# Temporal Learning for End-Effector Position Estimation under Aerodynamic Disturbances in Aerial Continuum Manipulation

arXiv: https://arxiv.org/abs/2609.28716 · HTML: https://mlsanity.com/paper/2609.28716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [Nonlinear MPC for Quadrotors in Close-Proximity Flight with Neural Network Downwash Prediction](https://mlsanity.com/paper/2304.07794/) (2023)
- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Robotics meets Fluid Dynamics: A Characterization of the Induced Airflow below a Quadrotor as a Turbulent Jet](https://mlsanity.com/paper/2403.13321/) (2024)
- [Systematic Analysis of Coupling Effects on Closed-Loop and Open-Loop Performance in Aerial Continuum Manipulators](https://mlsanity.com/paper/2602.18684/) (2026)
- [Strain-Parameterized Coupled Dynamics and Dual-Camera Visual Servoing for Aerial Continuum Manipulators](https://mlsanity.com/paper/2603.23333/) (2026)
- [An Experimental Study of Downwash Effects on a Continuum Manipulator Integrated with a Multirotor UAV](https://mlsanity.com/paper/2608.18507/) (2026)

## Abstract (arXiv)

This paper investigates temporal neural networks for mboxend-effector position mboxestimation of an aerial continuum manipulator (ACM) operating under aerodynamic effects induced by the unmanned aerial vehicle (UAV). An experimental dataset is collected under stationary (mboxrotor-off) and mboxfree-hovering conditions across continuum robot (CR) configurations and UAV altitudes, providing mboxend-effector position measurements with and without aerodynamic residuals. To establish a nominal framework, mboxstrain-parameterized kinematic models with progressively richer strain bases are evaluated to balance model complexity and prediction accuracy. The selected nominal model then serves as the baseline for 3D position residual estimation using a mboxclosed-form mboxcontinuous-time (CfC) neural network, with a multilayer perceptron (MLP) and a gated recurrent unit (GRU) used for comparison. On unseen test experiments, the CfC achieves an RMSE of (22.00±1.70~mm) over five random seeds, compared with (36.38±3.58~mm) for the MLP and (27.72±2.92~mm) for the GRU, corresponding to reductions of (39.52%) and (20.62%), respectively. These results demonstrate the effectiveness of mboxcontinuous-time learning for mboxend-effector position estimation under aerodynamic disturbances relative to static and mboxdiscrete-time learning methods.