cs.ROMar 17, 2026

Kamino: GPU-based Simulation of Rigid Multi-Body Physics with Kinematic Loops

Authors: Vassilios Tsounis, Guirec Maloisel, Christian Schumacher, Ruben Grandia, Agon Serifi, David Müller, Chris Amevor, Tobias Widmer, 

Organizations: Disney Research, Zurich, Switzerland · NVIDIA, Zurich, Switzerland

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Abstract

We present Kamino, a GPU-based physics solver for massively parallel simulations of heterogeneous highly-coupled mechanical systems. Implemented in Python using NVIDIA Warp and integrated into the Newton framework, it enables the application of data-driven methods, such as large-scale reinforcement learning, to complex robotic systems that exhibit strongly coupled kinematic and dynamic constraints such as kinematic loops. The latter are often circumvented by approximating the system's topology as a kinematic tree, and incorporating explicit loop-closure constraints or so-called mimic joints. Kamino aims at alleviating this burden by natively supporting these types of couplings. Moreover, Kamino supports heterogeneous worlds, allowing for batched simulation of structurally diverse robots on a single GPU. At its core lies a state-of-the-art constrained optimization algorithm based on ADMM, which computes constraint forces by solving the constrained rigid multi-body forward dynamics transcribed as a nonlinear complementarity problem. This leads to high-fidelity simulations that resolve contact dynamics without resorting to approximate models that simplify or convexify the problem. We demonstrate RL policy training on a biped with six nested kinematic loops, generating a feasible walking policy while simulating 4,0964{,}096 parallel environments on a single GPU.

Figures & tables

Figure 1: DR Legs (left) with kinematic graph overlaid for half of the left leg (middle). In the full kinematic graph (right), each leg contains two small kinematic loops nested in a third large one.
Figure 2: Simulation Models used in our experiments are (from left to right): BDX Droid, Olaf robot, DR Legs, two-finger robotic arm, Ant variants (3-, 4-, and 5-legged morphologies), Hoberman Sphere, and the Iron Man Audio-Animatronics® figure. © MARVEL, Disneyland Paris.
  KaminoMJWarpMuJoCo CPU ∗XPBD
ModelMetricmedianp90medianp90medianp90medianp90
BDXrJr_{J}1.12⋅10−41.12{\cdot}10^{-4}5.72⋅10−45.72{\cdot}10^{-4}1.63⋅10−71.63{\cdot}10^{-7}2.19⋅10−72.19{\cdot}10^{-7}1.48⋅10−71.48{\cdot}10^{-7}2.00⋅10−72.00{\cdot}10^{-7}6.12⋅10−36.12{\cdot}10^{-3}9.99⋅10−39.99{\cdot}10^{-3}
rkinr_{kin}5.90⋅10−45.90{\cdot}10^{-4}1.63⋅10−31.63{\cdot}10^{-3}9.60⋅10−29.60{\cdot}10^{-2}2.92⋅10−12.92{\cdot}10^{-1}9.82⋅10−29.82{\cdot}10^{-2}2.95⋅10−12.95{\cdot}10^{-1}6.51⋅1006.51{\cdot}10^{0}9.86⋅1009.86{\cdot}10^{0}
rCr_{C}2.95⋅10−42.95{\cdot}10^{-4}3.62⋅10−43.62{\cdot}10^{-4}3.05⋅10−23.05{\cdot}10^{-2}3.43⋅10−23.43{\cdot}10^{-2}2.55⋅10−32.55{\cdot}10^{-3}7.75⋅10−37.75{\cdot}10^{-3}2.06⋅10−42.06{\cdot}10^{-4}2.22⋅10−42.22{\cdot}10^{-4}
rvr_{v}3.05⋅10−73.05{\cdot}10^{-7}1.84⋅10−11.84{\cdot}10^{-1}1.02⋅10−21.02{\cdot}10^{-2}2.10⋅10−12.10{\cdot}10^{-1}1.51⋅10−21.51{\cdot}10^{-2}2.01⋅10−12.01{\cdot}10^{-1}9.06⋅10−39.06{\cdot}10^{-3}2.00⋅10−12.00{\cdot}10^{-1}
rprimalr_{primal}0.00⋅1000.00{\cdot}10^{0}3.73⋅10−93.73{\cdot}10^{-9}0.00⋅1000.00{\cdot}10^{0}1.49⋅10−81.49{\cdot}10^{-8}--0.00⋅1000.00{\cdot}10^{0}0.00⋅1000.00{\cdot}10^{0}
Table 1: Physical accuracy comparison. Performance metrics (see Appendix A.1.4 ) evaluated across models and solvers. We use median and 90th-percentile aggregation over time, to filter out challenging frames which present ground penetration upon fast impacts (no continuous collision detection), causing large residuals for all solvers. Collisions are not modeled for the Iron Man example. Configuration-level metrics ( rJr_{J} , rCr_{C} ) are evaluated with each solver running independent trajectories, to capture error accumulation over time. Other metrics, which measure the single-step accuracy, are evaluated on single-step problems, the same for each solver, sampled along a reference trajectory obtained by running Kamino at 10 kHz. We verified that the configuration-level residuals along the reference trajectory are low enough (largest p90 of 3⋅10−43{\cdot}10^{-4} across all examples) to provide valid starting points for all solvers. We use 2020 XPBD iterations for most examples, and 200200 for Iron Man, as the solver diverges with default settings. We use 200 PADMM iterations for Kamino. * We do not measure rprimal,rcmpl,rvir_{primal},r_{cmpl},r_{vi} for MuJoCo CPU as contact forces are unavailable.
Figure 3: Throughput. Maximal simulator throughput vs. problem size across systems and solver configurations, measured on an RTX Pro 6000 GPU.
Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

