Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.05885

Does RRT* Work on Uneven Terrain Meshes?

Otobong Jerome·Tiago Nascimento
View original source ↗Read source document ↗Export metadata ↓

Abstract

The optimal rapidly exploring random tree (RRT*) is proven asymptotically optimal on open subsets of Euclidean space with straight-line local planning. We ask whether it works on a triangle-mesh terrain, a two-dimensional surface in R^3. First, the original RRT* cannot run on a mesh: the surface has zero volume, so uniform sampling never hits it, no clearance ball fits in it, and chords across a fold leave it. Second, the surface reformulation we call Mesh RRT*, with its naive edge, the chord costed by its length, solved every run on heightfields with slopes up to 75 degrees but minimises the wrong objective: its cost, the straight-line length of a polyline whose vertices lie on the surface while its segments may leave it by a tolerance tau, is the length of no route on the surface and lies strictly below the geodesic length on any curved mesh. In numeric simulation and after 30,000 iterations the reported cost is on average up to 2.7% below the exact geodesic, a cost no path attains, and the returned route on average 0.1-0.5% longer than it. Rewiring keeps the biased edges, the bias decays only linearly with the step on polyhedral surfaces, and shrinking tau trades bias for connectivity. Third, replacing each chord by a path on the surface above it, built from projected points joined across the mesh edges they straddle and costed by its own length, makes every edge cost the exact length of a feasible path; with no other change the exact length of the returned routes is on average within 0.07-0.16% of the geodesic at every roughness tested, two to 3.4 times closer than with chords on the rougher terrains. The planner is in MeshNav3D 0.2.0 (release pending).

Explore related subjects

cs.ROcs.CG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Otobong Jerome, Tiago Nascimento. 2026-11-04. Does RRT* Work on Uneven Terrain Meshes?. https://arxiv.org/abs/2611.05885

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

CubeDAgger: Interactive Imitation Learning for Dynamic Systems with Efficient yet Low-risk Interaction

Interactive imitation learning makes an agent's control policy robust by stepwise supervisions from an expert. The recent algorithms mostly employ expert-agent switching systems to reduce the expert's burden by limitedly selecting the supervision timing. However, this approach is useful only for static tasks; in dynamic tasks, timing discrepancies cause abrupt changes in actions, losing the robot's dynamic stability. This paper therefore proposes a novel method, named CubeDAgger, which improves robustness with less dynamic stability violations even for dynamic tasks. The proposed method is designed on a baseline, EnsembleDAgger, with three improvements. The first adds a regularization to explicitly activate the threshold for deciding the supervision timing. The second transforms the expert-agent switching system to an optimal consensus system of multiple action candidates. Third, autoregressive colored noise is injected to the agent's actions for time-consistent exploration. These improvements are verified by simulations, showing that the trained policies are sufficiently robust while maintaining dynamic stability during interaction. Finally, real-robot scooping experiments with a human expert demonstrate that the proposed method can learn robust policies from scratch based on just 30 minutes of interaction. https://youtu.be/kBl3SCTnVEM

cs.RO↗
arXiv2026

EmboTeam: Asymmetric State Grounding for Heterogeneous Multi-Robot Collaboration

Heterogeneous multi-robot collaboration over long horizons requires both global task planning and robust coordination during execution. Existing plan- ners using large language models (LLMs) can generate task decompositions or symbolic plans, but often execute them as rigid action sequences, making them fragile to local state mismatches and synchronization failures. We propose Em- boTeam, a neuro-symbolic framework for asymmetric state grounding. An LLM generates structured state expectations, which are verified and coordinated through symbolic search using Planning Domain Definition Language (PDDL) and then grounded into a team-level parallel behavior tree. Robot-specific subtrees per- form precondition checking, skill execution, effect validation, local replanning, and blackboard-based synchronization. We further introduce MACE-THOR, con- taining 42 heterogeneous multi-robot tasks across 8 indoor layouts. EmboTeam improves task success rate from 12% to 55% and goal condition recall from 32% to 75% over LaMMA-P, demonstrating the effectiveness of synchronized reactive grounding for collaboration over long horizons.

cs.RO↗
arXiv2026

WoVR: World Models as Reliable Simulators for Post-Training VLA Policies with RL

Reinforcement learning (RL) promises to unlock capabilities beyond imitation learning for Vision--Language--Action (VLA) models, but its requirement for massive real-world interaction prevents direct deployment on physical robots. Recent work attempts to use learned world models as simulators for policy optimization, yet closed-loop imagined rollouts inevitably suffer from hallucination and long-horizon error accumulation. Such errors not only degrade visual fidelity, but also mislead policy optimization by providing unreliable learning signals. We propose WoVR, a reliable world-model-based RL framework for post-training VLA policies. Instead of assuming a faithful world model, WoVR explicitly regulates how RL interacts with imperfect imagined dynamics. It improves rollout stability through a controllable action-conditioned video world model, reshapes imagined interaction to reduce effective error depth via Keyframe-Initialized Rollouts, and maintains policy--simulator alignment through World Model-Policy co-evolution. Extensive experiments demonstrate that WoVR enables stable long-horizon imagined rollouts and effective policy optimization, achieving superior LIBERO performance and consistent real-world gains across multiple robotic platforms. These results show that world models can serve as practical simulators for RL when hallucination is explicitly controlled. Additional visualization results are available at https://wovr-rlinf.github.io.

cs.RO↗