Volumetric Ergodic Control

2025-11-14

AI Summary

Existing traversal control methods model robots as volumeless point masses, neglecting their physical dimensions and sensor spatial footprints—leading to suboptimal coverage efficiency. This paper proposes the first volumetric-state-based traversal control framework, explicitly representing both the robot body and its sensors as sampleable geometric volumes embedded within a nonlinear optimal control architecture; it supports arbitrary volumetric shapes and dynamical models. The method guarantees asymptotic full coverage while enabling real-time optimization of coverage trajectories. Experiments demonstrate over 2× improvement in coverage efficiency for search and manipulation tasks, achieving 100% task completion; efficacy is further validated in real-world applications such as robotic surface cleaning. The core contribution lies in the first explicit integration of volumetric awareness into traversal control, bridging the gap between geometric realism and coverage optimality.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a non-volumetric point, but 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.

Problem

• Extends ergodic control to volumetric robot representations
• Improves spatial coverage efficiency for physical systems
• Maintains theoretical guarantees while enabling real-time control

Innovation

• Volumetric ergodic control optimizes spatial coverage
• Preserves asymptotic guarantees with minimal computation
• Supports arbitrary sample-based volumetric robot models