Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds

Michael O'Connell; Guanya Shi; Xichen Shi; Kamyar Azizzadenesheli; Anima Anandkumar; Yisong Yue; Soon-Jo Chung

Source-linked AI summary

Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds

Michael O'Connell, Guanya Shi, Xichen Shi, Kamyar Azizzadenesheli, Anima Anandkumar, Yisong Yue, Soon-Jo Chung

arXiv:2205.06908v2May 13, 2022cs.ROcs.AIcs.LGeess.SY

TL;DR

Precise UAV control in dynamic, high-speed winds is difficult because wind-dependent aerodynamics are complex and poorly understood. Neural-Fly learns a shared aerodynamic representation for rapid online adaptation and achieves smaller tracking errors than nonlinear and adaptive controllers across challenging wind conditions.

Problem
Complex, unsteady aerodynamic interactions in wind degrade conventional UAV control, while prior simple drag models cannot extend to external wind conditions.
Method
Neural-Fly uses DAIML to learn a shared representation from flight data and a composite adaptation law to update linear coefficients online.
Results
Neural-Fly achieves centimeter-level position-error tracking and outperforms nonlinear, L1 adaptive, and INDI controllers across wind tests.
Takeaways & Limitations
The learning-based controller supports rapid adaptation across wind conditions, transfers across drones, and maintains performance using standard quadrotor hardware.
Takeaways & Limitations
OptiTrack localization precision of about 1 cm provides a practical lower bound for the system’s average tracking error.

Abstract

from arXiv · show

Executing safe and precise flight maneuvers in dynamic high-speed winds is important for the ongoing commoditization of uninhabited aerial vehicles (UAVs). However, because the relationship between various wind conditions and its effect on aircraft maneuverability is not well understood, it is challenging to design effective robot controllers using traditional control design methods. We present Neural-Fly, a learning-based approach that allows rapid online adaptation by incorporating pretrained representations through deep learning. Neural-Fly builds on two key observations that aerodynamics in different wind conditions share a common representation and that the wind-specific part lies in a low-dimensional space. To that end, Neural-Fly uses a proposed learning algorithm, domain adversarially invariant meta-learning (DAIML), to learn the shared representation, only using 12 minutes of flight data. With the learned representation as a basis, Neural-Fly then uses a composite adaptation law to update a set of linear coefficients for mixing the basis elements. When evaluated under challenging wind conditions generated with the Caltech Real Weather Wind Tunnel, with wind speeds up to 43.6 kilometers/hour (12.1 meters/second), Neural-Fly achieves precise flight control with substantially smaller tracking error than state-of-the-art nonlinear and adaptive controllers. In addition to strong empirical performance, the exponential stability of Neural-Fly results in robustness guarantees. Last, our control design extrapolates to unseen wind conditions, is shown to be effective for outdoor flights with only onboard sensors, and can transfer across drones with minimal performance degradation.

1 INTRODUCTION

Neural-Fly addresses the difficulty of precise agile UAV control in complex, changing winds by combining a learned aerodynamic representation with rapid online adaptation. It reports improved tracking against several adaptive and nonlinear controllers while supporting challenging gate-flight demonstrations.

Motivation: Complex, unsteady wind aerodynamics degrade conventional UAV control, while simple drag models limit tracking performance and cannot extend to external wind conditions.These challenges arise from interactions among the drone, induced airflow, and wind.
Results: Neural-Fly achieves centimeter-level position-error tracking for an agile trajectory in dynamic wind conditions on a standard UAV.The method is also demonstrated in low-clearance gate flights under gusty wind conditions.
Approach: Neural-Fly combines offline DAIML representation learning with online adaptive control for rapidly changing wind conditions.DAIML learns wind-condition-independent DNN basis functions, while online adaptation updates wind-dependent linear coefficients.
Contribution: Neural-Fly addresses basis-function design and adaptive-control stability by integrating a compact learned basis with regularized composite adaptation.The learned DNN is pretrained before deployment, while the adaptive law responds to wind conditions online.
Design rationale: Adapting only a small learned-model component enables real-time adaptation at the control-loop rate, unlike adapting an entire neural network.Whole-network adaptation is described as too data-hungry and high-dimensional for sufficiently fast onboard operation.

