AI summary
Problem
Standard ergodic control models robots as point masses, ignoring how their physical bodies and sensors interact with the environment, which limits coverage efficiency in practical tasks.
Approach
We introduce volumetric ergodic control (VEC), which replaces point-mass states with sample-based volumetric representations of robot bodies and sensors, preserving asymptotic coverage guarantees with minimal computational overhead.
Key results
- More than doubles coverage efficiency over standard ergodic control
- Maintains 100% task completion rate across all benchmarks
- Compatible with standard iLQR optimization and arbitrary sample-based models
- Validated in simulation and on a Franka robot arm for erasing tasks
Why it matters
Bridges the gap between theoretical coverage algorithms and real-world robotic applications by accounting for physical robot and sensor geometry.
Abstract
Ergodic control synthesizes optimal coverage be- haviors over spatial distributions for nonlinear systems. How- ever, existing formulations model the robot as a non-volumetric point, whereas in practice a robot interacts with the environ- ment 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 rep- resentation. 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/