An integral manifold approach for tip-position tracking of flexible multi-link manipulators

In this paper, a nonlinear control strategy for tip position trajectory tracking of a class of structurally flexible multilink manipulators is developed. Using the concept of integral manifolds and singular perturbation theory, the full-order flexible system is decomposed into corrected slow and fast subsystems. The tip-position vector is similarly partitioned into corrected slow and fast outputs. To ensure an asymptotic tracking capability, the corrected slow subsystem is augmented by a dynamical controller in such a way that the resulting closed-loop zero dynamics are linear and asymptotically stable. The tracking problem is then redefined as tracking the slow output and stabilizing the corrected fast subsystem by using dynamic output feedback. Consequently, it is possible to show that the tip position tracking errors converge to a residual set of O(ε²), where ε is the singular perturbation parameter. A major advantage of the proposed strategy is that the only measurements required are the tip positions, joint positions, and joint velocities. Experimental results for a single-link arm are also presented and compared with the case when the slow control is designed based on the rigid-body model of the manipulator