Learning-Based Observer for Coupled Disturbance
Jindou Jia, Meng Wang, Zihan Yang, Bin Yang, Yuhang Liu, Kexin Guo, Xiang Yu
AI summary
Problem
High-precision robotic control is hindered by coupled internal uncertainties and external disturbances that traditional observers struggle to estimate accurately. Existing methods rely on restrictive boundedness assumptions that create theoretical paradoxes or require unmeasurable disturbance data, while data-driven approaches often lack interpretability and theoretical guarantees.
Approach
The framework decomposes the coupled disturbance into an unknown parameter matrix and known state-dependent structures using Chebyshev series expansion. It then learns the parameters offline via a closed-form regularized least squares problem and estimates the time-varying component online using a polynomial disturbance observer.
Key results
- Theoretical decomposition of coupled disturbances into learnable parameters and known structures via Chebyshev polynomials
- Closed-form regularized least squares solution for offline parameter learning from historical data
- Polynomial disturbance observer enabling exponentially convergent online estimation without bounded disturbance assumptions
- Validated effectiveness through extensive simulations and indoor/outdoor flight tests on quadrotors
Why it matters
Offers a lightweight, interpretable, and theoretically rigorous alternative to black-box neural networks and conservative traditional observers, advancing robust control for drones and other robotic systems.
Abstract
Achieving high-precision control for robotic sys- tems is hindered by the low-fidelity dynamical model and external disturbances. Especially, the intricate coupling between internal uncertainties and external disturbances further exacer- bates this challenge. This study introduces an effective and con- vergent algorithm enabling accurate estimation of the coupled disturbance via combining control and learning philosophies. Concretely, by resorting to Chebyshev series expansion, the coupled disturbance is effectively decomposed into an unknown parameter matrix and two known structures dependent on system state and external disturbance respectively. A regu- larized least squares process is subsequently formalized to learn the parameter matrix using historical time-series data. Furthermore, a polynomial disturbance observer is specifically devised to achieve a high-precision estimation of the coupled disturbance by utilizing the learned structure portion. Extensive simulations and real flight tests valid the effectiveness of the proposed framework. We believe this work can offer a new pathway to integrate learning approaches into control frameworks for addressing longstanding challenges in robotic applications.