Non-smooth time-varying control for Lyapunov stabilization of the posture of the unicycle mobile robots

In this paper the problem of posture regulation for the unicycle mobile robot is solved via the explicit construction of a control Lyapunov function. The construction is achieved via dynamic extension of the inputs along with a non-smooth factorization of the first storage function considered, before a standard backstepping procedure is carried out. The control law obtained is non-smooth and time-varying, however, these properties are obtained as natural consequences of an explicit design procedure based on constructive design of a control Lyapunov function, rather than as a consequence of added periodic excitation.