Minimal modeling of multi-point contact with friction for a dexterous manipulator

Abstract

Presented here is the minimal mathematical modeling of multi-point contact with friction in a planar multiple rigid body system. System equations of motion are generated using Kane's form of the Gibbs-Appell equations. Pseudo-velocities are used to determine the non-active forces, which results in the determination of the friction forces, during manipulation of an object. The rigid body system consists of a planar finger-thumb combination performing the manipulation of a cylinder on the last link of each digit. The mathematical model predicts when the conditions exist for the cylinder to roll, slip, or stick. The state space of the model is of variable structure, but the switching between structures is simply determined.

Previous research has shown that friction forces during manipulation can be calculated using the linear complementarity problem (LCP) and the penalty/augmented Lagrange multiplier method. The LCP formulation and the Lagrange multiplier method add extra complication to the problem at hand and solution convergence is not guaranteed. In this paper we intend to show that the use of pseudo-velocities for the determination of friction forces avoids the complexities and pitfalls of the previously mentioned methods.