A Convex Polynomial Force-Motion Model for Planar Sliding: Identification and Application

TL;DR

This paper introduces a convex polynomial force-motion model for planar sliding that accurately captures frictional behavior, enabling efficient identification and practical robotic applications such as object pushing and dynamic simulations.

Contribution

The paper presents a novel convex polynomial model for planar sliding with a simple identification method, improving accuracy and efficiency over previous models.

Findings

Model accurately captures frictional force-motion relationships.

Identification procedure is statistically efficient and convex.

Validated through simulations and robotic experiments.

Abstract

We propose a polynomial force-motion model for planar sliding. The set of generalized friction loads is the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, the polynomial is confined to be convex even-degree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statistically-efficient model identification procedure using a sum-of-squares convex relaxation. Simulation and robotic experiments validate the accuracy and efficiency of our approach. We also show practical applications of our model including stable pushing of objects and free sliding dynamic simulations.