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.

翻译：机器人技术需要能够推理现实世界中从刚体、可变形物体到流体等多样化物理交互的仿真。当前的仿真器通过为不同材料类型拼接多个子求解器来解决这一问题，由此形成的组合式架构使得物理推理变得复杂。基于粒子的仿真器提供了一种引人注目的替代方案：通过统一的单一公式表示所有材料，从而实现无缝的跨材料交互。在基于粒子的仿真器中，位置动力学（PBD）是一种流行的求解器，以其计算效率和视觉真实感而闻名。然而，其缺乏物理精度限制了它在机器人领域的应用。为利用基于粒子求解器的优势同时满足机器人技术对物理保真度的需求，我们提出了 PBD-R，一种修订版的 PBD 公式，通过新颖的动量守恒约束和修正的速度更新来强制执行物理精确的刚体动力学。此外，我们引入了一个与求解器无关的基准测试，该测试包含解析解，用于评估物理精度。利用该基准测试，我们证明了 PBD-R 显著优于 PBD，并且在与 MuJoCo 竞争时达到可比的精度，同时所需计算量更少。