When a robot interacts with the world, inevitably it will touch the wrong thing or slip instead of sticking. How should feedback work when the contact mode is changing? Linearization is not useful and hybrid (MIQP) problems cannot be solved in real-time. I’ve been thinking about this problem since the start of my Ph.D., and we’ve finally made some real progress! An ADMM algorithm, which we call Consensus Complementarity Control (C3), jointly optimizes over trajectory and contact mode for real-time MPC.