initial position is not on the path of the moving circle, we prove that the length of the shortest Dubins path to the circle is a continuous function of the position of the target center. Leveraging this continuity, we propose an algorithm that uses the bisection search and finds the time-optimal solution. A lower bound to the solution is obtained when the agent’s initial position lies on the path of the moving circle, and a heuristic approach is discussed for such instances.