Physically Accurate Rigid-Body Dynamics in Particle-Based Simulation

Abstract: Robotics demands simulation that can reason about the diversity of real-world physical interactions, from rigid to deformable objects and fluids. Current simulators address this by stitching together multiple subsolvers for different material types, resulting in a compositional architecture that complicates physical reasoning. Particle-based simulators offer a compelling alternative, representing all materials through a single unified formulation that enables seamless cross-material interactions. Among particle-based simulators, position-based dynamics (PBD) is a popular solver known for its computational efficiency and visual plausibility. However, its lack of physical accuracy has limited its adoption in robotics. To leverage the benefits of particle-based solvers while meeting the physical fidelity demands of robotics, we introduce PBD-R, a revised PBD formulation that enforces physically accurate rigid-body dynamics through a novel momentum-conservation constraint and a modified velocity update. Additionally, we introduce a solver-agnostic benchmark with analytical solutions to evaluate physical accuracy. Using this benchmark, we show that PBD-R significantly outperforms PBD and achieves competitive accuracy with MuJoCo while requiring less computation.