Unit dual quaternion-based feedback linearization tracking problem for attitude and position dynamics

This paper provides a unified solution for the attitude and position tracking problem of a rigid body in 3-dimensional space, using the concept of the unit dual quaternion. The error dynamics described by a unit dual quaternion are deduced after the dual-quaternion-based dynamics of a single rigid body are given. Then by utilizing the feedback linearization principle, a unit dual quaternion based tracker is proposed based on the error dynamics, which is proven to render the equilibrium point of the closed loop system asymptotically stable, and includes the attitude and position regulation problems as particular cases. Furthermore, to solve the two equilibria problem, a switching parameter is introduced to improve the tracker, which causes the system to converge to the 'nearer' equilibrium with a 'shorter' path. Both the trackers uniquely deal with the rotational and translational dynamics simultaneously with non-singularity and maintain the interconnection between rotation and translation. Finally, the proposed control schemes with applications to the regulation problem and the tracking problem are simulated to illustrate the theoretical results.