🤖 AI Summary
To address the challenge of concurrently executing multiple tasks with dynamically adjustable priorities for redundant robots in safety-critical applications, this paper proposes a unified cooperative control framework integrating extended set-valued task modeling and Control Barrier Functions (CBFs). We formally define extended set-valued tasks that guarantee subspace asymptotic stability and forward invariance, and formulate a unified time-varying priority task stack optimization model. By synergistically combining CBFs with hierarchical quadratic programming (QP), the framework supports both kinematic and dynamic robot models while explicitly enforcing input constraints and enabling smooth priority transitions. Simulation and real-world robotic arm experiments demonstrate that the proposed method achieves high computational efficiency, provable closed-loop stability, and significantly outperforms existing hierarchical QP approaches in task execution fidelity and safety assurance.
📝 Abstract
The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot 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 space asymptotically stable or forward invariant using control barrier functions. We propose a formal mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations, quantitative comparisons to the state-of-the-art hierarchical quadratic programming, and experiments with robotic manipulators.
