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

Onur Beker; Andreas René Geist; Georg Martius

cs.RONov 6, 2026

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

Authors: Onur Beker, Andreas René Geist, Georg Martius

Organizations: University of Tübingen

Abstract

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.

Figures & tables

Figure 1. Benchmark scenes used to compare the throughput of Lodos-v2 against established simulation frameworks. Top: A representative frame from each scene, simulated using Lodos-v2’s exact mode. Bottom: The speed-up achieved by Lodos-v2 (using the per contact parameterization) over each baseline in terms of maximum achievable throughput, computed from Tables 1 and 2 .

scene	per contact	cone	ray	MJWarp	speed-up
	Lodos-v2, mj mode
cube_walled_5_polytope	1.61M @8192	–	–	1.11M @8192	1.45 $\times$
cube_walled_5_sdf	551k @4096	1.27M @8192	1.86M @8192	276k @2048	6.76 $\times$
arm_walled_5_polytope	985k @8192	–	–	163k @2048	6.04 $\times$
arm_walled_5_sdf	1.24M @4096	1.25M @8192	1.97M @8192	238k @2048	8.29 $\times$
shadow_grasp_polytope	1.18M @8192	–	–	432k @32768	2.73 $\times$

Table 1. Lodos-v2’s MuJoCo mode against MJWarp. Each configuration’s best throughput, in world-steps per second at the batch size after @ (k

=10^{3}

, M

=10^{6}

), and the speed-up of Lodos-v2’s fastest configuration over MJWarp’s best.

scene	per contact	cone	ray	Kamino	speed-up
	Lodos-v2, exact mode
cube_walled_5_polytope	711k @8192	–	–	589k @4096	1.21 $\times$
cube_walled_5_sdf	225k @2048	596k @8192	1.08M @4096	–	1.83 $\times^{\ddagger}$
arm_walled_5_polytope	408k @8192	–	–	58.3k @128	6.99 $\times$
arm_walled_5_sdf	523k @4096	544k @4096	1.12M @8192	–	19.26 $\times^{\ddagger}$
shadow_grasp_polytope	983k @8192	–	–	11.1k @512	88.33 $\times$

Table 2. Lodos-v2’s exact mode against Kamino. The best throughput achieved by each configuration and the speed-up of Lodos-v2’s fastest configuration. Kamino is evaluated only on the polytope versions of the scenes. The symbol ‡ indicates comparisons between Lodos-v2 on the original surfaces and Kamino on the corresponding polytope versions. The threading task has no polytope version, and therefore does not include a Kamino baseline. Similarly, Kamino was excluded from the twenty-hands scene because benchmarking was prohibitively slow (at a batch size of 16, each simulation step took 7.2 s).

Multibody Dynamics

Multibody dynamics studies how connected rigid or flexible bodies move and interact under forces, constraints, impacts, and friction.

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University of Tübingen · Max Planck Institute for Intelligent Systems

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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.

Abstract

Multibody Dynamics

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