6-DOF consensus control of multi-agent rigid body systems using rotation matrices

Nonlinear control protocols are proposed for consensus control of a multi-agent system of N heterogeneous rigid bodies in the framework of the tangent bundles TSO(3) and TSE(3) associated with Lie groups SO(3) and SE(3), respectively. The control objective is to stabilise the relative pose configurations with velocity synchronisation of the rigid bodies which share their states according to a static undirected communication topology. The feedback control design is conducted on the dynamic level, and uses the rotation matrix as opposed to various attitude parameterisations. Almost global asymptotic stability of the consensus subspace is demonstrated both analytically using an extension of the Morse–Lyapunov (M–L) approach, and through numerical simulations. Also, the presence of unstable non-consensus equilibria in the closed-loop dynamics is discussed and shown in illustrative examples.