A simple control strategy for a robot cart

Mobile robots have been receiving a great deal of attention by the research community. The key point is the presence of nonholonomic constraints which pose interesting issues both for planning and for control problems. Several works have studied the problem of open-loop motion planning. Strategies have been proposed aimed at finding a bounded sequence of inputs to steer the cart from any initial position to any other arbitrary configuration. On the other hand, the controllability and stabilization of non-holonomic mechanical systems like mobile carts have also been addressed. Although the cart model is both locally controllable and reachable, it has been shown that no pure smooth state feedback law exists which can locally stabilize the system. Closed-loop feedback control schemes have been designed to stabilize the cart about an arbitrary point in the state space; some schemes utilize continuous time-varying feedback laws whereas others are based on piecewise smooth feedback laws. The goal of this paper is to present a simple control strategy for steering a mobile robot cart of unicycle type around a target point.