Finite-time output-feedback position and attitude tracking of a rigid body

The position and attitude tracking of a rigid body without velocity measurements is addressed. Dual quaternions are used to describe the coupled rotational and translational motions of the rigid body, yielding compact forms of the kinematics and dynamics suitable for control law synthesis. An output-feedback pose (position and attitude) tracking controller is then designed by integrating techniques from passivity and homogeneity. More precisely, a passivity-enabling auxiliary system is proposed to provide necessary damping instead of velocity feedback and a homogeneous method is used to ensure finite-time convergence. The proposed controller guarantees uniform almost global finite-time stability of the closed-loop system and produces a well-defined vector field on the attitude configuration manifold, thus avoiding the unwinding phenomenon. Moreover, it can be split to obtain velocity-free controllers with finite-time convergence for the cases of translation-only or rotation-only control. Numerical examples verify the effectiveness of the proposed method.