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.

Figures (9)

• Figure 1: To leverage the benefits of particle-based simulation for robotics, we introduce PBD-R, a revised Position-Based Dynamics formulation that addresses the rigid-body physical accuracy gap in standard PBD. Contribution 1 (Top): PBD-R introduces modifications to PBD to achieve physical accuracy. Contribution 2 (Right): We introduce a solver-agnostic benchmark of seven physics tests with analytical solutions for evaluating simulator accuracy. Contribution 3 (Bottom): PBD-R outperforms PBD and achieves competitive accuracy to MuJoCo while requiring less computation.
• Figure 2: We provide this benchmark of physics tests and their analytical solutions to evaluate the physical accuracy of solvers. From left to right: pushed box (Test 1), box with torque (Test 2), box on slope (Test 3), pushed bunny (Test 4), bunny with torque (Test 5), bunny on slope (Test 6), and rod pushing a box (Test 7).
• Figure 3: Position $\ell_2$ error (left) and rotation error (right) across all seven benchmark tests, averaged over three seeds with standard deviation error bars; rotation errors exceeding $360^\circ$ indicate the simulated orientation has drifted by more than one full revolution from the reference. PBD-R (ours) consistently outperforms standard PBD and performs competitively with MuJoCo across both metrics.
• Figure 4: PBD-R computation time over varying number of spheres compared to MuJoCo over 100 frames of Pushed Box example.
• Figure 5: Sample trajectory from Test 7, Rod Pushing a Box (top-down view) with a friction coefficient $\mu=0.4$. Dashed black outlines show the analytical reference. PBD-R is shown at two resolutions ($n{=}3$ and $n{=}10$ spheres per axis, totaling 27 and 1000 spheres respectively). We use this test to study both the effect of sphere resolution on accuracy and the fidelity of surface contact dynamics under coupled translation and rotation.