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Unified Meta-Representation and Feedback Calibration for General Disturbance Estimation

Zihan Yang, Jindou Jia, Meng Wang, Yuhang Liu, Kexin Guo, Xiang Yu

TL;DR

This work presents a generalizable disturbance estimation framework that builds on meta-learning and feedback-calibrated online adaptation, and shows that simultaneous convergence of both the online learning error and the disturbance estimation error can be achieved.

Abstract

Precise control in modern robotic applications is always an open issue due to unknown time-varying disturbances. Existing meta-learning-based approaches require a shared representation of environmental structures, which lack flexibility for realistic non-structural disturbances. Besides, representation error and the distribution shifts can lead to heavy degradation in prediction accuracy. This work presents a generalizable disturbance estimation framework that builds on meta-learning and feedback-calibrated online adaptation. By extracting features from a finite time window of past observations, a unified representation that effectively captures general non-structural disturbances can be learned without predefined structural assumptions. The online adaptation process is subsequently calibrated by a state-feedback mechanism to attenuate the learning residual originating from the representation and generalizability limitations. Theoretical analysis shows that simultaneous convergence of both the online learning error and the disturbance estimation error can be achieved. Through the unified meta-representation, our framework effectively estimates multiple rapidly changing disturbances, as demonstrated by quadrotor flight experiments. See the project page for video, supplementary material and code: https://nonstructural-metalearn.github.io.

Unified Meta-Representation and Feedback Calibration for General Disturbance Estimation

TL;DR

This work presents a generalizable disturbance estimation framework that builds on meta-learning and feedback-calibrated online adaptation, and shows that simultaneous convergence of both the online learning error and the disturbance estimation error can be achieved.

Abstract

Precise control in modern robotic applications is always an open issue due to unknown time-varying disturbances. Existing meta-learning-based approaches require a shared representation of environmental structures, which lack flexibility for realistic non-structural disturbances. Besides, representation error and the distribution shifts can lead to heavy degradation in prediction accuracy. This work presents a generalizable disturbance estimation framework that builds on meta-learning and feedback-calibrated online adaptation. By extracting features from a finite time window of past observations, a unified representation that effectively captures general non-structural disturbances can be learned without predefined structural assumptions. The online adaptation process is subsequently calibrated by a state-feedback mechanism to attenuate the learning residual originating from the representation and generalizability limitations. Theoretical analysis shows that simultaneous convergence of both the online learning error and the disturbance estimation error can be achieved. Through the unified meta-representation, our framework effectively estimates multiple rapidly changing disturbances, as demonstrated by quadrotor flight experiments. See the project page for video, supplementary material and code: https://nonstructural-metalearn.github.io.
Paper Structure (20 sections, 2 theorems, 8 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 2 theorems, 8 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Offline Meta-Learning
  4. Online Adaptation
  5. Problem Formulation
  6. Methods
  7. Meta-learning for Non-Structural Disturbances
  8. Unified Meta-Representation
  9. Learning from Finite Time Window
  10. Ablation Study on Model Parameters
  11. Domain Randomization for Meta-learning
  12. Feedback-Calibrated Online Adaptation
  13. Empirical Study
  14. Simulated Experiments
  15. Real-world Experiments
  16. ...and 5 more sections

Key Result

Theorem 1

Under Assumption assumption_1, with $\bm{\theta} = \bm{\theta}^*$, the disturbance estimation error $\tilde{\bm{d}} = \hat{\bm{d}} - \bm{d}$ exponentially converges to a bounded set regularized by $\bm{L}$ and $\bar{d_\gamma}$.

Figures (10)

  • Figure 1: Schematic of the proposed framework. The meta-representation is learned from a finite time window of past observations with domain-randomized disturbances. The online adaptation is calibrated with a feedback mechanism to attenuate the learning residual, which can be further integrated with a baseline controller for disturbance rejection.
  • Figure 2: The result of ablation study, including model performance (prediction loss in mean squared error) on meta-learn dataset (a), shifted dataset (b) and the effect of online parameter estimation (c).
  • Figure 3: Distribution differences of disturbances in the dataset of meta-learn (Learn), shifted (Shifted), simulations (Sim) and real-world scenarios (S1 and S2).
  • Figure 4: Trajectory tracking results of the simulated cases.
  • Figure 5: Scenario.1, the quadrotor maneuvers in circular trajectory with suspended payload and aerodynamic drag. Boxplots of both estimation error and tracking error are provided. 3D trajectories are colored by the tracking error.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2