ModelBodiesActuatedPassiveLoops
DR Legs31311212242466
BDX151514140000
Olaf272720209933
Iron Man6767232357571313
Hoberman Sphere24024000421421182182
Ant- 3377660000
Appendix
Table A.1: Models Simulated with Kamino. All counts refer to a single instance in maximal coordinates; loops denote independent closed kinematic chains.
Figure A.1: Elementary physics validation examples. Box on plane, bouncing ball, stacked boxes, and four-bar linkage.
Figure A.2: Box on Plane trajectory plots.
Figure A.3: Bouncing Ball trajectories.
Figure A.4: Stacked Boxes. Vertical position over time for a two-box system, where one box is dropped onto another resting on a plane. We evaluate three mass configurations: heavy bottom ( 100 kg100\text{\,}\mathrm{kg} , 1 kg1\text{\,}\mathrm{kg} ), heavy top (swapped masses), and equal mass ( 1 kg1\text{\,}\mathrm{kg} ).
Figure A.5: Four-Bar Linkage energy plots.
Sim. rateKaminoMJWarpXPBD
SoftStiffSoftMediumStiff
400 Hz400\text{\,}\mathrm{Hz}6.0×10−36.0{\times}10^{-3}1.8×10−31.8{\times}10^{-3}3.7×10−33.7{\times}10^{-3}9.4×10−39.4{\times}10^{-3}1.1×10−21.1{\times}10^{-2}1.4×10−31.4{\times}10^{-3}
1000 Hz1000\text{\,}\mathrm{Hz}1.6×10−31.6{\times}10^{-3}3.6×10−43.6{\times}10^{-4}1.5×10−31.5{\times}10^{-3}1.8×10−31.8{\times}10^{-3}1.0×10−41.0{\times}10^{-4}2.2×10−42.2{\times}10^{-4}
Appendix
Table A.2: Four-Bar Linkage constraint residuals. For each solver configuration, we report the maximal absolute position-level constraint residual over the trajectory (in meters for translation constraints, and in radians for rotation constraints).
Figure A.6: Throughput scaling across solver configurations. Simulator throughput (in samples per second) as a function of the number of parallel worlds for different problems and solver configurations. Measurements are performed on an RTX Pro 6000 Workstation GPU.
Figure A.7: Throughput across GPU hardware. DR Legs throughput scaling across different GPU models (RTX 4090, RTX 5090, RTX Pro 6000 Workstation Edition) using the best-performing solver configuration (LLT with sparse Jacobian).
Figure A.8: Memory Usage. Left: Total GPU memory usage for Iron Man as a function of the number of parallel worlds. Right: GPU memory usage per world against problem size. Measurements are done on an RTX Pro 6000 GPU.
