Leader-Following Formation Control in a Rotating Frame for Agents with Double-Integrator Dynamics: Generalized Stability Results and Experiments

We present a formation control algorithm for double-integrator agents, where the desired interagent positions vary in time according to a rotating coordinate frame, which is represented by the rotation matrix R(t) SO(m). This algorithm applies to formations where: i) each agent has relative-position-and-velocity feedback of its neighbor agents, and the neighbor sets are such that the interagent communication (i.e., feedback) structure represents a strongly connected directed graph; ii) at least one agent has a measurement of its position and velocity relative to the leader; and iii) all agents have a measurement of R. The main analytic result shows that each agent converges to the desired relative positions with the other agents and the potentially moving leader. Notably, this analytic result does not require either undirected communication or every agent to have access to a measurement of its position and velocity relative to the leader. We also present results from rotorcraft experiments that demonstrate leader-following formation control in a rotating frame.