Understanding the mechanics of manipulation is essential for robots to autonomously interact with the physical world. One of the common manipulation scenarios involves pushing objects in a plane subject to dry friction. We propose a planar friction (force-motion) model that relates an applied robot action to the resultant object motion.
The difficulty lies in that the contact between the object and supporting surface is an area-to-area contact with unknown pressure distribution. We don’t know which part of the area is supporting how much weight nor do we know the coefficient of friction. This makes object motion hard to predict. The key observation is the space of generalized friction force forms a convex set based on the principle of maximum dissipation (a generalized Coulomb’s friction law) . The boundary of such set is termed as limit surface . The geometry of such surface, albeit convex, can be complicated. Fortunately, we have shown that level sets of sum of squares convex polynomials turn out to be good geometric approximations. Another advantage is the model is very data-efficient, i.e., model identification only requires few force and velocity data collected by the robot pushing the object with a point finger. There are some additional nice provable properties of the models, and with these properties, we are able to perform applications including stable pushing and free sliding dynamics simulation.
 J. J. Moreau, “Unilateral contact and dry friction in finite freedom dynamics,” in Nonsmooth Mechanics and Applications, pp. 1–82, Springer, 1988.
 S. Goyal, A. Ruina, and J. Papadopoulos, “Planar sliding with dry friction. Part 1. Limit surface and moment function,” Wear, vol. 143, pp. 307–330, 1991.
Paper: A Convex Polynomial Force-Motion Model for Planar Sliding: Identification and Application: Jiaji Zhou, Robert Paolini, James Bagnell, Matthew T. Mason
Read the award winning paper here.