Physically Accurate Rigid-Body Dynamics in Particle-Based Simulation

Ava Abderezaei; Nataliya Nechyporenko; Joseph Miceli; Gilberto Briscoe-Martinez; Alessandro Roncone

cs.ROMar 15, 2026

Physically Accurate Rigid-Body Dynamics in Particle-Based Simulation

Authors: Ava Abderezaei, Nataliya Nechyporenko, Joseph Miceli, Gilberto Briscoe-Martinez, Alessandro Roncone

Organizations: Department of Computer Science, University of Colorado Boulder, CO, USA

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 & tables

Fig. 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.

Fig. 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).

Test	Name	Analytical Solution	What is tested
1	Pushed box	$x(t)=\frac{1}{2}\frac{(F-\mu Mg)}{M}\,t^{2}$	Translation accuracy with a constant force applied at CoM with ground friction
2	Box with torque	$\theta(t)=\frac{1}{2}\frac{\tau}{\lambda}\,t^{2}$	Rotation accuracy with a constant torque applied at CoM for a shape with isotropic inertia
3	Box on slope	$x(t)=\frac{1}{2}(g\sin\theta-\mu g\cos\theta)\,t^{2}$	Accuracy in resolution of gravity, normal force, and friction on an incline
4	Pushed bunny	$x(t)=\frac{1}{2}\frac{(F-\mu Mg)}{M}\,t^{2}$	Same as (1) but on a asymmetric mesh
5	Bunny with torque	$\theta_{z}(t)=\frac{1}{2}\frac{\tau_{z}}{I_{zz}}\,t^{2}$	Same as (2) but on an asymmetric mesh with anisotropic inertia
6	Bunny on slope	$x(t)=\frac{1}{2}(g\sin\theta-\mu g\cos\theta)\,t^{2}$	Same as (3) on an asymmetric mesh.

TABLE I : Physics test suite. The tests cover four distinct rigid-body behaviors across different objects result in in seven different tests.

F

: applied force magnitude,

\tau

: applied torque magnitude,

M

: total mass,

\mu

: kinetic friction coefficient,

\theta

: slope angle,

\lambda

: principal moment about the rotation axis,

I_{zz}

: moment of inertia about the

z

-axis. CoM: center of mass. Test configurations are illustrated in Fig. 2 .

Parameter	Value
Box mass	$m$	$=$	$4\,\mathrm{kg}$
Bunny mass	$m$	$=$	$2.18\,\mathrm{kg}$
Friction coef. in Tests (1), (3), (4), (6), (7)	$\mu$	$=$	$0.4$
Friction coef. for Tests (2) and (5)	$\mu$	$=$	$0$
Force in Test (1)	$F$	$=$	$17\,\mathrm{N}$
Force in Test (4)	$F$	$=$	$10\,\mathrm{N}$

TABLE II : Default parameters for all physics tests unless noted.

Panel of Figure 5 — Fig. 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.

Fig. 4 : PBD-R computation time over varying number of spheres compared to MuJoCo over 100 frames of Pushed Box example.

Fig. 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.

Panel of Figure 8 — Fig. 6 : Rotation error during simulation for varying total number of spheres, $n$ , in (left) rotate box and (right) rotate bunny examples with constant applied torque. This figure highlights that resolution alone does not determine rotational accuracy; the quality of the volumetric sampling matters as well.

Fig. 7 : Sweep over the friction coefficient and applied force for Test 1 ( Pushed Box ). The left column plots report the $\ell_{2}$ position error, while the right column plots show the rotation error. Across the sweep, PBD-R achieves the lowest error, whereas PBD performs the worst. MuJoCo performs well in the regime of low friction and small applied forces, but its accuracy degrades as forces increase.

Fig. 8 : The bunny starts tumbling in the Pushed Bunny experiment (Test 4) using MuJoCo.

Fig. 9 : Effect of sphere discretization resolution on trajectory accuracy for Test 7, Rod Pushing a Box across fiction parameters, and push positions. Adding more spheres results in higher accuracy.

Ablation	Metric	$t{=}2$ s	$t{=}10$ s	Mean	$\times$
Velocity Update	Pos. (m)	2e-4	1.33	0.32	310 $\times$
Velocity Update	Vel. (m/s)	9e-3	0.21	0.18	2403 $\times$
Linear Momentum	Pos. (m)	0.03	3.95	0.73	703 $\times$
Linear Momentum	Lin. (kg ${\cdot}$ m/s)	0.12	6.88	1.58	5063 $\times$
Angular Momentum	Rot. (deg)	14.99	135.85	64.74	1906 $\times$
Angular Momentum	Ang. (kg ${\cdot}$ m 2 /s)	6e-3	5e-3	6e-3	828 $\times$

TABLE III : Ablation study. Each row shows the error when a component is removed from PBD-R (ours maintains

{\approx}0

error across all metrics). The

\times

column shows the ratio of ablated to ours.

Physics-Based Simulation

Physics-based simulation models physical systems with equations and numerical solvers, increasingly augmented by learned models for speed and control.

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Abstract

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