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)=21M(F−μMg)t2
Translation accuracy with a constant force applied at CoM with ground friction
2
Box with torque
θ(t)=21λτt2
Rotation accuracy with a constant torque applied at CoM for a shape with isotropic inertia
3
Box on slope
x(t)=21(gsinθ−μgcosθ)t2
Accuracy in resolution of gravity, normal force, and friction on an incline
4
Pushed bunny
x(t)=21M(F−μMg)t2
Same as (1) but on a asymmetric mesh
5
Bunny with torque
θz(t)=21Izzτzt2
Same as (2) but on an asymmetric mesh with anisotropic inertia
6
Bunny on slope
x(t)=21(gsinθ−μgcosθ)t2
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, τ : applied torque magnitude, M : total mass, μ : kinetic friction coefficient, θ : slope angle, λ : principal moment about the rotation axis, Izz : moment of inertia about the z -axis. CoM: center of mass. Test configurations are illustrated in Fig. 2 .
Parameter
Value
Box mass
m
=
4kg
Bunny mass
m
=
2.18kg
Friction coef. in Tests (1), (3), (4), (6), (7)
μ
=
0.4
Friction coef. for Tests (2) and (5)
μ
=
0
Force in Test (1)
F
=
17N
Force in Test (4)
F
=
10N
TABLE II : Default parameters for all physics tests unless noted.
Fig. 3 : Position ℓ2 error (left) and rotation error (right) across all seven benchmark tests, averaged over three seeds with standard deviation error bars; rotation errors exceeding 360∘ 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 μ=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.
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 ℓ2 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
×
Velocity Update
Pos. (m)
2e-4
1.33
0.32
310 ×
Vel. (m/s)
9e-3
0.21
0.18
2403 ×
Linear Momentum
Pos. (m)
0.03
3.95
0.73
703 ×
Lin. (kg ⋅ m/s)
0.12
6.88
1.58
5063 ×
Angular Momentum
Rot. (deg)
14.99
135.85
64.74
1906 ×
Ang. (kg ⋅ m 2 /s)
6e-3
5e-3
6e-3
828 ×
TABLE III : Ablation study. Each row shows the error when a component is removed from PBD-R (ours maintains ≈0 error across all metrics). The × column shows the ratio of ablated to ours.
Accurate simulation of rigid-body interactions is essential for predictive physical world models. Despite recent progress in modeling object dynamics, capturing how local contacts between surfaces shape object motion remains challenging. While end-to-end world models predict interactions across entire scenes or objects, in practice, rigid-body contact is inherently local, and only nearby surfaces can directly exchange contact forces. Motivated by this observation, we introduce Rigid-body Contact Reasoning (RiCo), which represents interactions between objects through sparse neighborhoods of contact surface points. RiCo combines each point's state with the relative geometry, motion, and physical properties of nearby surfaces, then reasons across the object's points to determine how these local contacts jointly affect its motion. By confining cross-object reasoning to nearby surfaces while propagating contact information within each rigid body, RiCo retains fine-grained interaction details without the cost of modeling every pair of scene points. Such properties enable RiCo a higher accuracy and contact fidelity. Experiments on MOVi-benchmark demonstrate that RiCo reduces 100-frame position and orientation errors by 31-35% and approximately 38%, respectively, compared with baselines. Moreover, RiCo achieves high contact fidelity, with ground-truth-relative penetration-time and mean-depth differences of 11.0% and 2.22 mm, respectively. RiCo further generalizes zero-shot from small-scale training scenarios to scenes containing 270 objects. Our real-world multi-ball collision experiments further provide preliminary evidence of sim-to-real transfer.
Ruixiang Ouyang, Guanren Qiao, Fansen Meng +4
The Chinese University of Hong Kong, Shenzhen · DexForce Co., Ltd. · South China University of Technology +1
It has been difficult to accurately model the physics of the interaction between a robot and the objects it manipulates, including contact mechanics, coupled contact dynamics, deformations, stiffness and friction. We present RoboSimStudio (RSS), an interactive toolkit that makes choices of solver, contact model, and physical parameters explicit and editable, allowing both humans and coding agents to quickly create and iteratively refine simulations based on observed physical behavior. We implement RSS with the open Newton physics simulation system and describe experiments with human-guided real2sim using (1) visual evaluation, (2) force-feedback and (3) agentic Real2Sim2Real. Code, video and additional information can be found on the project website: https://robosimstudio.github.io
Simulating deformable objects is essential for a wide range of robotic manipulation applications, yet accurately predicting their dynamics remains challenging. We propose Physics-Guided Residual Dynamics (PGRD), a hybrid simulation framework that combines the advantages of physics-based and learning-based approaches. Specifically, PGRD combines an optimizable spring-mass simulator as a backbone with a learned neural network that predicts residual corrections to the physics-based predictions. We adopt a velocity-based formulation to ensure stable simulation and a sliding-window transformer architecture to capture temporal dependencies. We show that PGRD produces more accurate results than both purely physics-based and learning-based methods on a set of diverse real-world deformable objects. We further demonstrate the utility of PGRD in two applications: manipulation planning via Model Predictive Control, including a language-conditioned setting with a generated goal image; and interactive simulation via action-conditioned video prediction by 3D Gaussian Splatting.