Dynamics and Control of Elastic Joint Manipulators

The investigations presented in this paper are based on our previousstudies where the modeling and control problems of rigid body manipulatorswere treated through the so-called vector-parametrization of the SO(3)group. The nice property of this parametrization, which also displays a Liegroup structure, is that it drastically simplifies some considerations andreduces the computational burden in solving direct kinematic problems,inverse kinematic problems and dynamic modeling by more than 30 hitherto.This statement, which is valid for models built through vector-parameter,becomes stronger in pure vector-parameter considerations. It is provedadditionally that the computational effectiveness of the vector-parameterapproach increases with the increasing number of the revolute degrees offreedom. Here we show that this can be used successfully in the problems ofelastic joint manipulators where, besides the real n links,nfictious links are included and an additional nrevolute degrees of freedom are involved. The present paper also considersthe role of group representations of the rotation motions in the modelingand control of manipulators with elastic joints. Dynamic models‘through’ vector-parameter and in ‘pure’vector-parameter form are developed and the inverse dynamic problem isdiscussed. It is shown that the nonlinear equations of motion are globallylinearizable by smooth invertible coordinate transformation and nonlinear state feedback.