Passive Multi-Task Compliance Control With Strict Priority Through Energy Tanks

A robot with kinematical redundancy with respect to a main task may perform additional tasks simultaneously with the main one. Often, it is desirable to prioritize the performance of some tasks over that of others. To create a strict priority between the different tasks, meaning the performance of higher-prioritized tasks is unaffected by lower-prioritized tasks, null-space projections are often used. Null-space projections may, however, cause the closed-loop system to lose the desirable passivity property, which is necessary to ensure stable interactions with passive environments. In previous works, an energy tank has therefore been introduced to compensate for the potential activity stemming from the null-space projections. However, if the energy tank becomes empty when using these previous methods, the performance of the lower-prioritized tasks suffers more than when using a classical, non-passive hierarchical control scheme. Thus, a new approach to handling this case is proposed in this work. In the event of the energy tank becoming empty and unable to compensate for any null-space projection-induced activity, the hierarchy is ceded to preserve the passivity of the system, leading to better performance of the lower-prioritized tasks compared to previous passivation schemes. Output strict passivity of the closed-loop system is proven irrespective of the amount of energy available from the energy tank, and the performance of the proposed method is validated and compared to that of a classical hierarchical impedance controller and that of an earlier passivation method through simulation and experiments of redundant robotic manipulators.