Arvi Gjoka

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry. It supports static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code.We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.

We propose a computational design pipeline for pneumatically-actuated soft robots interacting with their environment through contact. We optimize the shape of the robot with a shape optimization approach, using a physically-accurate high-order finite element model for the forward simulation. Our approach enables fine-grained control over both deformation and contact forces by optimizing the shape of internal cavities, which we exploit to design pneumatically-actuated robots that can assume user-prescribed poses, or apply user-controlled forces. We demonstrate the efficacy of our method on two artistic and two functional examples.