  We present a novel convex formulation that models rigid and deformable bodies
coupled through frictional contact. The formulation incorporates a new
corotational material model with positive semi-definite Hessian, which allows
us to extend our previous work on the convex formulation of compliant contact
to model large body deformations. We rigorously characterize our approximations
and present implementation details. With proven global convergence, effective
warm-start, the ability to take large time steps, and specialized sparse
algebra, our method runs robustly at interactive rates. We provide validation
results and performance metrics on challenging simulations relevant to robotics
applications. Our method is made available in the open-source robotics toolkit
Drake.
