Inertia equivalence principle and adaptive control of redundant parallel manipulators

Presents an inertia equivalence principle that exposes the relation between the dynamics of a parallel manipulator, and that of its arbitrary reduced tree systems. This principle, along with the D´Alembert principle, leads to a precise proof of the nontrivial fact that the virtual work principle is also valid for the two different physical systems, a parallel manipulator and its reduced tree system, under a given condition. The dynamics of parallel manipulators and its properties are then given. Two control algorithms are then provided. Firstly, we implement a geometric control algorithm that is based on the Riemannian metric structure associated with the kinetic energy of the manipulator. Motivated by this, an adaptive control algorithm is then proposed in which only dynamic parameters are required to be updated. Geometric reinterpretation of this algorithm as the passive port controlled system is given. Its asymptotic stability is therefore obvious. The new content of this algorithm compared with the traditional ones is discussed. Experimental results are reported that demonstrate the effectiveness of the algorithms.