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Provably Safe Finite-Time Guidance for Marine Vehicles

Bhawana Singh, Karim Ahmadi Dastgerdi, Nikolaos Athanasopoulos, Wasif Naeem, Benoit Lecallard

TL;DR

This work addresses provably safe, finite-time waypoint navigation for marine vehicles in environments with static and dynamic obstacles. A cascade architecture combines a predefined-time heading autopilot with an LOS-based waypoint guidance law, generating intermediate virtual waypoints to guarantee both finite-time convergence to the waypoint and safety constraints such as a minimum distance $C_s$ from obstacles. Lyapunov-based analysis yields predefined-time convergence of the heading error within $t_p$ and finite-time convergence to the waypoint within $T_F$, with switching rules that respect COLREGs. Simulations on the Imazu benchmarks demonstrate improved safety distances over Velocity Obstacle and geometric LOS methods while maintaining competitive path length and travel time.

Abstract

We consider a new control strategy for marine navigation, equipped with finite-time convergence characteristics. We provide mathematical guarantees for waypoint reaching and obstacle avoidance for different encounter scenarios, by deriving conditions under which (i) convergence to waypoint and (ii) safe obstacle avoidance is achieved while (iii) satisfying input constraints. We propose a predefined-time heading control to enforce ship heading error convergence and waypoint reaching in finite time. Using this as a building block, we develop a provably safe algorithm for safe waypoint navigation by strategically and automatically introducing intermediate virtual waypoints. Using Imazu problems as benchmarks, we show that the proposed method is better than other existing strategies such as Velocity Obstacle Avoidance and biased Line-of-Sight methods, in terms of the safe distance between the ship and the obstacles, cross track error, control effort, waypoint reaching time and ship path length.

Provably Safe Finite-Time Guidance for Marine Vehicles

TL;DR

This work addresses provably safe, finite-time waypoint navigation for marine vehicles in environments with static and dynamic obstacles. A cascade architecture combines a predefined-time heading autopilot with an LOS-based waypoint guidance law, generating intermediate virtual waypoints to guarantee both finite-time convergence to the waypoint and safety constraints such as a minimum distance from obstacles. Lyapunov-based analysis yields predefined-time convergence of the heading error within and finite-time convergence to the waypoint within , with switching rules that respect COLREGs. Simulations on the Imazu benchmarks demonstrate improved safety distances over Velocity Obstacle and geometric LOS methods while maintaining competitive path length and travel time.

Abstract

We consider a new control strategy for marine navigation, equipped with finite-time convergence characteristics. We provide mathematical guarantees for waypoint reaching and obstacle avoidance for different encounter scenarios, by deriving conditions under which (i) convergence to waypoint and (ii) safe obstacle avoidance is achieved while (iii) satisfying input constraints. We propose a predefined-time heading control to enforce ship heading error convergence and waypoint reaching in finite time. Using this as a building block, we develop a provably safe algorithm for safe waypoint navigation by strategically and automatically introducing intermediate virtual waypoints. Using Imazu problems as benchmarks, we show that the proposed method is better than other existing strategies such as Velocity Obstacle Avoidance and biased Line-of-Sight methods, in terms of the safe distance between the ship and the obstacles, cross track error, control effort, waypoint reaching time and ship path length.
Paper Structure (25 sections, 5 theorems, 53 equations, 24 figures, 1 table)

This paper contains 25 sections, 5 theorems, 53 equations, 24 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Marine Craft Dynamics
  4. Obstacle Dynamics
  5. Control Design Objectives
  6. Finite-time and Predefined-Time Stability
  7. Convention on the International Regulations (COLREGs)
  8. Waypoint Reaching
  9. Waypoint Reaching Guidance Law
  10. Static Obstacle Avoidance
  11. Single Static Obstacle
  12. Switching Rule
  13. Safe Waypoint Reaching
  14. Switching Strategy based on Risk Assessment
  15. Multiple Static Obstacles
  16. ...and 10 more sections

Key Result

Lemma 1

Consider the system (sw). Suppose there exists a positive definite continuously differentiable function $V:\mathbb{R}^{n}\to\mathbb{R}_{\geq 0}$ such that for $\alpha>0$ and $0<k<1$. Then, the system (sw) is finite-time stable about the origin and the time of convergence is given by $T_f=\frac{V(x(t_0))^{1-k}}{\alpha(1-k)}$.

Figures (24)

  • Figure 1: Illustration of CPA, DCPA and TCPA
  • Figure 2: The Artemis eFoiler EF-12 in the Belfast harbour.
  • Figure 3: The proposed guidance and control system for waypoint navigation and collision avoidance.
  • Figure 4: COLREGs rules on (a) Overtaking, (b) Head-on, and (c) Crossing (Source: cho2021intent)
  • Figure 5: Relative angles for collision risk assessment and COLREGs decision making.
  • ...and 19 more figures

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Lemma 1: Theorem 4.2, bhat2000finite
  • Lemma 2
  • Remark 1
  • Theorem 1
  • Example 1
  • Remark 2
  • Remark 3
  • Remark 4
  • ...and 7 more