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 considered; namely, the problem of steering an underactuated rigid body to a target position along a desired direction is addressed. A simple time-invariant strategy is determined on the basis of standard vector kinematics and a Lyapunov-like stability analysis. The resulting control law guarantees almost global 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 desired to move in both the forward and backward directions. KEY WORDS—nonholonomic systems, position control, underactuated vehicles, time-invariant control