Physically-Informed Neural Network for Quadrotor Trajectory Recovery During Global Navigation Satellite System Signal Loss

Mechanical Engineering and Machine Science


Аuthors

Sidorenko D. D.*, Timofeev A. N.**, Romanov P. I.***

Peter the Great St. Petersburg Polytechnic University, 29, Polytechnicheskaya str., St. Petersburg, 195251, Russia

*e-mail: danilden1@yandex.ru
**e-mail: ae.tarasov@rtc.ru
***e-mail: pavel.ssau@gmail.com

Abstract

Thermal mapping of extended industrial infrastructure such as oil and gas pipelines and high-voltage power lines is one of the priority tasks of modern autonomous aerial robotics. A small-scale quadrotor equipped with a thermal imaging camera, an inertial measurement unit, and a GNSS receiver is able to survey continuously kilometer-long segments of the infrastructure. However, metallic structures create the GNSS-signal shadowing and multipath zones, making complete signal outages, lasting from 3 to 240 seconds, a standard operational situation rather than an emergency. Without external correction, a consumer-grade MEMS inertial navigation system rapidly accumulates position error, increasing by the O(t2) law, which reaches hundreds of meters during signal outages of 240 s. The platform mass limitations (1–3 kg) and industrial medium conditions such as dust, smoke, and thermal homogeneity of the industrial surfaces rule out standard GNSS-denied navigation methods such as visual and lidar odometry.
This article proposes the rotor speed telemetry application, namely a signal already available onboard without additional sensors, as an alternative source of navigation information. It follows from the quadrotor dynamic model that in the mode of wind gusts compensation  rotations of rotors hold information on the control impacts, which is principally unavailable to the accelerometer and gyroscope of the inertial system. Statistical analysis confirms a low Pearson correlation (|r| ≈ 0.24) between the IMU channels and differential rotor speeds despite a 57-fold increase in the variance σ (Δn13) in the aggressive flight mode.
The article presents and verifies a physically-informed neural network based on a spatial-temporal state-space model (Mamba) with a dynamic loss functional. A physical regularizer based on the quadratic propeller thrust law F = kn² is embedded into the loss function, along with residuals for total thrust and control moments computed directly from rotor speed telemetry. The proposed architecture united for the first time the blocks with selective spatial states (Mamba) with physical regularizer explicitly depending on the rotor speed. A systematic comparison of the four neural network, such as proposed, generalized basic and Transsformer, was performed 
Experiments were being conducted in the PX4/Gazebo simulator with two datasets: a standard flight dataset and a wind-gust compensation dataset. When fine-tuned on only 10% of the aggressive-mode data, the proposed network demonstrates an RMSE of 14.3 m for a 240-second GNSS outage, which is better than the baseline model trained on the full dataset (17.0 m). The optimal performance (RMSE = 9.4 m) is being obtained with 25% of the data, corresponding to approximately two minutes of calibration flight. Superiority of the neural network with dynamic functional is explained by the high variance of rotor speeds (σ = 5971 rpm, which is six times greatly than in the common flight mode), which generates a higher contrast of the learning signal while further learning. The method was validated as well on the real-world AI-IO dataset, where it consistently outperformed the baseline model across all outage durations. The proposed operational protocol – a single two-minute calibration flight prior to the mission – ensures the model adaptation to the new dynamic mode directly under the field conditions.

Keywords:

physics-informed neural network, spatial-temporal state-space model, unmanned aerial vehicle, global navigation satellite system, fine-tuning with limited data, thermal camera, rotor revolutions per minute

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