  This paper presents a reactive controller for planar manipulation tasks that
leverages machine learning to achieve real-time performance. The approach is
based on a Model Predictive Control (MPC) formulation, where the goal is to
find an optimal sequence of robot motions to achieve a desired object motion.
Due to the multiple contact modes associated with frictional interactions, the
resulting optimization program suffers from combinatorial complexity when
tasked with determining the optimal sequence of modes.
  To overcome this difficulty, we formulate the search for the optimal mode
sequences offline, separately from the search for optimal control inputs
online. Using tools from machine learning, this leads to a convex hybrid MPC
program that can be solved in real-time. We validate our algorithm on a planar
manipulation experimental setup where results show that the convex hybrid MPC
formulation with learned modes achieves good closed-loop performance on a
trajectory tracking problem.
