# VID-Fusion: Robust Visual-Inertial-Dynamics Odometry for Accurate External Force Estimation

arXiv: https://arxiv.org/abs/2011.03993 · HTML: https://mlsanity.com/paper/2011.03993/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control](https://mlsanity.com/paper/2302.11694/) (2023)
- [Probabilistic Constrained Reinforcement Learning with Formal Interpretability](https://mlsanity.com/paper/2307.07084/) (2023)
- [Interpretable Stochastic Model Predictive Control using Distributional Reinforced Estimation for Quadrotor Tracking Systems](https://mlsanity.com/paper/2205.07150/) (2022)
- [HDVIO2.0: Wind and Disturbance Estimation with Hybrid Dynamics VIO](https://mlsanity.com/paper/2504.00969/) (2025)

## Abstract (arXiv)

Recently, quadrotors are gaining significant attention in aerial transportation and delivery. In these scenarios, an accurate estimation of the external force is as essential as the 6 degree-of-freedom (DoF) pose since it is of vital importance for planning and control of the vehicle. To this end, we propose a tightly-coupled Visual-Inertial-Dynamics (VID) system that simultaneously estimates the external force applied to the quadrotor along with the 6 DoF pose. Our method builds on the state-of-the-art optimization-based Visual-Inertial system, with a novel deduction of the dynamics and external force factor extended from VIMO. Utilizing the proposed dynamics and external force factor, our estimator robustly and accurately estimates the external force even when it varies widely. Moreover, since we explicitly consider the influence of the external force, when compared with VIMO and VINS-Mono, our method shows comparable and superior pose accuracy, even when the external force ranges from neglectable to significant. The robustness and effectiveness of the proposed method are validated by extensive real-world experiments and application scenario simulation. We will release an open-source package of this method along with datasets with ground truth force measurements for the reference of the community.