On dubins paths to intercept a moving target at a given time

In this work we examine the problem of intercepting a moving target with a pursuer that only moves forwards at constant speed and whose radius of turn is bounded from below. We assume that the target is moving on a straight line at constant speed and that the target's velocity is known to the pursuer with no measurement error. We analyze both the problem of minimum-time interception, as well as the problem of interception at a predefined time. We establish lower and upper bounds on the minimum time to interception that are easy to compute. We examine the relation between shortest paths and minimum time interception paths, give conditions for the two types of paths to coincide and show cases where they differ. Finally, we propose two algorithms for the elongation of an admissible path and provide conditions that guarantee continuous elongation. The above analysis is also conducted in scenarios where the target is located near or inside the circles of minimum turning radius that correspond to the pursuer's initial configuration.