A Dual Quaternion Solution to Attitude and Position Control for Rigid-Body Coordination

This paper focuses on finding a dual quaternion solution to attitude and position control for multiple rigid body coordination. Representing rigid bodies in 3-D space by unit dual quaternion kinematics, a distributed control strategy, together with a specified rooted-tree structure, are proposed to control the attitude and position of networked rigid bodies simultaneously with notion concision and nonsingularity. A property called pairwise asymptotic stability of the overall system is then analyzed and validated by an example of seven quad-rotor formation in the Urban Search And Rescue Simulation (USARSim) platform. As a separate but related issue, a maximum depth condition of the rooted tree is found with respect to error accumulation along each path using dual quaternion algebra, such that a given safety bound on attitude and position errors can be satisfied.