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

arXiv: https://arxiv.org/abs/1602.06056 · HTML: https://mlsanity.com/paper/1602.06056/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2016.

## Built on by (most cited first, 4 of 4)

- [Nonprehensile Planar Manipulation through Reinforcement Learning with Multimodal Categorical Exploration](https://mlsanity.com/paper/2308.02459/) (2023)
- [Integrated Object Deformation and Contact Patch Estimation from Visuo-Tactile Feedback](https://mlsanity.com/paper/2305.14470/) (2023)
- [Robotic Waste Sorter with Agile Manipulation and Quickly Trainable Detector](https://mlsanity.com/paper/2104.01260/) (2021)
- [A Differentiable Recipe for Learning Visual Non-Prehensile Planar Manipulation](https://mlsanity.com/paper/2111.05318/) (2021)

## Abstract (arXiv)

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.