Adaptive SINDy: Residual Force System Identification Based UAV Disturbance Rejection

2026-03-09

AI Summary

This study addresses the degradation of drone stability under turbulent wind disturbances by proposing a novel control framework that integrates Sparse Identification of Nonlinear Dynamics (SINDy) with Recursive Least Squares (RLS) adaptive control. For the first time, the data-driven SINDy algorithm is employed to identify in real time the residual forces induced by wind perturbations, while RLS dynamically adjusts the control inputs to compensate for these disturbances. The approach uniquely balances model interpretability with strong generalization capability. Validated on the lightweight Crazyflie platform, the system achieves high-precision trajectory tracking in both Gazebo simulations and real-world flights, yielding RMSEs of 12.2 cm and 17.6 cm—and MAEs of 13.7 cm and 10.5 cm—for circular and lemniscate trajectories, respectively. These results significantly outperform conventional PID and Incremental Nonlinear Dynamic Inversion (INDI) controllers, with no flight failures observed throughout testing.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The stability and control of Unmanned Aerial Vehicles (UAVs) in a turbulent environment is a matter of great concern. Devising a robust control algorithm to reject disturbances is challenging due to the highly nonlinear nature of wind dynamics, and modeling the dynamics using analytical techniques is not straightforward. While traditional techniques using disturbance observers and classical adaptive control have shown some progress, they are mostly limited to relatively non-complex environments. On the other hand, learning based approaches are increasingly being used for modeling of residual forces and disturbance rejection; however, their generalization and interpretability is a factor of concern. To this end, we propose a novel integration of data-driven system identification using Sparse Identification of Non-Linear Dynamics (SINDy) with a Recursive Least Square (RLS) adaptive control to adapt and reject wind disturbances in a turbulent environment. We tested and validated our approach on Gazebo harmonic environment and on real flights with wind speeds of up to 2 m/s from four directions, creating a highly dynamic and turbulent environment. Adaptive SINDy outperformed the baseline PID and INDI controllers on several trajectory tracking error metrics without crashing. A root mean square error (RMSE) of up to 12.2 cm and 17.6 cm, and a mean absolute error (MAE) of 13.7 cm and 10.5 cm were achieved on circular and lemniscate trajectories, respectively. The validation was performed on a very lightweight Crazyflie drone under a highly dynamic environment for complex trajectory tracking.

Problem

• UAV disturbance rejection
• wind turbulence
• nonlinear dynamics
• system identification
• robust control

Innovation

• Adaptive SINDy
• Sparse Identification of Nonlinear Dynamics
• Recursive Least Squares
• Disturbance Rejection
• UAV Control