On a control for a class of nonholonomic systems with drift using time-state control form

We propose a new control method for a class of nonholonomic systems with drift. We consider a conservative mechanical (Lagrangian) system which has one cyclic coordinate. Such a system may yield a nonholonomic system with a non-vanishing drift term. Sufficient condition for small time local controllability of the system with sufficiently large inputs is derived, but only an open-loop path planning is proposed. In this paper, we give a feedback control method for the system using the time-state control form via time-varying coordinate and input transformations