When a robotic system is redundant with respect to a given task, the remaining degrees of freedom can be used to satisfy additional objectives. With current robotic systems having more and more degrees of freedom, this can lead to an entire hierarchy of tasks that need to be solved according to given priorities. In this paper, the first compliant control strategy is presented that allows to consider an arbitrary number of equality and inequality tasks, while still preserving the natural inertia of the robot. The approach is therefore a generalization of a passivity-based controller to the case of an arbitrary number of equality and inequality tasks. The key idea of the method is to use a Weighted Hierarchical Quadratic Problem to extract the set of active tasks and use the latter to perform a coordinate transformation that inertially decouples the tasks. Thereby unifying the line of research focusing on optimization-based and passivity-based multi-task controllers. The method is validated in simulation.

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