Modeling of wheeled mobile robots as differential-algebraic systems

We formulate the problem of wheeled mobile robot (WMR) modeling under wheel slip, while moving over rough terrain, as the integral of a differential algebraic equation (DAE) of either first or second order. That is, the elements of the model include both differential equations and kinematic constraints. While such a formulation is typical of Lagrangian dynamics in augmented form, we show how identical principles apply to kinematic models of motion. In effect, we show in this paper that the very high fidelity models traditionally used in offline simulation can be readily adapted for use in real time for both control and estimation of the motion of arbitrary WMRs over arbitrary rolling terrain, while slipping. While such models are more correct and general than the naive methods that are typically used, we also show that they are orders of magnitude more efficient than such naive methods for equivalent accuracy.