Steering a Chaplygin Sleigh Using Periodic Impulses

The control of the motion of nonholonomic systems is of practical importance from the perspective of robotics. In this paper, we consider the dynamics of a cartlike system that is both propelled forward by motion of an internal momentum wheel. This is a modification of the Chaplygin sleigh, a canonical nonholonomic system. For the system considered, the momentum wheel is the sole means of locomotive thrust as well the only control input. We first derive an analytical expression for the change in the heading angle of the sleigh as a function of its initial velocity and angular velocity. We use this solution to design an open-loop control strategy that changes the orientation of sleigh to any desired angle. The algorithm utilizes periodic impulsive torque inputs via the motion of the momentum wheel.