Modeling and motion/force tracking for nonholonomic dynamic systems with affine constraints

This paper is devoted to the problem of modeling and position/force tracking for nonholonomic dynamic systems with affine constraints. The rigorous derivation of dynamic model is given. By reasonably introducing so-called internal state vector, a reduced dynamic model, which is suitable for control design, is addressed. Based on the sliding-mode theory, an adaptive control strategy is then derived, guaranteeing that 1) the trajectory tracking error converges to zero; 2) the tracking error of constraints force is bounded with a controllable bound. The efficiency of the controller is demonstrated by a mechanics system: a boat on a running river.