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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.

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Compliant mechanisms have been studied extensively as an alternative to traditional rigid body design with advantages like part number reduction, compliance, and multistable configurations. Most of the past research on compliant mechanisms has been restricted to the case where they are subject to holonomic constraints. In this paper, we develop a model of a planar compliant mechanism with nonholonomic constraints as a mobile robot that can move on the ground. The only actuation that is assumed is a torque on the system. It is shown that the dynamics of this system is similar to that of a well-known nonholonomic system, called the Chaplygin sleigh, but with an added degree-of-freedom and an additional quartic potential. The interaction of compliance and the nonholonomic constraint lead to multiple stable limit cycle oscillations in a reduced velocity space that correspond to oscillations about different stable physical configurations. These limit cycle oscillations produce motion of the compliant mechanism in the plane with differing characteristics. The modeling framework in this paper can form the basis for the design of underacted mobile compliant nonholonomic robots or mobile robots that incorporate compliant mechanisms as mechanical switches.