  We propose a hybrid model predictive control algorithm, consensus
complementarity control (C3), for systems that make and break contact with
their environment. Many state-of-the-art controllers for tasks which require
initiating contact with the environment, such as locomotion and manipulation,
require a priori mode schedules or are so computationally complex that they
cannot run at real-time rates. We present a method, based on the alternating
direction method of multipliers (ADMM), capable of highspeed reasoning over
potential contact events. Via a consensus formulation, our approach enables
parallelization of the contact scheduling problem. We validate our results on
three numerical examples, including two frictional contact problems, and
physical experimentation on an underactuated multi-contact system.
