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Trajectory Tracking for Uncrewed Surface Vessels with Input Saturation and Dynamic Motion Constraints

Ram Milan Kumar Verma, Shashi Ranjan Kumar, Hemendra Arya

Abstract

This work addresses the problem of constrained motion control of the uncrewed surface vessels. The constraints are imposed on states/inputs of the vehicles due to the physical limitations, mission requirements, and safety considerations. We develop a nonlinear feedback controller utilizing log-type Barrier Lyapunov Functions to enforce static and dynamic motion constraints. The proposed scheme uniquely addresses asymmetric constraints on position and heading alongside symmetric constraints on surge, sway, and yaw rates. Additionally, a smooth input saturation model is incorporated in the design to guarantee stability even under actuator bounds, which, if unaccounted for, can lead to severe performance degradation and poor tracking. Rigorous Lyapunov stability analysis shows that the closed-loop system remains stable and that all state variables remain within their prescribed bounds at all times, provided the initial conditions also lie within those bounds. Numerical simulations demonstrate the effectiveness of the proposed strategies for surface vessels without violating the motion and actuator constraints.

Trajectory Tracking for Uncrewed Surface Vessels with Input Saturation and Dynamic Motion Constraints

Abstract

This work addresses the problem of constrained motion control of the uncrewed surface vessels. The constraints are imposed on states/inputs of the vehicles due to the physical limitations, mission requirements, and safety considerations. We develop a nonlinear feedback controller utilizing log-type Barrier Lyapunov Functions to enforce static and dynamic motion constraints. The proposed scheme uniquely addresses asymmetric constraints on position and heading alongside symmetric constraints on surge, sway, and yaw rates. Additionally, a smooth input saturation model is incorporated in the design to guarantee stability even under actuator bounds, which, if unaccounted for, can lead to severe performance degradation and poor tracking. Rigorous Lyapunov stability analysis shows that the closed-loop system remains stable and that all state variables remain within their prescribed bounds at all times, provided the initial conditions also lie within those bounds. Numerical simulations demonstrate the effectiveness of the proposed strategies for surface vessels without violating the motion and actuator constraints.
Paper Structure (15 sections, 2 theorems, 65 equations, 7 figures, 1 table)

This paper contains 15 sections, 2 theorems, 65 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Input saturation model with asymmetric bounds
  4. Barrier Lyapunov function
  5. Main Results
  6. Control under static state constraints and input saturation
  7. Control under asymmetric dynamic state constraints
  8. Control under asymmetric dynamic state constraint with the actuator saturation
  9. Simulation Results
  10. Tracking under static state constraints with input saturation
  11. Tracking under dynamic state constraints
  12. Elliptical trajectory
  13. Eight-shaped trajectory
  14. Tracking under dynamic state constraints with input saturation
  15. Conclusions

Key Result

Lemma 1

kpt2009 For any positive constants $k_{a_1}, k_{b_1}$, let $Z_1 := \left\{z_1 \in \mathbb{R}: -k_{a_1}<z_1 <k_{b_1}\right\}\subset \mathbb{R}$ and $\mathbb{N} := \mathbb{R}^l \times \mathbb{Z}_1 \subset \mathbb{R}^{l+1}$ be open sets. Consider the system $\dot \eta= h(t,\eta),$ where $\eta := [w,~~z

Figures (7)

  • Figure 1: Planar motion of the USV under static and dynamic motion constraints.
  • Figure 2: Performance validation of proposed controller for a surface vessel with elliptical trajectory under static state constraints and input saturation.
  • Figure 3: Performance validation of proposed controller for a USV with an eight-shaped trajectory under static state constraints and input saturation.
  • Figure 4: Performance validation of proposed controller for a USV with elliptical trajectory under asymmetric dynamic constraints on position and heading of the USV.
  • Figure 5: Performance validation of proposed controller for a USV following an eight-shaped trajectory under asymmetric dynamic constraints on position and heading of the USV.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Remark 1
  • Lemma 1
  • Lemma 2