Formation Control in a Leader-Fixed Frame for Agents with Extended Unicycle Dynamics that Include Orientation Kinematics on SO(m)
Christopher Heintz, Jesse B. Hoagg · 2019
We present a formation control algorithm for agents with extended unicycle dynamics that include orientation kinematics on SO(m) and first-order speed dynamics. The desired interagent positions are expressed in a leader-fixed coordinate frame, which is aligned with and rotates with the leader's velocity vector. 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 represents a strongly connected directed graph. We assume that at least one agent has access to a measurement its position relative to the leader. The analytic result shows that for almost all initial conditions, the agents converge to the desired relative positions. We also present results from software-in-the-loop simulations with 3 fixed-wing unmanned air vehicles (UAVs) that demonstrate the leader-fixed formation-control algorithm.