DiffGIPC: Differentiable Mixed-Coordinate Contact Dynamics on GPU

Contact-rich design and control in robotics require efficient gradients through interactions between deformable and nearly rigid bodies. Representing all components with full-space finite elements (FEM) introduces unnecessary motion degrees of freedom for nearly rigid bodies, while high stiffness makes repeated forward and backward solves costly. We present DiffGIPC, a GPU-accelerated framework for differentiable simulation and gradient-based optimization that couples affine body dynamics (ABD) with FEM-based deformable bodies under Incremental Potential Contact (IPC). We derive gradients for affine rest shapes, initial states, and joint controls while retaining only twelve motion DoFs per affine body in each backward system. The formulation differentiates shape-dependent mass and surface-point maps and retains collision, friction, and joint coupling, allowing one body's parameters to be optimized for their effects on other objects. GPU-parallel derivative evaluation, device-controlled adjoint solves, and local gradient accumulation accelerate the backward pass. A reusable PyTorch interface connects supported physical parameters to user-defined parameter maps and losses across design, identification, motion, placement, and articulated control. Experiments demonstrate peak speedups over DiffIPC of approximately 150x with full-space FEM and over 2900x with affine bodies for combined simulation and gradient evaluation.