A wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The connections between the rigid body motion of the robot, and the steering and driving controls of wheels are developed. In particular, conditions are obtained that guarantee that rolling without skidding or sliding can occur. Explicit differential equations are derived to describe the rigid body motions that arise from rolling trajectories. The simplest wheel configuration that permits control of arbitrary rigid body motions is determined. The question of slippage due to misalignment of the wheels is investigated based on a physical model of friction. Examples are presented to illustrate the models.