# A Quasi-static Model and Simulation Approach for Pushing, Grasping, and Jamming

## TL;DR

This paper introduces a novel quasi-static model for planar robotic manipulation that accurately captures grasping and jamming behaviors by explicitly modeling manipulator limits, enabling efficient analysis and control of complex contact interactions.

## Contribution

The work presents a new quasi-static model that directly maps manipulator velocities to object motion, explicitly models limiting behaviors, and proves solution existence, enhancing analysis of contact-rich manipulation.

## Key findings

- Model captures grasping and jamming behaviors.
- Solutions are formulated as Linear Complementarity Problems.
- Proves existence of solutions for any manipulator motion.

## Abstract

Quasi-static models of robotic motion with frictional contact provide a computationally efficient framework for analysis and have been widely used for planning and control of non-prehensile manipulation. In this work, we present a novel quasi-static model of planar manipulation that directly maps commanded manipulator velocities to object motion. While quasi-static models have traditionally been unable to capture grasping and jamming behaviors, our approach solves this issue by explicitly modeling the limiting behavior of a velocity-controlled manipulator. We retain the precise modeling of surface contact pressure distributions and efficient computation of contact-rich behaviors of previous methods and additionally prove existence of solutions for any desired manipulator motion. We derive continuous and time-stepping formulations, both posed as tractable Linear Complementarity Problems (LCPs).