On the rendezvous problem for multiple nonholonomic agents

In this note, a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced. The proposed nonholonomic control law is discontinuous and time-invariant and using tools from nonsmooth Lyapunov theory and graph theory the stability of the overall system is examined. Similarly to the linear case, the convergence of the multi-agent system relies on the connectivity of the communication graph that represents the inter-agent communication topology. The control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph. Moreover, the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework.