The ties that bind: Motion planning for multiple tethered robots

Abstract We consider the problem of motion planning for a number of small, circular robots in a common planar workspace. Each robot is tethered to a point on the boundary of the workspace by a flexible cable of finite length. These cables may be pushed and bent by robots that come in contact with them but remain taut at all times. The robots have a target point to reach on the workspace and, as each moves to its target, its cable gets stretched out into the workspace. For any set of target points, there may be many final cable configurations of differing complexity that allow all robots to reach their targets. Assuming a final configuration of the cables has been specified, the motion planning task addressed here is to produce reasonably short paths for the robots that will achieve this configuration. This is formulated as a problem in computational geometry and an O( n 3 log n ) algorithm is presented for achieving this task for n robots.