Abstract
In this paper feedback control problems of two types of the underactuated mechanical systems are addressed. One of these underactuated systems is snakeboard. The snakeboard is shown to be kinematically controllable. Since kinematically controllable implies small time locally configuration controllable (STLCC), the snakeboard is also STLCC. The other type of the underactuated mechanical system is rigid body. Hovercraft, underwater vehcle and spacecraft are examples of the rigid bodies. The rigid bodies are also shown to be kinematically controllable and STLCC. However, untill now for these systems feedback control problem of steering from a given configuration at rest to a desired configuration at rest has not been achieved completely. We propose an explicit feedback solution to this problem and illustrate the control strategies with application to the snakeboard, hovercraft and spacecraft. Several simulations show the validity of the proposed control strategies.
