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Integrated Guidance and Control for Path-Following with Bounded Inputs

Ram Milan Kumar Verma, Shashi Ranjan Kumar, Hemendra Arya

Abstract

Precise motion control of underactuated surface vessels is a crucial task in various maritime applications. In this work, we develop a nonlinear motion control strategy for surface vessels inspired by the pursuit guidance philosophy. Any sufficiently smooth path can be seen as a continuum of virtual targets moving along a specified path, which the pursuer is trying to catch. Contrary to the traditional path-following methods, this work develops an integrated guidance and control approach capable of following any smooth path (unlike the ones composed of a finite number of straight lines and circles). The approach relies on steering the vehicle such that its velocity vector aligns with the line-of-sight (the line joining the moving virtual target and the surface vessel), resulting in a tail-chase scenario. This leads to a path-following behavior. This integrated approach also overcomes the disadvantages inherent in the traditional two-loop-based approaches. Additionally, the proposed work takes into account the asymmetric actuator constraints in the design, which makes the design close to realistic scenarios. Furthermore, the control law has been derived within a nonlinear framework using sliding mode, and thus remains applicable for a wider envelope. The stability of the proposed control strategy is formally proven. Numerical simulations for various specified paths validate the controller's accurate path-following performance.

Integrated Guidance and Control for Path-Following with Bounded Inputs

Abstract

Precise motion control of underactuated surface vessels is a crucial task in various maritime applications. In this work, we develop a nonlinear motion control strategy for surface vessels inspired by the pursuit guidance philosophy. Any sufficiently smooth path can be seen as a continuum of virtual targets moving along a specified path, which the pursuer is trying to catch. Contrary to the traditional path-following methods, this work develops an integrated guidance and control approach capable of following any smooth path (unlike the ones composed of a finite number of straight lines and circles). The approach relies on steering the vehicle such that its velocity vector aligns with the line-of-sight (the line joining the moving virtual target and the surface vessel), resulting in a tail-chase scenario. This leads to a path-following behavior. This integrated approach also overcomes the disadvantages inherent in the traditional two-loop-based approaches. Additionally, the proposed work takes into account the asymmetric actuator constraints in the design, which makes the design close to realistic scenarios. Furthermore, the control law has been derived within a nonlinear framework using sliding mode, and thus remains applicable for a wider envelope. The stability of the proposed control strategy is formally proven. Numerical simulations for various specified paths validate the controller's accurate path-following performance.
Paper Structure (17 sections, 1 theorem, 62 equations, 9 figures, 1 table)

This paper contains 17 sections, 1 theorem, 62 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. USV dynamics
  4. Engagement kinematics
  5. Input saturation model with asymmetric bounds
  6. Main results
  7. Integrated guidance and control design
  8. Design with control input saturation
  9. Simulations
  10. Without input saturation model
  11. Elliptical reference path
  12. 8-shaped reference path
  13. With input saturation model
  14. Elliptical reference path
  15. 8-shaped reference path
  16. ...and 2 more sections

Key Result

Lemma 1

The acceleration of USV perpendicular to LOS is related to the yaw rate $r$ and acceleration in body frame $\dot u$ and $\dot v$ with the relation given by where $\beta$ is the sideslip angle of the USV.

Figures (9)

  • Figure 1: Schematic representation of the surface vessel's position, orientation, and body-frame velocities.
  • Figure 2: Kinematic engagement of USV with virtual reference point, $T$, on the path, $\mathcal{P}$.
  • Figure 3: Representation of the overall implementation of IGC design.
  • Figure 4: Schematic of implementation of IGC with the consideration of input saturation.
  • Figure 5: Path-following performance for the case of an elliptical reference path.
  • ...and 4 more figures

Theorems & Definitions (3)

  • Lemma 1
  • proof
  • Remark 1