On the Kinematics of Wheeled Mobile Robots

A wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The relationship between the rigid body motion of the robot and the steering and drive rates of wheels is 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 in such ideal rolling trajectories. The simplest wheel configuration that permits access of arbitrary rigid-body motions is determined. Then the question of slippage due to misalignment of the wheels is investigated by minimization of a nonsmooth convex dis-sipation functional that is derived from Coulomb's Law of friction. It is shown that this minimization principle is equivalent to the construction of quasi-static motions. Examples are presented to illustrate the models.