Hierarchical Control for Partially Feasible Tasks With Arbitrary Dimensions: Stability Analysis for the Tracking Case

Hierarchical impedance-based tracking control has attracted much interest recently due to its advantages of no external forces/torques feedback and inertia reshaping. Desired trajectories on each hierarchy level can be asymptotically tracked following the order of priorities. However, tasks specified by users are required to have the same dimensions as the DOF of robot and are simultaneously feasible and independent. In this article, all these restrictions are removed and a passivity-based hierarchical tracking controller with strict priorities is developed for an arbitrary number of conflicting tasks. Based on the theory of constrained optimization, a new control objective is proposed to achieve automatic tracking of hierarchy-consistent trajectory that is local optimal following the hierarchy order. Formal proof of asymptotic stability for tracking case of partially feasible, conflicting tasks is provided. The effectiveness of proposed method is evaluated in simulations and experiments on Franka Emika Panda robot.