Curvature Constrained Paths to Intercept a Target Moving on a Circle

We present a path planning problem for a pursuing agent to intercept a target traveling on a circle. The target is cooperative, and its position, heading and speed are precisely known by the pursuing agent. The pursuing agent has nonholonomic motion constraints, and therefore the path traveled by the pursuing agent must satisfy the minimum turn radius constraints. We consider the class of Dubins paths as candidate solutions, and analyze the characteristics of the six modes of Dubins paths where the final position is restricted to lie on the target circle with heading in the tangential direction of the circle. For each Dubins mode, we derive the feasibility limits, discontinuities and local extrema. Using this analysis the intercepting paths are found by a systematic bisection search in the feasible regions of each of the Dubins modes. We prove that the algorithm outputs the optimal solution, if the optimal intercepting path is a Dubins path; otherwise, it outputs the best found intercepting path and a tight lower bound to the optimal solution.