Closed form minimum infinity-norm resolution for single-degree kinematically redundant manipulators

Redundant systems are of interest in engineering because they bring additional capability for a task completion, allowing the system to perform sub-tasks or to improve performances. However, this also means that an extra degree of complexity is added to its resolution. For this purpose, proposed resolution schemes are classically based on the 2-norm minimization, also called pseudo-inverse, whose popularity stems from its easy analytical resolution, but suffers from not considering physical constraints, like input bounds. To tackle this issue, the infinity-norm resolution has been proposed, which determines a minimum-effort solution, taking into consideration individual magnitudes and offering the full physically realisable outputs space. Despite its guaranteed merits, it has only been considered for a few, low-order system because of its lack of analytical resolution. This paper proposes a novel approach on the minimum infinity-norm resolution for single-degree systems, which represent a large part of the most popular redundant configurations. This approach offers a closed-form solution, thus giving an analytical resolution allowing convenient computation and a description of the solution based on parameters of the system. Implementation of this new method is simulated on single-degree kinematically redundant systems to show the superiority of infinity-norm resolution over 2-norm resolution.