Avoiding discontinuities while using the minimum infinity norm to resolve kinematic redundancy

Abstract

Frequently in the practice of mechatronics, we see systems driven by multiple actuators where those actuators must work in a highly coupled fashion to achieve the desired results. In some cases, it may be desirable to provide more actuators than are strictly necessary, in which case the system becomes underdetermined, or redundant. Such underdetermined systems require the use of optimization. Schemes to resolve the redundancy in a manner consistent with a secondary task, such as the minimization of applied torques or expended energy. In a previous paper (1998), we explored the ramifications of using a local optimization algorithm based on the least infinity norm. While a beneficial algorithm in many respects, it sometimes provides solutions which exhibit non-unique and discontinuous characteristics over time. In this paper, we propose one possible remedy for these problems, and continue to reveal more structure behind the least infinity norm and the infinity inverse, applying our results to redundancy resolution of a robot manipulator.