Adaptive consensus control of rigid body attitude motion based on rotation matrices

In this paper, we focus on the consensus problem in terms of angular velocity and attitude for heterogeneous rigid bodies over a fixed undirected connected graph. The bodies’ inertia matrices are partially or entirely unknown. We formulate the rigid body kinematics in terms of the 3D rotation group SO(3) which is a Lie group. First, we present the decentralized control protocol for N reference rigid bodies whose inertia matrices are the identity matrix. Then, we present a model reference adaptive control algorithm to guarantee that each actual rigid body asymptotically tracks the corresponding reference model; therefore, they can reach consensus as their reference counterparts do. Finally, we demonstrate the efficacy of the proposed method through a numerical example and compare its performance with the nominal controller without adaptation.