Justh, Eric W.Krishnaprasad, Perinkulam S.This paper presents a Lie group setting for the problem of control of formations, as a natural outcome of the analysis of a planar two-vehicle formation control law. <p>The vehicle trajectories are described using planar Frenet-Serret equations of motion, which capture the evolution of both the vehicle position and orientation for unit-speed motion subject to curvature (steering) control. The set of all possible (relative) equilibria for arbitrary <I>G</I>-invariant curvature controls is described (where <I>G = SE(2)</I> is a symmetry group for the control law). A generalization of the control law for <I>n</I> vehicles is presented, and the corresponding (relative) equilibria are characterized. Work is on-going to discover stability and convergence results for the <I>n</I>-vehicle problem. <p>The practical motivation for this work is the problem of formation control for meter-scale UAVs; therefore, an implementation approach consistent with UAV payload constraints is also discussed.en-USSensor-Actuator NetworksTechnical Report