2 RESULTS

Neural-Fly combines data-efficient offline representation learning with online adaptive control for trajectory tracking in changing winds. Experiments compare the approach with baseline and adaptive controllers across wind conditions, including conditions beyond training and agile gate-tracking tasks.

Offline Learning and Online Adaptive Control Development: After training, t-SNE shows clustered linear coefficients whose physical organization reflects wind speed, separating shared representation from wind-specific information.The learned coefficients become more clustered over training, with the upper-right region corresponding to higher wind speed.
Experimental Platform: 12 minutes of flight data per wind condition support representation learning across six static conditions spanning 0 to 22.0 km/h.The training data comprise randomized two-minute trajectories collected at 50 Hz; experiments extend to wind speeds up to 43.6 km/h.
Offline Learning and Online Adaptive Control Development: Neural-Fly combines DAIML offline learning with online adaptation of wind-dependent linear coefficients.DAIML learns a shared aerodynamic representation, while the adaptive control phase updates coefficients that mix its basis functions.
Trajectory Tracking Performance: Neural-Fly and Neural-Fly-Transfer outperform all other controllers across constant and sinusoidal wind tests, including winds exceeding the training range.Neural-Fly performs slightly better than the transferred representation because its model was trained on the same drone used in experiments.
Agile Flight Through Narrow Gates: Neural-Fly precisely tracks agile trajectories and passes narrow gates under complex, non-stationary aerodynamic effects.The effects depend on UAV attitude, relative velocity, and interactions between propellers and wind.

3 DISCUSSION

Neural-Fly maintains precise tracking across changing and unknown wind conditions, including outdoor flights and transfer across vehicle configurations. Its performance is constrained by localization accuracy and control-loop delays, while planning-control coupling remains an open question.

State-of-the-art Tracking Performance: Neural-Fly outperforms nonlinear, INDI, and L1 controllers across wind conditions up to 43.6 km/h (12.1 m/s).It achieves 2.9 cm mean tracking error in 0 km/h wind.
Limitations: The practical tracking-error floor is about 1 cm because of OptiTrack localization precision, while code, communication, and attitude delays limit further improvement.Measured code execution and communication delay ranges from at least 15 ms to as much as 30 ms.
Challenges Caused by Unknown and Time-varying Wind Conditions: Neural-Fly identifies previously unknown, changing wind conditions quickly and maintains precise tracking despite training on static, approximately uniform wind data.The sinusoidal wind test emulates unsteady or gusty conditions.
Challenges Caused by Unknown and Time-varying Wind Conditions: The method separates wind-invariant state dependence from wind-specific linear weights, enabling adaptation during dynamic trajectories with average tracking error below 8.7 cm.This separation supports repeatable quantitative testing in time-varying wind.
Generalization to New Trajectories and New Aircraft: Neural-Fly is orthogonal to desired-trajectory design, but coupling between planning and learning-based control near actuation limits requires further study.Future work proposes combining Neural-Fly with MPC to handle actuation limits.
Generalization to New Trajectories and New Aircraft: Transfer experiments indicate that the learned representation is robust to vehicle-design changes and can generalize across different quadrotors.The control formulation also applies generally to robotic systems described by Euler–Lagrange dynamics.

4 MATERIALS AND METHODS

Neural-Fly models unknown wind-dependent dynamics with a shared state representation and condition-specific linear coefficients. DAIML addresses domain shift across wind conditions, while the resulting representation supports online adaptation and transfer.

Dynamics Model: The dynamics model represents unmodeled aerodynamic effects as f(q, ˙q, w), where w denotes potentially time-varying environmental conditions such as wind.Different wind profiles produce different aerodynamic disturbances.
Dynamics Representation: Neural-Fly decomposes unknown dynamics into a shared representation ϕ(q, ˙q) and wind-specific linear coefficients a(w).The representation captures state dependence, while coefficients are updated for each condition.
Data Collection: Training data are collected from randomized trajectories flown for two minutes in several static wind conditions, producing wind-indexed subdatasets.The dataset includes time-stamped state and control data used to estimate noisy unmodeled dynamics.
Meta-Learning Goal: The meta-learning objective seeks a representation for which condition-specific latent coefficients allow accurate approximation of the unknown dynamics.The representation is shared across wind conditions, while each coefficient vector is condition-specific.
Domain Shift Problems: Domain shift arises because changing wind conditions alter the state distribution, allowing a DNN to memorize wind-specific state distributions instead of learning invariant dynamics.This creates an overfitting risk for the basic representation-learning objective.
The Domain Adversarially Invariant Meta-Learning (DAIML) Algorithm: DAIML learns the shared representation with a DNN while using a discriminator to remove wind-condition information from the representation.The discriminator predicts the environment index, whereas the representation makes that prediction harder.

