We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.

We present a computation-driven approach to design optimization and motion synthesis for robotic creatures that locomote using arbitrary arrangements of legs and wheels. Through an intuitive interface, designers first create unique robots by combining different types of servomotors, 3D printable connectors, wheels and feet in a mix-and-match manner. With the resulting robot as input, a novel trajectory optimization formulation generates walking, rolling, gliding and skating motions. These motions emerge naturally based on the components used to design each individual robot. We exploit the particular structure of our formulation and make targeted simplifications to significantly accelerate the underlying numerical solver without compromising quality. This allows designers to interactively choreograph stable, physically-valid motions that are agile and compelling. We furthermore develop a suite of user-guided, semi-automatic, and fully-automatic optimization tools that enable motion-aware edits of the robot's physical structure. We demonstrate the efficacy of our design methodology by creating a diverse array of hybrid legged/wheeled mobile robots which we validate using physics simulation and through fabricated prototypes.