Passive Hierarchical Impedance Control Via Energy Tanks

Modern robotic systems with a large number of actuated degrees of freedom can be utilized to perform several tasks at the same time while following a given order of priority. The most frequently used method is to apply null space projections to realize such a strict hierarchy, where lower priority tasks are executed as long as they do not interfere with any higher priority objectives. However, introducing null space projectors inevitably destroys the beneficial and safety-relevant feature of passivity. Here, two controllers are proposed to restore the passivity: one with local energy tanks on each hierarchy level and one with a global tank for the entire system. The formal proofs of passivity show that no energy is generated by these controllers. Once the tanks are empty, passivity is still guaranteed at the cost of some control performance. Simulations and experiments on a torque-controlled robot validate the approaches and predestine them for the usage in safety-relevant applications.