  While many robotic tasks, like manipulation and locomotion, are fundamentally
based in making and breaking contact with the environment, state-of-the-art
control policies struggle to deal with the hybrid nature of multi-contact
motion. Such controllers often rely heavily upon heuristics or, due to the
combinatoric structure in the dynamics, are unsuitable for real-time control.
Principled deployment of tactile sensors offers a promising mechanism for
stable and robust control, but modern approaches often use this data in an ad
hoc manner, for instance to guide guarded moves. In this work, by exploiting
the complementarity structure of contact dynamics, we propose a control
framework which can close the loop on rich, tactile sensors. Critically, this
framework is non-combinatoric, enabling optimization algorithms to
automatically synthesize provably stable control policies. We demonstrate this
approach on three different underactuated, multi-contact robotics problems.
