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Stochastic Safety-critical Control Compensating Safety Probability for Marine Vessel Tracking

Too Matsuo, Yuki Nishimura, Kenta Hoshino, Daisuke Tabuchi

Abstract

A marine vessel is a nonlinear system subject to irregular disturbances such as wind and waves, which cause tracking errors between the nominal and actual trajectories. In this study, a nonlinear vessel maneuvering model that includes a tracking controller is formulated and then controlled using a linear approximation around the nominal trajectory. The resulting stochastic linearized system is analyzed using a stochastic zeroing control barrier function (ZCBF). A stochastic safety compensator is designed to ensure probabilistic safety, and its effectiveness is verified through numerical simulations.

Stochastic Safety-critical Control Compensating Safety Probability for Marine Vessel Tracking

Abstract

A marine vessel is a nonlinear system subject to irregular disturbances such as wind and waves, which cause tracking errors between the nominal and actual trajectories. In this study, a nonlinear vessel maneuvering model that includes a tracking controller is formulated and then controlled using a linear approximation around the nominal trajectory. The resulting stochastic linearized system is analyzed using a stochastic zeroing control barrier function (ZCBF). A stochastic safety compensator is designed to ensure probabilistic safety, and its effectiveness is verified through numerical simulations.

Paper Structure

This paper contains 23 sections, 5 theorems, 93 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Control Design for Trajectory Tracking
  4. Safety Probability Analysis
  5. Stochastic Safety-critical Compensation by Linear State Feedback
  6. Stochastic Safety-critical Compensation by Nonlinear State Feedback
  7. Numerical Simulation
  8. Parameter Settings
  9. Simulation Results
  10. Theory
  11. Notations
  12. Stochastic System
  13. Safety-probability Analysis and Design
  14. Safety Probability
  15. Safety Probability Analysis and Linear Control Design For Stochastic Linear Systems
  16. ...and 8 more sections

Key Result

Theorem 1

Let the system system be considered. If there exists a stochastic ZCBF $h(x)$, then the system becomes safe in $(\chi_{h>\mu},\chi,1-e^{-b\mu})$ by designing $u=\phi(x)$ that satisfies all the conditions in Definition definition. $\space\blacklozenge$

Figures (7)

  • Figure 1: marine vessel maneuvering kinematic model fossen.
  • Figure 3: The brief sketch of the Lyapunov function $V(x)$, the stochastic ZCBF $h(x)$, the safe set $\chi$ and the initial state set $\chi_{h>\mu}$ for a state space $(x_1,x_2)^T$.
  • Figure 4: Trajectories with $u=u_{tra}$ and safety boundary.
  • Figure 6: Trajectories with $u=u_{tra}+u_{com}$ and safety boundary.
  • Figure 8: Time responses of $v_{com}$.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Remark 1
  • Definition 1
  • Theorem 1
  • Remark 2
  • Theorem 2
  • Corollary 1
  • Corollary 2
  • Definition 2: FCiP, nishimura
  • Theorem 3