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.

Highlights

  • We develop a data-driven but physics-based method for modeling planar friction

  • We propose to use the sub-level sets and gradients of a function to represent rigid body planar friction loads and velocities, respectively

  • The maximum work inequality implies that such a function needs to be convex

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Summary

INTRODUCTION

We develop a data-driven but physics-based method for modeling planar friction. In the case of planar robot pushing, indeterminacy of the pressure distribution between the object and support surface leads to uncertainty in the resultant velocity given a particular push action. Despite such inherent difficulty, algorithms and analysis have been developed with provable guarantees. Lynch and Mason [2] developed a stable pushing strategy when objects remain fixed to the end effector with two or more contact points. Our contribution lies in developing a precise and statistically-efficient (i.e., requiring only a few collected force-velocity data pairs) model with a computationally efficient identification procedure. We assume a quasi-static regime [7] where forces and moments are balanced with negligible inertia effects

BACKGROUND
RELATED WORK
REPRESENTATION AND IDENTIFICATION
Polynomial sublevel set representation
Sum-of-squares Convex Relaxation
Identification
EXPERIMENTS
Simulation Study
Robotic Experiment
Stable Push Action Generation
Free Sliding Dynamics Simulation
CONCLUSION AND FUTURE WORK
Full Text
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