Improving the performance of auxiliary null space tasks via time scaling-based relaxation of the primary task

Kinematic redundancy enhances the dexterity and flexibility of robot manipulators. By exploiting the redundant degrees of freedom, auxiliary null space tasks can be carried out in addition to the primary task. Such auxiliary tasks are often formulated in terms of a performance or safety criterion that shall be minimized. If the optimization criterion, however, is defined in global terms, then it is directly affected by the primary task. As a consequence, the task achievement of the auxiliary task may be unnecessarily detrimented by the main task. In addition to modifying the primary task via constraint relaxation, a possible solution for improving the performance of the auxiliary task is to relax the primary task temporarily via time scaling. This gives the null space task more time for achieving its objective. In this paper, we propose several such time scaling schemes and verify their performance for a DLR/KUKA Lightweight Robot with one redundant degree of freedom. Finally, we extend the concept to multiple prioritized tasks and provide a simulation example.