Formation control for agents modeled with extended unicycle dynamics that includes orientation kinematics on SO(m) and speed constraints

We present a formation control algorithm for agents with extended unicycle dynamics that include orientation kinematics on SO(m), first-order uncertain speed dynamics, and hard constraints on speed. The desired interagent positions are expressed in a leader-fixed coordinate frame. Thus, the desired interagent positions vary in time as the leader-fixed frame rotates. We assume that each agent has relative-position feedback of its neighbor agents, where the neighbor sets are such that the interagent communication (i.e., feedback) structure is a quasi-strongly connected directed graph. We assume that at least one agent (which is a center vertex of the graph) has access to a measurement its position relative to the leader. The main analytic results show that for almost all initial conditions, each agent converges to its desired relative position with the leader and the other agents, and each agent's speed satisfies the speed constraints for all time. We also present an adaptive extension of the formation control algorithm that addresses uncertain speed dynamics, which are parameterized as an unknown linear combination of known basis functions. Finally, we present numerical simulations to demonstrate both the non-adaptive and adaptive formation control methods.