An Algorithm for Achieving Equilibrium Grasp for Pyramidal-like Objects

Abstract

This paper discusses an algorithm for achieving an equilibrium grasp for a pyramidal-like object placed on a horizontal table under the gravitational field. Assuming that the contact friction is small enough to ensure that any direct grasp surely fails in achieving an equilibrium one, we first show that there exists an algorithm for achieving an equilibrium grasp by using two fingers. After showing the two-fingers-algorithm easily fails in keeping an equilibrium grasp for a horizontal disturbance, we propose the three-fingers-algorithm. We define the concept of gravitationally stable equilibrium, where a gravitational force always pulls the object back to an equilibrium state. We also discuss the finger placement enabling the grasp to keep the stability. Finally, we validate the idea experimentally by using a slightly modified version of the three-fingers-algorithm.