  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.
