Continuously Shaping Prioritized Jacobian Approach for Hierarchical Optimal Control With Task Priority Transition

Hierarchical control is widely employed for redundant robots to manage multiple simultaneous tasks with distinct priority levels. A novel hierarchical optimal control strategy was recently introduced to achieve performance-optimal tracking under static and strict priority constraints. However, in complex and dynamic environments, robots must possess the capability to switch hierarchical behaviors online to adapt to varying operational scenarios. Existing continuous priority-switching methods often sacrifice hierarchical control performance and fail to asymptotically track the hierarchical optimal trajectory. In this article, a continuously shaping prioritized Jacobian algorithm is proposed and integrated into a newly developed continuous hierarchical optimal control framework with priority transitions. This approach not only ensures optimal control performance but also facilitates continuous priority switching. The continuity and accuracy of the proposed algorithm, as well as the bounded stability of the closed-loop system state variables, are thoroughly analyzed in this work. The effectiveness of the proposed method is validated through simulations and experiments on the Franka Emika Panda robot.