Output-feedback control for stabilization on SE(3)

This paper addresses the problem of stabilizing systems that evolve on SE(3). The proposed solution consists of an output-feedback controller that guarantees almost global asymptotic stability of the desired equilibrium point, in the sense that the equilibrium point is stable, and we have convergence for all initial conditions, except for those in a nowhere dense set of measure zero. The output vector is formed by the position coordinates of a collection of landmarks fixed in the environment. The resulting closed-loop system exhibits the following properties: (i) the position and orientation subsystems are decoupled, (ii) the position error is globally exponentially stable, and (iii) the orientation error is almost globally exponentially stable. Results are also provided, that allow one to select landmark configurations, so as to control how the position and orientation of the rigid body converge to their final equilibrium values.