Proposal of the-law-of-inertia (friction/gravity-free) robots

Robot dynamics under static and Coulomb frictions are shown to be equivalent to a nonlinear position-dependent circuit including a set of on-off switches and analyzed as a variable structure system. It is shown that, under the existence of static and Coulomb frictions at each joint, an ordinary PD feedback with gravity compensation, for set-point position control leads to a trapping of motion at some immovable state within a finite time without reaching the given target position. On the contrary, by introducing regressors for uncertain parameters of gravity forces and static and Coulomb frictions it is possible to show that a proper update law of such regressors together with an adequate PD feedback renders the target state of the robot system globally, asymptotically stable without incurring any offset and without measuring any force/torque signals. It is shown that regressors can be treated as an operator with positivity and thereby regarded as a time-varying capacitor. These observations suggest a proposal of robots that are subject to only the law of inertia, that is, a proposal of inertia-only robots or gravity/friction-free robots