Inertia equivalence principle and adaptive control of parallel manipulators with redundant actuation

This paper aims to present a precise proof of the nontrivial fact that a virtual work principle is also valid for two different physical systems, a parallel manipulator and its arbitrary reduced tree system, through introducing the so called inertia equivalence principle that exposes the relation between the dynamics of the two systems. Dynamics of parallel manipulators and its properties are then derived based on geometric projection. The role of redundant action in removing singularities is also clarified. Two control algorithms are studied. First, we implement a geometric control algorithm that is based on the Riemannian metric structure. Motivated by this, an adaptive control algorithm is then proposed in which only the dynamic parameters need to be updated. Geometric reinterpretation of this algorithm as the passive system is given. Its asymptotic stability is therefore an obvious fact. The new content of this algorithm compared with the traditional ones is discussed. Experimental results are then reported.