# Volumetric Ergodic Control

arXiv: https://arxiv.org/abs/2511.11533 · HTML: https://mlsanity.com/paper/2511.11533/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 14 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [Dex-Net 2.0: Deep Learning to Plan Robust Grasps with Synthetic Point Clouds and Analytic Grasp Metrics](https://mlsanity.com/paper/1703.09312/) (2017)
- [Fit2Form: 3D Generative Model for Robot Gripper Form Design](https://mlsanity.com/paper/2011.06498/) (2020)
- [Ergodic Exploration of Distributed Information](https://mlsanity.com/paper/1708.09352/) (2017)
- [Maximum diffusion reinforcement learning](https://mlsanity.com/paper/2309.15293/) (2023)
- [Real-Time Area Coverage and Target Localization using Receding-Horizon Ergodic Exploration](https://mlsanity.com/paper/1708.08416/) (2017)
- [Ergodic Exploration using Tensor Train: Applications in Insertion Tasks](https://mlsanity.com/paper/2101.04428/) (2021)
- [Fast Ergodic Search with Kernel Functions](https://mlsanity.com/paper/2403.01536/) (2024)
- [Ergodic Coverage In Constrained Environments Using Stochastic Trajectory Optimization](https://mlsanity.com/paper/1707.04294/) (2017)
- [Decentralized Ergodic Control: Distribution-Driven Sensing and Exploration for Multi-Agent Systems](https://mlsanity.com/paper/1806.05220/) (2018)
- [Stein Variational Ergodic Search](https://mlsanity.com/paper/2406.11767/) (2024)
- [Embodied Active Learning of Generative Sensor-Object Models](https://mlsanity.com/paper/2410.11130/) (2024)
- [Flow Matching Ergodic Coverage](https://mlsanity.com/paper/2504.17872/) (2025)
- [Scale-Invariant Fast Functional Registration](https://mlsanity.com/paper/2209.12763/) (2022)
- [Adaptive Coverage Path Planning for Efficient Exploration of Unknown Environments](https://mlsanity.com/paper/2302.03164/) (2023)
- [Whole-Body Ergodic Exploration with a Manipulator Using Diffusion](https://mlsanity.com/paper/2306.16898/) (2023)
- [Ergodic Exploration over Meshable Surfaces](https://mlsanity.com/paper/2503.05026/) (2025)

## Built on by (most cited first, 2 of 2)

- [Crazyflow: An Accurate, GPU-Accelerated, Differentiable Drone Simulator in JAX](https://mlsanity.com/paper/2606.01478/) (2026)
- [Ergodic Control and Controlled Diffusion for Robot Learning: Review and Tutorial](https://mlsanity.com/paper/2609.13295/) (2026)

## Abstract (arXiv)

Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a non-volumetric point, whereas in practice a robot interacts with the environment through its body and sensors with physical volume. In this work, we introduce a new ergodic control formulation that optimizes spatial coverage using a volumetric state representation. Our method preserves the asymptotic coverage guarantees of ergodic control, adds minimal computational overhead for real-time control, and supports arbitrary sample-based volumetric models. We evaluate our method across search and manipulation tasks -- with multiple robot dynamics and end-effector geometries or sensor models -- and show that it improves coverage efficiency by more than a factor of two while maintaining a 100% task completion rate across all experiments, outperforming the standard ergodic control method. Finally, we demonstrate the effectiveness of our method on a robot arm performing mechanical erasing tasks. Project website: https://murpheylab.github.io/vec/