My thesis work focuses on the robust treatment of collisions in a variety of domains. We start by looking at finite element hyper-elastic materials in our paper, "Incremental Potential Contacts." Our approach is unconditionally robust, requires no parameter tuning, and provides a direct way of controlling the trade-off between running time and accuracy. Matching experimental data in one shot is finally an achievable goal.

We follow up this work by proposing a large-scale benchmark for continuous collision detection (CCD) methods. We evaluate each method on accuracy, correctness, and efficiency. Surprisingly, many algorithms miss collisions, and those that do not are overly conservative. To address these shortcomings we introduce a new method that is provably conservative, results in fewer false positives, and is on par with the fastest methods. Additionally, our method is the first method to provide minimum separation CCD (MSCCD) with guarantees.

Using both the IPC formulation and our conservative MSCCD, we propose a method for simulating rigid body dynamics with an intersection-free guarantee at every step. We do this by introducing a novel CCD method for curved trajectories (roto-translations). Our method works by using a series of linear CCD queries with minimal separation to bound the error in linearizing. We show the robustness of our method in several scenes including complicated mechanisms, frictional contact, and large time steps.