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Nonlinear model predictive control-based guidance law for path following of unmanned surface vehicles

G. Bejarano, J. M. Manzano, J. R. Salvador, D. Limon

TL;DR

This work addresses path following for unmanned surface vehicles under disturbances by introducing a nonlinear model predictive control based guidance law. It develops a discretized PF model with a virtual target on the path and a horizon-based optimization that enforces input constraints and provides a robust, ISS-friendly design; a practical linearized variant (PNMPC) reduces computational cost. Through simulations on a Cybership II, the NMPC approach achieves faster convergence and smaller PF errors than LOS-based laws, while the PNMPC variant delivers similar performance with dramatically reduced compute time. The framework enables predictive guidance on lower-cost USVs and lays groundwork for obstacle avoidance and predictive low-level control integration in future work.

Abstract

This work proposes a nonlinear model predictive control-based guidance strategy for unmanned surface vehicles, focused on path following. The application of this strategy, in addition to overcome drawbacks of previous line-of-sight-based guidance laws, intends to enable the application of predictive strategies also to the low-level control, responsible for tracking the references provided by the guidance strategy. The stability and robustness of the proposed strategy are theoretically discussed. Furthermore, given the non-negligible computational cost of such nonlinear predictive guidance strategy, a practical nonlinear model predictive control strategy is also applied in order to reduce the computational cost to a great extent. The effectiveness and advantages of both proposed strategies over other nonlinear guidance laws are illustrated through a complete set of simulations.

Nonlinear model predictive control-based guidance law for path following of unmanned surface vehicles

TL;DR

This work addresses path following for unmanned surface vehicles under disturbances by introducing a nonlinear model predictive control based guidance law. It develops a discretized PF model with a virtual target on the path and a horizon-based optimization that enforces input constraints and provides a robust, ISS-friendly design; a practical linearized variant (PNMPC) reduces computational cost. Through simulations on a Cybership II, the NMPC approach achieves faster convergence and smaller PF errors than LOS-based laws, while the PNMPC variant delivers similar performance with dramatically reduced compute time. The framework enables predictive guidance on lower-cost USVs and lays groundwork for obstacle avoidance and predictive low-level control integration in future work.

Abstract

This work proposes a nonlinear model predictive control-based guidance strategy for unmanned surface vehicles, focused on path following. The application of this strategy, in addition to overcome drawbacks of previous line-of-sight-based guidance laws, intends to enable the application of predictive strategies also to the low-level control, responsible for tracking the references provided by the guidance strategy. The stability and robustness of the proposed strategy are theoretically discussed. Furthermore, given the non-negligible computational cost of such nonlinear predictive guidance strategy, a practical nonlinear model predictive control strategy is also applied in order to reduce the computational cost to a great extent. The effectiveness and advantages of both proposed strategies over other nonlinear guidance laws are illustrated through a complete set of simulations.
Paper Structure (17 sections, 5 theorems, 42 equations, 15 figures)

This paper contains 17 sections, 5 theorems, 42 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Nonlinear model predictive control
  4. Problem statement
  5. Stability
  6. Practical nonlinear model predictive control
  7. Case study
  8. Comparison between the proposed NMPC guidance and other existing laws
  9. Description of the case study
  10. Design of the proposed NMPC-based guidance law
  11. Results
  12. Comparison between the NMPC-based guidance law and the PNMPC-based simplified law
  13. Separate dynamics
  14. Low-level closed-loop dynamics
  15. Frequency-varying disturbance
  16. ...and 2 more sections

Key Result

Theorem 1

Consider that Assumptions ass_path-ass_terminalcost hold. Then, in absence of disturbances, given $\mathbf{x}(0)\in X_N(\lambda)$, the closed-loop system is asymptotically stable.

Figures (15)

  • Figure 1: Traditional PF control strategy
  • Figure 2: Path following geometry
  • Figure 3: Desired path and comparison between performances of the NMPC with respect to existing LOS laws
  • Figure 4: Surge-related variables of both the SGLOS and the NMPC-based guidance laws
  • Figure 5: Angle variables of existing LOS and the NMPC-based guidance laws
  • ...and 10 more figures

Theorems & Definitions (11)

  • Theorem 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 1
  • Remark 2
  • Definition 1: ISS stability as defined by limon2009input
  • ...and 1 more