We propose a new approach for executing the main Cartesian tasks assigned to a robot while guaranteeing wholebody collision avoidance. The robot degrees of freedom are fully utilized by introducing relaxed constraints in the definition of operational and collision avoidance tasks. Desired priorities for each task are assigned using the so-called Task Priority Matrix (TPM) method [1], which is independent from the redundancy resolution law and handles efficiently switchings of priorities. To

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... re smooth motion during such task reorderings, a control scheme with a suitable task allocation algorithm is developed at the acceleration level. The proposed approach is validated with MATLAB simulations and an experimental evaluation using the 7-dof KUKA LWR manipulator.