Figure A.9: RL training curves. Mean episode reward for the DR Legs task and heterogeneous Ant variants during training.
NameWeightReward Term
Tracking
Linear velocity xy5.05.0exp⁡(−10.52 ∥vxy,t−v^xy,t∥22)\exp\left(-\frac{1}{0.5^{2}}\,\lVert\mathbf{v}_{xy,t}-\hat{\mathbf{v}}_{xy,t}\rVert_{2}^{2}\right)
Angular velocity z2.02.0exp⁡(−10.52 (ωz,t−ω^z,t)2)\exp\left(-\frac{1}{0.5^{2}}\,(\omega_{z,t}-\hat{\omega}_{z,t})^{2}\right)
Path deviation2.02.0exp⁡(−10.12 ∥pxy,t−p^xy,t∥22)\exp\left(-\frac{1}{0.1^{2}}\,\lVert\mathbf{p}_{xy,t}-\hat{\mathbf{p}}_{xy,t}\rVert_{2}^{2}\right)
Contact matching10.010.0∑f∈{L,R}\mathds1[cf,t=c^f(θt)]\sum_{f\in\{L,R\}}\mathds{1}[c_{f,t}=\hat{c}_{f}(\theta_{t})]
Foot clearance5.05.0∑f∈{L,R}exp⁡(−10.022 (zf,t−h^f(θt))2)\sum_{f\in\{L,R\}}\exp\left(-\frac{1}{0.02^{2}}\,(z_{f,t}-\hat{h}_{f}(\theta_{t}))^{2}\right)
Appendix
Table A.3: Reward terms for the DR Legs walking policy. Hats ⋅^\hat{\cdot} denote reference quantities derived from the gait phase θt\theta_{t} . The indicator function \mathds1[⋅]\mathds{1}[\cdot] evaluates to 11 if the condition is satisfied and 00 otherwise. The total reward is the weighted sum of all terms.
NameWeightReward Term
Tracking
Linear velocity tracking10.010.0exp⁡(−10.252⋅∥vxy,t−v^xy,t∥22)\exp\left(-\frac{1}{0.25^{2}}\cdot\lVert\mathbf{v}_{xy,t}-\hat{\mathbf{v}}_{xy,t}\rVert_{2}^{2}\right)
Angular velocity tracking10.010.0exp⁡(−10.52⋅∥ωz,t−ω^z,t∥22)\exp\left(-\frac{1}{0.5^{2}}\cdot\lVert\omega_{z,t}-\hat{\omega}_{z,t}\rVert_{2}^{2}\right)
Regularization
Hip angle penalty−1.0-1.0∥qhip∥22\lVert\mathbf{q}_{\text{hip}}\rVert_{2}^{2}
Joint velocities−0.005-0.005∥q˙∥22\lVert\dot{\mathbf{q}}\rVert_{2}^{2}
Appendix
Table A.4: Reward terms for the Ant variants policy. Hats ⋅^\hat{\cdot} denote reference commands. The total reward is the weighted sum of these terms.
 3-leg4-leg5-legHeterogeneous
Samples per second286,510286{,}510130,308130{,}30853,36053{,}36086,24686{,}246
Appendix
Table A.5: Simulation throughput for Ant variants. Throughput is measured across 2,0482{,}048 parallel environments.
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