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Adaptive SINDy: Residual Force System Identification Based UAV Disturbance Rejection

Fawad Mehboob, Amir Atef Habel, Roohan Ahmed Khan, Mikhail Derevianchenko, Clement Fortin, Dzmitry Tsetserukou

TL;DR

This work proposes 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.

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.

Adaptive SINDy: Residual Force System Identification Based UAV Disturbance Rejection

TL;DR

This work proposes 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.

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.
Paper Structure (15 sections, 14 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 15 sections, 14 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Sparse Identification of Non-Linear Dynamics (SINDy)
  4. Adaptive Control Algorithm
  5. Implementation Details
  6. Wind disturbance injection (external wrench)
  7. Ornstein--Uhlenbeck (OU) gust model
  8. Wind force composition and application
  9. Data Collection
  10. Experiment protocol and error metrics
  11. Results
  12. ArduPilot SITL Disturbance Rejection
  13. Crazyflie SITL Disturbance Rejection
  14. Real Flight Results
  15. Conclusion and Future Work

Figures (5)

  • Figure 1: Crazyflie Under Windy Environment, 4 ducted fans blowing air at up to 2 m/s on the drone from four directions.
  • Figure 2: Adaptive SINDy system architecture for system identification based residual force estimation coupled with RLS adaptive control to reject disturbance.
  • Figure 3: Error Heatmap Comparison for ArduPilot non-convex trajectory tracking under wind disturbance in Gazebo simulation
  • Figure 4: Error Heatmap Comparison for Crazyflie non-convex trajectory tracking under disturbances in Gazebo simulation.
  • Figure 5: Real flight trajectory overlays (blue dashed: reference, orange solid: achieved). The Adaptive SINDy controller tracks all three trajectory types. The oscillatory nature of the achieved trajectory illustrate the turbulent nature of the environment.