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Humans are capable of managing multiple tasks simultaneously. It is widely assumed that human motor control can be emulated by impedance control. To achieve human-like behavior, however, the impedance parameters of multiple tasks may vary during task execution. We propose an algorithm that shapes task impedance as a function of the robot's time-varying inertial properties. These properties involve virtually constrained masses and virtually constrained inertias that counteract a task in order to comply with a given constraint. In this work, we not only detect task conflicts, but also show how to handle them. Our method is able to control kinematically redundant robots. We developed a damping-design method that does not interfere with our desired Cartesian task-space behavior. The control approach was verified in experiments on a real robot. We compared our impedance shaping method with two alternative control approaches: simple impedance superposition and nullspace projection. Our method preserved the passivity while improving the Cartesian task performance of an impedance controller. The method has computational advantages, beneficial to control robots with many degrees of freedom.

The control of kinematically redundant robots is often approached using nullspace projection, which requires precise models and can be computationally challenging. Humans have many more degrees of freedom than are required to accomplish their tasks, but given neuromechanical limitations, it seems unlikely that biology relies on precise models or complex computation. An alternative biologically-inspired approach leverages the compositionality of mechanical impedance. In theory, nullspace projection eliminates any conflict between two tasks. In contrast, superposition of task-space impedance and a full-rank joint-space impedance may impose a task conflict. This work compared nullspace projection with impedance superposition during unconstrained motion and forceful physical interaction. In practice, despite their theoretical differences, we did not observe a substantial influence of the nullspace projector weighting matrix. We found that nullspace projection and impedance superposition both resulted in measurable task conflict. Remarkably, when the dimensionality of the nullspace was increased, impedance superposition was comparable to nullspace projection.