Rendezvous of unicycles: A bearings-only and perimeter shortening approach

We study the rendezvous problem of multiple nonholonomic unicycle-type robots. Simple decentralized control laws are proposed in which each agent makes a decision only based upon the bearing angles of the other robots in its reference frame. The convergence is first proved when the interaction topology between robots is connected; then for the complete interaction case, it is proved that under the proposed control law, the perimeter of the convex hull defined by the positions of robots decays all the time. Consequently, all the robots converge to a common point. It is also proved that the meeting point is located in a bounded region which is determined by the robots’ initial positions. Simulations illustrate the theoretical results and the performance with measurement errors.