Lodos: A Lightweight Simulator Designed for Contact-Rich Interactions with Detailed Meshes

Onur Beker; Andreas René Geist; Georg Martius

cs.RONov 6, 2026

Lodos: A Lightweight Simulator Designed for Contact-Rich Interactions with Detailed Meshes

Authors: Onur Beker, Andreas René Geist, Georg Martius

Organizations: University of Tübingen · Max Planck Institute for Intelligent Systems

Abstract

In recent years, massively parallelized rigid-body simulation has played a central role in robotics research, enabling rapid progress in areas such as reinforcement learning, stochastic optimal control, and randomized smoothing-based trajectory optimization. Particularly in contact-rich settings, the scalability of such simulations in large part depends on well-optimized representations of collision geometry, often requiring a coarse approximation of the underlying surfaces using primitives such as spheres, capsules, cylinders, and boxes. Whenever the complexity of the surfaces or the precision demands of the application render such approximations insufficient, it is instead necessary to employ mesh-mesh collisions, which impose a significant reduction in throughput. This paper proposes a simulation framework designed from scratch to address this bottleneck, with novel routines for broadphase and narrowphase collision detection as well as the subsequent contact dynamics computation. As experimentally validated, the framework matches existing well-established simulators in terms of physical faithfulness, and can achieve approximately an order of magnitude higher throughput in the detailed mesh-mesh collision setting that it specializes in. The source code is available at https://github.com/martius-lab/lodos.

Figures & tables

Panel of Figure 1 — Fig. 2: Left: Cubic spline interpolation. In 1D, evaluating the spline $s(t^{\star})$ requires accessing only four entries in the coefficient array (more generally $4^{N}$ in $N$ -D). Right: A collision geometry is represented via two pieces of information: i) an SDF implemented with a 3D spline, and ii) zero volume spheres (i.e. vertices) densely distributed on the 2D surface of the mesh and inscribed spheres distributed within the 3D volume of the mesh.

Panel of Figure 2 — Fig. 3: Left: Selecting vertices for the narrowphase using tiled sphere hierarchies. Right: The resulting dense contact force field.

Fig. 4: Antipodal pinching and lifting of a cube, with (top) and without (bottom) the proposed friction correction scheme.

Fig. 5: Final frames from 15-second simulations of a masonry arch.

Fig. 6: Final frames from a $5\,\mathrm{s}$ simulation in which a position controller, with parameters optimized in MuJoCo to maintain a delicate prismatic grasp, is transferred directly to Lodos.

			Step time per world (µs) at batch size $B$																	Speed-up over MJWarp
Scene	Simulator	$N_{\mathrm{s}}$	$2^{0}$	$2^{3}$		$2^{6}$		$2^{9}$		$2^{12}$		$2^{13}$		$2^{14}$		$2^{15}$		$2^{16}$		Whole step	Contact pipeline
In-hand	MJWarp		904	147		21	.8	4	.08	2	.75	—		—		—		—
reorientation	Lodos-MJ-N	0	523	74	.3	10	.7	2	.12	0	.438	0	.317	0	.299	0	.313	0	.346	9.19 $\times$	14.0 $\times$
		1	656	102		15	.9	3	.07	0	.590	0	.409	0	.367	0	.374	0	.419	7.49 $\times$	11.0 $\times$
		2	799	136		21	.3	3	.91	0	.733	0	.501	0	.440	0	.437	0	.495	6.29 $\times$	9.90 $\times$
20-armadillo	MJWarp		1335	216		40	.1	17	.9	—		—		—		—		—

TABLE I: Simulation throughput across batch sizes, and speed-up over MJWarp.

Fig. 7: Throughput characterization experiments that involve complex mesh-mesh collisions. Left : $20$ armadillos falling on a plane. Right : A Sharpa Wave hand holding an armadillo.

Fig. 8: Trajectory optimization experiment using iLQR, with linearizations of the system dynamics estimated via zeroth-order randomized smoothing using Lodos-MJ-1.

Fig. 9: Stochastic MPC experiment where MPPI is used to manipulate an armadillo in hand with a Sharpa Wave hand, tracking four consecutive goal orientations. The plots show the mean and standard deviation across

5

randomly sampled goal sequences.

Robotics Simulation

Robotics simulation builds virtual robots and environments to model, train, and evaluate autonomous systems before real-world deployment.

See all 333 papers

Lodos-v2: An Efficient Primal Formulation of the Exact Frictional Contact Problem
Nov 6, 2026Onur Beker, Andreas René Geist, Georg MartiusMultibody Dynamics Dynamical Systems
University of Tübingen
CRISP: Contact-Rich Robotic Simulation Platform with Extensive Geometries and Contact Solvers
Sep 18, 2026Somang Lee, Sunkyung Park, Jinhee Yun +2Robotics Simulation Physics-Based Simulation
Department of Mechanical Engineering, Seoul National University
RiCo: Neural Simulation of Rigid-Body Interactions via Local Contact Reasoning
Oct 8, 2026Ruixiang Ouyang, Guanren Qiao, Fansen Meng +4Physics-Based Simulation Multibody Dynamics
The Chinese University of Hong Kong, Shenzhen · DexForce Co., Ltd. · South China University of Technology +1

Nov 6, 2026J/K move · Enter open · S save

Lodos-v2: An Efficient Primal Formulation of the Exact Frictional Contact Problem

Onur Beker, Andreas René Geist, Georg Martius

University of Tübingen

Multibody Dynamics Dynamical Systems Convex Relaxation

Open paper AskPDF arXiv

Lodos-v2 is a GPU-based simulation framework for massively parallel rigid-body dynamics with contact. It is specifically designed to achieve high throughput in scenes involving collisions among large numbers of detailed meshes. Its predecessor, Lodos-v1, had two main limitations. First, it solved the standard convex relaxation of cone-complementarity-based contact dynamics, thereby inheriting well-known physical artifacts, including lift-off and artificial compliance in the normal direction, as well as creep in the tangential direction. Second, its contact-group reparameterization scheme, which rescales spring-damper forces using a single factor per collision pair, could not be integrated with other constraints required by a full-fledged simulator, such as joint limits and welds. Lodos-v2 addresses both limitations through two main contributions. First, it introduces an efficient algorithm for solving the exact frictional contact problem by sequentially solving a cascade of convex relaxations in primal form within an outer proximal minimization loop. Second, it extends the contact-group reparameterization scheme of Lodos-v1 to the primal formulation of cone-complementarity-based contact dynamics, enabling its integration with the other constraints of a full-fledged simulator. Experiments demonstrate that these contributions result in throughput improvements over established rigid-body simulation frameworks. The source code is available at https://github.com/martius-lab/lodos.

Abstract

Robotics Simulation

Explore similar work

Lodos-v2: An Efficient Primal Formulation of the Exact Frictional Contact Problem

CRISP: Contact-Rich Robotic Simulation Platform with Extensive Geometries and Contact Solvers

RiCo: Neural Simulation of Rigid-Body Interactions via Local Contact Reasoning