Research Article Open Access

A Mixed Nonlinear Complementarity Formulation for Second-Order Frictional Grasping with Multifingered Robot Grippers

International Journal of Digital Technology Driven Engineering Vol. 1 No. 1 (2026): Inaugural Issue Published 2026-10-27 DOI pending
  1. Ahmad M. Al-Fahed Nuseirat1*
  1. Independent Researcher, P.O. Box 1234, 11821 Amman, Jordan

Corresponding author: Ahmad M. Al-Fahed Nuseirat, anuseirat@gmail.com.

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Keywords:

Frictional grasping, Second-order grasp analysis, Mixed complementarity problem, Contact mechanics, Equilibrium feasibility, Multi-fingered robot grippers

Abstract

This paper presents a mixed nonlinear complementarity problem (MNCP) formulation for an object grasped by a frictional multifingered robot gripper, in which the contact kinematics are expanded to second order. The proposed approach extends the first-order contact kinematics used in prior complementarity formulations of frictional grasping by introducing a quadratic term, Γ(δη, δη), which captures curvature-dependent geometric effects that are absent from a linearized contact description.

The formulation accounts for unilateral hard-finger contacts with isotropic or anisotropic Coulomb friction, expressed through complementarity conditions, and is solved using a semismooth Newton method based on the Fischer–Burmeister function.

Numerical examples demonstrate the influence of the second-order geometric terms on the contact-force distribution and on the available friction margin. An analytically solvable benchmark reproduces the closed-form solution to machine precision, providing an independent verification of the equilibrium, friction, and complementarity implementation.

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