Attitude and pose formation control for multiple 3D rigid bodies based on unit quaternion representation

Abstract

This paper discusses rigid body formation control for multi-agent systems in 3D spaces and proposes a formation control law to achieve attitude formation and pose formation for multiple rigid bodies. The proposed formation control strategy extends the available attitude synchronization law to an attitude formation control law, and further employs the consensus-based position control to achieve a rigid body formation control in 3D spaces. Each agent’s attitude state is represented by a unit quaternion, and each agent’s position is represented by a vector in $\mathbb{R}^3$. We show that the formation system with the proposed control law is stable at the desired equilibrium by providing a Lyapunov argument for the attitude component. We also employ the stability analysis of cascade systems for the overall rigid body formation system by using available results on linear consensus dynamics.