Moving multiple tethered robots between arbitrary configurations

We considered the problem of motion planning for a number of small, disc-like 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 are given a set of target points to which they must move. Upon arrival at these points, a new set of target points are given. Associated with each set of target points is a configuration of the cables that must be achieved when all robots are at these target points. The motion planning task addressed here is to produce relatively short paths for the robots from an initial (nontrivial) configuration of the cables to a configuration corresponding to the next set of target points. An O(n²logn) algorithm is presented for achieving this task for n robots