I. Introduction
The definition and execution of tasks in the operational (or task) space is one of the most common approaches in robotics. While this strategy applies to both kinematic and force–torque control, especially the latter one is getting more and more important in the emerging field of physical human–robot interaction these days. If the robot is kinematically redundant with respect to the given task, it is possible to perform additional subtasks simultaneously as exemplified in Fig. 1. A common approach is to execute them in a prioritized manner by means of null space projections that have already been introduced to robotics decades ago [1]–[3] and have become standard tools since. One can ensure that lower priority subtasks do not disturb the execution of more important ones. To stay with the example in Fig. 1, one could assign a task hierarchy with safety-critical objectives such as collision avoidance having high priority. As a result, subtasks with lower priorities, e.g., the optimization of the joint configuration, would consequently not compromise safety.