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Two concepts are advocated for the task specification and control of mechanical manipulators: 1) coding tasks in terms of velocity fields; 2) designing controllers so that the manipulator when under feedback control, interacts in an energetically passive manner with its physical environment. Based on these two concepts, a new passive velocity field controller is proposed which mimics the behavior of a passive energy storage element, such as a flywheel or a spring. It stores and releases energy while interacting with the manipulator, but does not generate any. The controller has the interesting property that it stabilizes any multiple (positive or negative) of the desired velocity field, and exponentially stabilizes the particular multiple of the desired velocity field which is determined by the total kinetic energy of the manipulator control system.
Li et al. (Fri,) studied this question.