Volumetric Harmonic Field Navigation for Quadrotors
Abstract
Quadrotor navigation in cluttered 3-D environments requires global guidance while local motion remains subject to collision and motion limits. Harmonic potentials provide dense guidance from a global boundary value problem, but coupling a volumetric harmonic field to constrained physical quadrotor motion remains an open experimental problem. We couple a precomputed volumetric harmonic field with a constrained predictive planner that queries the field at predicted positions instead of extracting a global reference path. In Structured 3-D tests, harmonic guidance yields larger minimum clearance and lower RMS jerk than matched Dijkstra guidance, at the cost of longer paths; the same pattern remains when both methods use the same passage. Long maze tests span routes far beyond one prediction horizon, and Crazyflie trials validate physical execution. To the best of our knowledge, this is the first physical quadrotor demonstration of volumetric harmonic field navigation. The results show that globally constructed harmonic guidance can directly support local constrained motion generation on a physical quadrotor.
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BibTeX
@misc{jia2026volumetric,
title = {{Volumetric Harmonic Field Navigation for Quadrotors}},
author = {Shuxiu Jia and Amartya Mukherjee and Yating Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15680},
eprint = {2609.15680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15680},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Volumetric Harmonic Field Navigation for Quadrotors
AU - Shuxiu Jia
AU - Amartya Mukherjee
AU - Yating Yuan
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.15680
UR - https://arxiv.org/abs/2609.15680
AB - Quadrotor navigation in cluttered 3-D environments requires global guidance while local motion remains subject to collision and motion limits. Harmonic potentials provide dense guidance from a global boundary value problem, but coupling a volumetric harmonic field to constrained physical quadrotor motion remains an open experimental problem. We couple a precomputed volumetric harmonic field with a constrained predictive planner that queries the field at predicted positions instead of extracting a global reference path. In Structured 3-D tests, harmonic guidance yields larger minimum clearance and lower RMS jerk than matched Dijkstra guidance, at the cost of longer paths; the same pattern remains when both methods use the same passage. Long maze tests span routes far beyond one prediction horizon, and Crazyflie trials validate physical execution. To the best of our knowledge, this is the first physical quadrotor demonstration of volumetric harmonic field navigation. The results show that globally constructed harmonic guidance can directly support local constrained motion generation on a physical quadrotor.
ER -