Title: Curvature Effects of Bodies in Contact--Part II:
Elastic Effects and Stability
Authors: E. Rimon and J. Burdick
In : Submitted to IEEE Trans. on Robotics and Automation, 1994.
ABSTRACT
A class of configuration-space based elastic deformation models is
introduced, and are shown to explain the restraining forces which are produced
by surface curvature effects in systems which are kinematically immobilized to
2^nd order. In addition, a lumped parameter energy dissipation, or
damping, model is introduced to account for elastic hysteresis effects during
the deformation of contacting bodies. Using the elastic deformation and
energy loss models, we prove that any object which is kinematically
immobilized to 1^st or 2^nd order is also dynamically locally
asymptotically stable with respect to perturbations. This proof provides
physical justification for using 2^nd order effects for the purposes of
immobilization in practical applications. Simulations illustrate the concepts.