Extending the resolution range of the cascaded generalized inverse

By far the most popular method of resolving redundant systems involves application of the 2-norm-optimizing Moore-Penrose pseudo-inverse. Pseudo-inverse resolution resolves systems uniquely, continuously, and most notably with simple implementation for general systems. However, resolution using 2-norm fails to exploit general systems´ full realizable output space when input bounds are present. The Cascaded Generalized Inverse (CGI) was introduced to address this problem by iteratively reallocating oversaturated input resolutions to other, under-utilized inputs. In this paper, it is demonstrated that although successful in extending the resolution range of 2-norm, CGI still fails to capture the full benefit of a system´s realizable output space. To remedy this, an Extended CGI (eCGI) is introduced to allow a larger space of successful resolution through selective desaturation of saturated inputs through CGI. eCGI is demonstrated in resolving kinematic redundancy and was shown in a numerical example to increase the maximum controllable end-effector acceleration over what is possible with CGI to the full physically achievable space.