Almost global stabilization of fully-actuated rigid bodies

This paper addresses the problem of stabilizing a fully-actuated rigid body. The problem is formulated by considering the natural configuration space for rigid bodies, the Special Euclidean group SE(3). The proposed solution consists of a landmark-based controller for force and torque actuation that guarantees almost global asymptotic stability of the desired equilibrium point. As such the equilibrium point is asymptotically stable and only a nowhere dense set of measure zero lies outside its region of attraction. The controller uses velocity measurements and the position coordinates of a collection of landmarks fixed in the environment. As an additional feature, the control law is designed so as to verify prescribed bounds on the actuation.