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We propose a polynomial model for planar sliding mechanics. For the force-motion mapping, we treat the set of generalized friction loads as the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. 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. We then derive the kinematic contact model that resolves the contact modes and instantaneous object motion given a position controlled manipulator action. The inherently stochastic object-to-surface friction distributions are modeled by sampling polynomial parameters from distributions that preserve sum-of-squares convexity. Thanks to the model smoothness, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. Simulation and robotic experiments on pushing and grasping validate the accuracy and efficiency of our approach.

Abstract-Based on the convex force-motion polynomial model for quasi-static sliding, we derive the kinematic contact model to determine the contact modes and instantaneous object motion on a supporting surface given a position controlled manipulator. The inherently stochastic object-to-surface friction distribution is modelled by sampling physically consistent parameters from appropriate distributions, with only one parameter to control the amount of noise. Thanks to the high fidelity and smoothness of convex polynomial models, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. The motion equations for both single and multiple frictional contacts are given. Simulation based on the model is validated with robotic pushing and grasping experiments. 1

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