Cusp-free, time-invariant, 3D feedback control law for a nonholonomic floating robot

In this paper the feedback control of a nonholonomic 3D vehicle is consider ed: namely, the problem of steering an underactuated rigid body to a target position along a desired direction is addressed. A simple rime-invariant s trategy is determined on the basis of standard vector kinematics and a Lyap unov-like stability analysis. The resulting control law guarantees almost g lobal exponential convergence of the configuration error to zero with paths that do not exhibit any cusps, thus satisfying a major requirement for the application of such results on real systems that are not allowed or desire d to move in both the forward and backward directions.