1 repeat

The excerpted algorithm steps describe sampling adaptation and training batches, then optimizing the representation and discriminator networks.

DAIML Procedure: The algorithm samples a wind-condition subdataset before drawing disjoint adaptation and training batches.The adaptation batch is denoted B_a and the training batch B.
DAIML Procedure: The procedure trains the representation network ϕ with stochastic gradient descent and spectral normalization.The supplied excerpt does not specify the full loss expression.

10 until convergence

Neural-Fly combines a learned aerodynamic representation with online adaptive control to predict changing disturbances and support robust trajectory tracking. Its design links representation learning, composite adaptation, and exponential convergence guarantees.

Offline representation learning: DAIML learns a wind-condition-independent deep neural network representation whose outputs serve as aerodynamic basis functions.The learned basis is adapted across wind conditions by updating linear mixing coefficients.
Online adaptive control: The online controller updates wind-dependent coefficients using both aerodynamic prediction error and position tracking error.A Kalman-filter-based composite adaptation law provides automatic gain tuning and supports adaptation without persistent excitation.
Controller structure: The control architecture combines nominal model feedforward terms, prediction-error feedback, adaptive parameter updates, and covariance-based gain tuning.The implementation uses the learned representation and estimated linear parameters within the online control law.
Stability and robustness: Theoretical analysis shows that tracking error exponentially converges to an error ball determined by representation error, measurement noise, and the rate of wind-condition change.The stability theorem assumes bounded derivatives of the desired trajectory and gives robustness to imperfect learning and time-varying winds.
Learned disturbance compensation: Neural-Fly replaces the slow integral compensation of the nonlinear baseline with a learned force prediction term for unmodeled dynamics and disturbances.Learning-based variants outperform the constant-basis variant because the compact representation predicts aerodynamic disturbances online.

SUPPLEMENTARY MATERIALS

The supplementary materials document supporting analyses, implementation details, tuning, and formal guarantees for Neural-Fly.

SUPPLEMENTARY MATERIALS: The supplementary materials cover drone configuration, learning expressiveness, DAIML hyperparameters, controller discretization, stability proofs, gain tuning, force prediction, and localization error analysis.They also include training and validation losses and analyses of domain-invariant representations.

SUPPLEMENTARY MATERIALS

The supplementary material supports Neural-Fly’s representation, adaptation, and stability claims with theoretical results, experimental details, and analyses of controller behavior and measurement precision.

Expressiveness: The representation theorem decomposes analytic dynamics into wind-invariant features and wind-dependent coefficients, with coefficient dimension scaling as O((log(1/ϵ))^m).The construction uses Chebyshev-polynomial approximations and supports arbitrary approximation precision.
Expressiveness: A four-layer neural network can approximate the unknown dynamics through the factorized form ϕ(x)a(w), providing the basis for the learned architecture.The theorem extends to vector-valued functions with bounded input spaces.
Stability and robustness: The stability proof shows the combined velocity-tracking and adaptation error converges exponentially to a bounded error ball, implying exponential convergence of tracking error.A corollary bounds the remaining state error, completing the theorem’s exponential stability and robustness argument.
Stability and robustness: The adaptation law remains robust without persistent excitation or effective learning because the stability rate α remains strictly positive even when ϕ ≡ 0.The authors nevertheless expect some measurement information about all coefficient elements in practice.
Controller analysis: Reactive baseline controllers trade responsiveness against robustness: integral action risks overshoot and instability, while faster residual adaptation amplifies measurement noise.Neural-Fly’s learned model predicts future aerodynamic effects after coefficient adaptation, although extrapolation creates model mismatch.