Robust impedance shaping via bilateral manipulation

The impedance shaping bilateral control scheme is investigated. To illustrate the difficulties caused by variable physical scaling effects, and to introduce the concept of impedance shaping, a simple example is given. When implemented on an actual master-slave manipulator the impedance shaping control law and k_φ = 1/α (the velocity scale factor) will not result in robust behavior for any selection of parameter values. This is because both the force and acceleration feedback terms represent noncolocated control. A robust controller can be realized, however, simply by replacing the actual force exerted on the slave with the control force applied to the slave, and rolling off the acceleration feedback term. Moreover, the acceleration feedback term can be used to compensate for the effects of slave inertia.