Adaptive motion and force tracking control for nonholonomic dynamic systems subject to affine constraints

Motion and force control is an issue of great practical importance to the mechanical industry. This paper investigates the problem of modeling and position/force tracking for nonholonomic dynamic systems with affine constraints (NDSAC). The rigorous derivation of the dynamic model is given and a reduced dynamic model, which is suitable for control design, is developed. We consider two cases: (i) the reference signal and its time derivative are zero and (ii) the time derivative of reference signal is varying. In the first case, a continuous estimator and an adaptive control law to account for parametric uncertainties are proposed. In the second case, another adaptive control algorithm is developed. In both cases, the motion tracking error and its time derivative converge to zero, and the tracking error of Lagrangian multiplier is bounded with a controllable bound. The efficiency of the controller is demonstrated by a mechanics system: a boat on a running river.