  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.
