On the continuity of Cascaded Generalized Inverse redundancy resolution, with application to kinematically redundant manipulators

Redundancy in systems is valued for its ability to add additional dexterity in task completion, but its utilization implies an added degree of complexity which must be resolved at runtime. The majority of resolution methods have focused on resolution using some variant of the 2-norm optimizing pseudo-inverse. While tractable, the pseudo-inverse fails to consider input bounds and often resolves systems with input values unrealizable given physical parameters. The Cascaded Generalized Inverse (CGI) was introduced to incorporate maximum input bounds and extend the output space of the pseudo-inverse by iteratively reallocating joint contributions to underutilized inputs. This paper discusses the discontinuities which arise in resolution of systems utilizing CGI, and proposes a constrained CGI, which overcomes this discontinuity. Proof of continuity is provided, and the constrained and unconstrained CGI systems are simulated and compared with application to kinematically-redundant robotic manipulators.