  We propose a control framework which can utilize tactile information by
exploiting the complementarity structure of contact dynamics. Since 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 combinatorial
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. This framework can close the loop on
tactile sensors and it is non-combinatorial, enabling optimization algorithms
to automatically synthesize provably stable control policies. We demonstrate
this approach on multiple numerical examples, including quasi-static friction
problems and a high dimensional problem with ten contacts. We also validate our
results on an experimental setup and show the effectiveness of the proposed
method on an underactuated multi-contact system.
