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An environmental disturbance observer framework for autonomous surface vessels

Daniel Menges, Adil Rasheed

Abstract

This paper proposes a robust disturbance observer framework for maritime autonomous surface vessels considering model and measurement uncertainties. The core contribution lies in a nonlinear disturbance observer, reconstructing the forces on a vessel impacted by the environment. For this purpose, mappings are found leading to synchronized global exponentially stable error dynamics. With the stability theory of Lyapunov, it is proven that the error converges exponentially into a ball, even if the disturbances are highly dynamic. Since measurements are affected by noise and physical models can be erroneous, an unscented Kalman filter (UKF) is used to generate more reliable state estimations. In addition, a noise estimator is introduced, which approximates the noise strength. Depending on the severity of the measurement noise, the observed disturbances are filtered through a cascaded structure consisting of a weighted moving average (WMA) filter, a UKF, and the proposed disturbance observer. To investigate the capability of this observer framework, the environmental disturbances are simulated dynamically under consideration of different model and measurement uncertainties. It can be seen that the observer framework can approximate dynamical forces on a vessel impacted by the environment despite using a low measurement sampling rate, an erroneous model, and noisy measurements.

An environmental disturbance observer framework for autonomous surface vessels

Abstract

This paper proposes a robust disturbance observer framework for maritime autonomous surface vessels considering model and measurement uncertainties. The core contribution lies in a nonlinear disturbance observer, reconstructing the forces on a vessel impacted by the environment. For this purpose, mappings are found leading to synchronized global exponentially stable error dynamics. With the stability theory of Lyapunov, it is proven that the error converges exponentially into a ball, even if the disturbances are highly dynamic. Since measurements are affected by noise and physical models can be erroneous, an unscented Kalman filter (UKF) is used to generate more reliable state estimations. In addition, a noise estimator is introduced, which approximates the noise strength. Depending on the severity of the measurement noise, the observed disturbances are filtered through a cascaded structure consisting of a weighted moving average (WMA) filter, a UKF, and the proposed disturbance observer. To investigate the capability of this observer framework, the environmental disturbances are simulated dynamically under consideration of different model and measurement uncertainties. It can be seen that the observer framework can approximate dynamical forces on a vessel impacted by the environment despite using a low measurement sampling rate, an erroneous model, and noisy measurements.
Paper Structure (12 sections, 1 theorem, 60 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 12 sections, 1 theorem, 60 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theory
  3. Model
  4. Weighted Moving Average
  5. Unscented Kalman Filter
  6. Disturbance Observer Design
  7. Observer Framework
  8. Method and setup
  9. Ferry specification
  10. Scenario description
  11. Results and discussions
  12. Conclusion and future work

Key Result

Lemma 1

If the matrix $\boldsymbol{M}$ is symmetric and invertible, its inverse $\boldsymbol{M}^{-1}$ is likewise symmetric, since $(\boldsymbol{M}^{-1})^\top =~(\boldsymbol{M}^\top)^{-1}$. Since the entries of the mass matrix are positive, $\boldsymbol{M}$ is positive definite and thus invertible.

Figures (7)

  • Figure 1: Kinematics of a vessel
  • Figure 2: Observer framework
  • Figure 3: Real states (), measured states with measurement noise (), WMA filtered measurements (), filtered states from the first UKF (), and filtered states from the second UKF ().
  • Figure 4: Observed disturbances $\boldsymbol{\hat{\tau}_d}$ () compared to the real disturbances $\boldsymbol{\tau_d}$ ().
  • Figure 5: Noise estimation without mean smoothing (), and the final smoothed noise strength estimation () triggering the switches $s_1$ (), $s_2$ (), and $s_3$ ().
  • ...and 2 more figures

Theorems & Definitions (1)

  • Lemma 1