M. Moallem et al., AN INTEGRAL MANIFOLD APPROACH FOR TIP-POSITION TRACKING OF FLEXIBLE MULTILINK MANIPULATORS, IEEE transactions on robotics and automation, 13(6), 1997, pp. 823-837
In this paper, a nonlinear control strategy for tip position trajector
y tracking of a class of Structurally flexible multi-link manipulators
is developed. Using the concept of integral manifolds and singular pe
rturbation theory, the full-order flexible system is decomposed into c
orrected slow and fast subsystems. The tip-position vector is similarl
y partitioned into corrected slow and fast outputs. To ensure an asymp
totic tracking capability, the corrected slow subsystem is augmented b
y a dynamical controller in such a way that the resulting closed-loop
zero dynamics are linear and asymptotically stable. The tracking probl
em is then redefined as tracking the slow output and stabilizing the c
orrected fast subsystem by using dynamic output feedback. Consequently
, it is possible to show that the tip position tracking errors converg
e to a residual set of O(epsilon(2)), where epsilon is the singular pe
rturbation parameter. A major advantage of the proposed strategy is th
at the only measurements required are the tip positions, joint positio
ns, and joint velocities. Experimental results for a single-link arm a
re also presented and compared with the case when the slow control is
designed based on the rigid-body model of the manipulator.