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The ability of executing multiple tasks simultaneously is an importantfeature of redundant robotic systems. As a matter of fact, complex behaviorscan often be obtained as a result of the execution of several tasks. Moreover,in safety-critical applications, tasks designed to ensure the safety of therobot and its surroundings have to be executed along with other nominal tasks.In such cases, it is also important to prioritize the former over the latter.In this paper, we formalize the definition of extended set-based tasks, i.e.,tasks which can be executed by rendering subsets of the task spaceasymptotically stable or forward invariant. We propose a mathematicalrepresentation of such tasks that allows for the execution of more complex andtime-varying prioritized stacks of tasks using kinematic and dynamic robotmodels alike. We present and analyze an optimization-based framework which iscomputationally efficient, accounts for input bounds, and allows for the stableexecution of time-varying prioritized stacks of extended set-based tasks. Theproposed framework is validated using extensive simulations and experimentswith robotic manipulators.

Beyond Jacobian-based tasks: Extended set-based tasks for multi-task execution and prioritization