DiffPD: Differentiable Projective Dynamics with Contact

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods. Simulators using explicit time-stepping scheme require tiny time steps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method to solve the expensive linearized dynamics. Inspired by Projective Dynamics (PD), we present DiffPD, an efficient differentiable soft-body simulator with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in PD to achieve a super-linear convergence rate. To handle contacts, DiffPD solves contact forces by analyzing a linear complementarity problem (LCP) and its gradients. With the assumption that contacts occur on a small number of nodes, we develop an efficient method for gradient computation by exploring the low-rank structure in the linearized dynamics. We evaluate the performance of DiffPD and observe a speedup of 4-19 times compared to the standard Newton's method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control.