Distributed Roto-Translation Formation Control of Multi-Rigid-Body Using Dual Quaternion Laplacian

This article highlights the pivotal role of dual quaternion Laplacians in the control of rigid-body roto-translation formations. We propose a new distributed and linear control framework (Dual Quaternion Laplacian Coordination Framework, DQLaCoF) aimed at managing multiple rigid-body formations within the SE(3) space, leveraging the dual quaternion Laplacian. It is established that the system's pairwise asymptotic stability is contingent upon the presence of a directed spanning tree in the communication topology graph. Notably, this framework is capable of simultaneously controlling both the position and orientation of rigid bodies while maintaining the integrity of state variables as unit dual quaternions, adhering to the principles of rigid body kinematics. We explore scenarios with and without leaders in the formation. The efficacy of our proposed control strategy is substantiated through simulation studies involving the formation control of multiple quad-rotors.