In this paper, we implement the GPU-accelerated subsystem-based Alternating Direction Method of Multipliers (SubADMM) for interactive simulation. The challenging objective for interactive simulations is to deliver realistic results under tight performance, even for large-scale scenarios. We aim to achieve this by exploiting the parallelizable nature of SubADMM to the fullest extent. We introduce a new subsystem division strategy to make SubADMM ‘GPU friendly' along with custom kernel designs and optimization regarding efficient memory access patterns. We successfully implement the GPUaccelerated SubADMM and show the accuracy and speed of the framework for large-scale scenarios, highlighted with an interactive ‘Hand demo’ scenario. We also show improved robustness and accuracy compared to other state-of-the-art interactive simulators with several challenging scenarios that introduce large-scale ill-conditioned dynamics problems.

Collision detection is a fundamental problem across various fields such as robotics, physical simulation, and computer graphics. While numerous studies have provided efficient solutions, based on the well-known Gilbert, Johnson, and Keerthi (GJK) algorithm and Expanding Polytope Algorithm (EPA), existing methods utilizing GJK-EPA often struggle with smooth strictly convex shapes like ellipsoids. This paper proposes a novel approach to the collision detection problem converting it to a problem compatible with an unconstrained Riemannian optimization problem. Moreover, we presents a specific method of solving the problem based on twice differentiable support functions and the Riemannian trust region (RTR) method. The method exhibits fast and robust convergence rate, leveraging the well-established theory of Riemannian optimization. The evaluation studies comparing our method to GJK-EPA method are done with pre-defined primitive shapes. Additionally, a test result with several more complex shapes is demonstrated exhibiting the method’s effectiveness and applicability.