Passive Decoupled Multi-Task Controller for Redundant Robots

Kinematic redundancy in robots makes it possible to execute several control tasks simultaneously. As some tasks are usually more important than others, it is reasonable to dynamically decouple them in order to ensure their execution in a hierarchical way or even without any interference at all. The most widely used technique is to decouple the system by feedback linearization. However, that requires to actively shape the inertia and consequently modify the natural dynamics of the robot. Here we propose a passivity-based multi-task tracking controller that preserves these inertial properties but fully compensates for task-space cross-couplings using external force feedback. Additionally, three formal proofs are provided: uniform exponential stability for trajectory tracking, passivity during physical interaction, and input-to-state-stability. The controller is validated in simulations and experiments and directly compared with the hierarchical PD+ approach and the feedback linearization. The proposed approach is well suited for safe physical human-robot interaction and dynamic trajectory tracking if measurements or estimations of the external forces are available.