ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)

When a particle moves along a smooth curve, the condition of zero lateral velocity should be satisfied. In the same way, different wheeled structures are all restrained by such nonholonomic constraint when they move along smooth curves on a plane. In this paper, holonomic and nonholonomic constraint equations of various kinds of wheeled structures are clarified, combined with the holonomic constraint relationship between the rotation speed of wheels and their motion speed. Then, the corresponding dynamical equations are readily derived by means of the Euler-Lagrange equation of nonholonomic mechanical systems. In addition, the target trajectory curve is converted to a form of speed target based on such nonholonomic constraint, and the relative curvature of target trajectory curve is introduced to design an appropriate dynamical tracking target. Furthermore, the motion law of the wheeled mobile structure can be organically combined with the dynamical equation by adopting such dynamical tracking target, and the original motion task can be simplified into a common trajectory tracking control problem. Consequently, an appropriate robust controller is designed to track the relative curvature of target trajectory curve on the basis of dynamical tracking target, such that the wheeled mobile structure can precisely follow the target trajectory curve. Theoretical analysis and simulation results indicate that the dynamical tracking target method can essentially solve the problem that the initial speed error is large enough and the position error is continuously accumulated. Even if the forward speed error system is not stable, the actual motion trajectory can almost be coincide with the target trajectory curve.