Robust Impedance Shaping Telemanipulation

When a human operator performs a task via a bilateral manipulator, the “feel” of the task is embodied in the mechanical impedance of the manipulator. Traditionally, a bilateral manipulator is designed for transparency; i.e., so that the impedance reflected through the manipulator closely approximates that of the task. “Impedance shaping bilateral control,” introduced here, differs in that it treats the bilateral manipulator as a means of constructively altering the impedance of a task. This concept is particularly valuable if the characteristic dimensions (e.g., force, length, time) of the task impedance are very different from those of the human limb. It is shown that a general form of impedance shaping control consists of a conventional power-scaling bilateral controller augmented with a real-time interactive task simulation (i.e., a virtual environment). An approach to impedance shaping based on kinematic similarity between tasks of different scale is introduced and illustrated with an example. It is shown that an important consideration in impedance shaping controller design is robustness; i.e., guaranteeing the stability of the operator/manipulator/task system. A general condition for the robustness of a bilateral manipulator is derived. This condition is based on the structured singular value (µ). An example of robust impedance shaping bilateral control is presented and discussed.