Dynamic analysis of Continuous Cascaded Generalized Inverse resolution of kinematically redundant manipulators with flexible joints

In the resolution of redundancy in systems, by far the most popular approach involves optimization with respect to the 2-norm, due to it's ease of use, uniqueness, and continuity of resolution. Due to the 2-norm's inability to consider input bounds, however, such methods fail to exploit systems' full feasible output range. The Cascaded Generalized Inverse (CGI) was introduced to extend the realizable output range of the pseudo-inverse, but in doing so, introduces discontinuity in the resolution scheme. This paper analyzes the effects of such discontinuity on the dynamic performance of one popular redundant application: kinematically redundant manipulators. Joint flexibility is simulated and it is shown that discontinuity arising in CGI imparts joint velocity error and oscillation in the system dynamics. The Continuous Cascaded Generalized Inverse (cCGI), which we previously proposed, is a variation of CGI which guarantees continuity in resolution. cCGI was also simulated successfully extending the resolution range of the pseudo-inverse, but without the same dynamic consequences seen in CGI resolution.