Computing Optimal Trajectories for a Tethered Pursuer in Straight-Line Motion

Abstract In this paper, we address a trajectory planning problem for a marsupial robotic system composed of a ground robot and an aerial robot (drone) connected by a taut tether with maximum length L . We consider a scenario where both robots move along parallel lines in a vertical plane. The drone follows a predefined back-and-forth trajectory at constant speed, and the goal is to determine an optimal path for the ground robot. Specifically, we seek a minimum-link trajectory–a back-and-forth path with the fewest direction changes–and a constant speed for the ground robot such that the distance between the two robots never exceeds L . This problem can be framed within the context of a pursuit-evasion game, where the evader’s trajectory is known, and the goal is to compute an optimal trajectory for the pursuer. Employing geometric modeling techniques, we develop an optimal algorithm to compute a parameterized minimum-link trajectory for the ground-based pursuer, given the a priori known trajectory of the aerial evader. In addition, we solve three interconnected geometric optimization problems by systematically exploiting their inherent relationships.