On the state agreement problem for multiple unicycles

In this contribution, a feedback control strategy that drives a system of multiple nonholonomic kinematic unicycles to agreement is introduced. Each agent is assigned with a specific subset of the rest of the team, called the agent's communication set, that includes the agents with which it can communicate in order to achieve the desired objective. The proposed nonholonomic control law is discontinuous and time-invariant and tools from nonsmooth stability theory and graph theory are used to check the stability of the overall system. 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.