A reverse priority approach to multi-task control of redundant robots

A novel method to handle multiple robotic tasks with priorities is presented. The occurrence of singularities, both of the kinematic and algorithmic type, may affect the correct hierarchy in task execution. Existing methods deal with singularities either by using damped least squares solutions or by relaxing the enforcement of secondary tasks. Damped pseudo-inversion mitigates undesired effects near singularities, at the cost of non-negligible task errors and deformation even of the highest priority task. When secondary tasks are not enforced, hierarchy is preserved but these tasks are not executed accurately even when this would be possible. In our approach, joint motion contributions are added following the reverse order of task priorities and working with suitable projection operators. Higher priority tasks are processed at the end, avoiding possible deformations caused by singularities occurring in lower priority tasks. The proposed Reverse Priority (RP) method allows executing at best all tasks while still preserving the desired hierarchy. The effectiveness of the RP method is shown through numerical simulations and with experiments on a 7-dof KUKA LWR.