Minimization of energy in quasistatic manipulation

Abstract

Quasistatic mechanical systems, in which mass or acceleration is sufficiently small for the inertial term ma in F=ma to be negligible compared to dissipative forces, are discussed. It is pointed out that many instances of robotic manipulation can be well approximated as quasistatic systems, with the dissipative force being dry friction. Energetic formulations of Newton's laws have often been found useful in the solution of mechanics problems involving multiple constraints. An intuitive minimum power principle is outlined which states that a system chooses at every instant the lowest-energy, or `easiest', motion in conformity with the constraints. Surprisingly, the principle is in general false; but it is proved that the principle is correct in the useful special case that Coulomb friction is the only dissipative or velocity-dependent force acting in the system