Path planning for a tethered mobile robot

In this paper we investigate the problem of navigation for a planar mobile robot tethered to a base by a flexible cable of length L. Obstacles present in the environment, coupled with the cable length constraint, makes the problem highly non-trivial. We adopt a topological approach along with graph search-based techniques to solve this problem, wherein we use the notion of a homotopy augmented graph to capture the information about the homotopy class of the cable. This lets us plan traversable optimal trajectories from an initial robot position and cable configuration to a final position of the robot. We demonstrate the algorithm by planning trajectories in several cluttered environments and with different cable lengths. As a demonstration of practical applicability, using a dynamic simulation testbed we simulate a robot-cable system following a planned trajectory.