Computing Optimal Trajectories for a Tethered Pursuer in Straight-Line Motion
研究由地面机器人和系绳无人机组成的袋鼠式机器人系统，在无人机沿直线往复运动时，计算地面机器人最少转向次数的最优路径，确保两者距离不超过绳长L。
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.