Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Switched Vector Field-based Guidance for General Reference Path Following in Planar Environment

Subham Basak, Satadal Ghosh

TL;DR

The paper tackles planar general-path following for unmanned vehicles by introducing a switched vector-field guidance law that ties the desired heading $\chi^d$ to both cross-track error $d$ and the UAV's course $\chi$. By switching between high- and low-s curvature vector-field formulations and incorporating a course-angle term, the method achieves faster convergence while respecting kino-dynamic limits, with finite-time convergence guarantees and chattering mitigation. Theoretical convergence and curvature-feasibility analyses are complemented by numerical simulations demonstrating improved performance over several baseline methods under varying initial conditions and wind. This approach offers a practical, implementable path-following strategy for autonomous vehicles operating in planar environments with real-world dynamic constraints.

Abstract

Reference path following is a key component in the functioning of almost all engineered autonomous agents. Among several path following guidance methods in existing literature, vector-field-based guidance approach has got wide attention because of its simplicity and guarantee of stability under a broad class of scenarios. However, the usage of same cross-track-error-dependent structure of desired vector field in most of the existing literature irrespective of instantaneous cross-track error and course angle of unmanned vehicle makes it quite restrictive in attaining faster convergence and also leads to infeasibly high turn rate command for many scenarios. To this end, this paper presents a novel switched vector field-based guidance for following a general reference path, in which the structure of the desired vector field depends on instantaneous cross-track-error and vehicle's course angle. While the developed method ensures faster convergence, it also ensures that the guidance command always stays within a realistic threshold satisfying its curvature constraint, thus making it more real-life implementable for autonomous vehicles with kino-dynamic constraints. Theoretical analysis for convergence of the developed guidance scheme is presented. Possibilities of undesirable chattering at phase transitions are also eliminated. Numerical simulation studies are presented to validate the satisfactory performance of the developed algorithm.

Switched Vector Field-based Guidance for General Reference Path Following in Planar Environment

TL;DR

The paper tackles planar general-path following for unmanned vehicles by introducing a switched vector-field guidance law that ties the desired heading to both cross-track error and the UAV's course . By switching between high- and low-s curvature vector-field formulations and incorporating a course-angle term, the method achieves faster convergence while respecting kino-dynamic limits, with finite-time convergence guarantees and chattering mitigation. Theoretical convergence and curvature-feasibility analyses are complemented by numerical simulations demonstrating improved performance over several baseline methods under varying initial conditions and wind. This approach offers a practical, implementable path-following strategy for autonomous vehicles operating in planar environments with real-world dynamic constraints.

Abstract

Reference path following is a key component in the functioning of almost all engineered autonomous agents. Among several path following guidance methods in existing literature, vector-field-based guidance approach has got wide attention because of its simplicity and guarantee of stability under a broad class of scenarios. However, the usage of same cross-track-error-dependent structure of desired vector field in most of the existing literature irrespective of instantaneous cross-track error and course angle of unmanned vehicle makes it quite restrictive in attaining faster convergence and also leads to infeasibly high turn rate command for many scenarios. To this end, this paper presents a novel switched vector field-based guidance for following a general reference path, in which the structure of the desired vector field depends on instantaneous cross-track-error and vehicle's course angle. While the developed method ensures faster convergence, it also ensures that the guidance command always stays within a realistic threshold satisfying its curvature constraint, thus making it more real-life implementable for autonomous vehicles with kino-dynamic constraints. Theoretical analysis for convergence of the developed guidance scheme is presented. Possibilities of undesirable chattering at phase transitions are also eliminated. Numerical simulation studies are presented to validate the satisfactory performance of the developed algorithm.
Paper Structure (17 sections, 5 theorems, 27 equations, 6 figures)

This paper contains 17 sections, 5 theorems, 27 equations, 6 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem Definition
  3. Navigation Dynamics
  4. Definitions Related to Reference Path
  5. Guidance for General Reference Path Following
  6. Vector Field Description
  7. Dependence of Vector Field on Cross-track Error
  8. Dependence on Instantaneous UAV Course Angle ($\chi$)
  9. Overall Guidance Strategy
  10. Convergence Analysis
  11. Case - 1 $(\vert d \vert>d_s$ and $|\chi -\chi^d(d)|>({\pi}/{2}))$
  12. Case - 2 $(\vert d \vert \geq d_s$ and $|\chi -\chi^d(d)|\leq{\pi}/{2})$
  13. Case - 3 $(\vert d \vert < d_s$)
  14. Final Result
  15. Curvature Constraints
  16. ...and 2 more sections

Key Result

Proposition 1

When $\vert d \vert>d_s$and$|\chi -\chi^d(d)|>({\pi}/{2})$, where $\chi^d(d,\chi)=\chi^d(d)+{\pi}/{2}$ as given in eq:chi_d_turn_line_final, applying $\chi^c$ command as given in eq:chi_c_turn_line brings $\Tilde{\chi}$ to zero in finite time.

Figures (6)

  • Figure 1: General reference path following geometry
  • Figure 2: Variation of $\vert \Dot{d} \vert$ and $|\Dot{\chi}^d(d)-\Dot{\chi^p}|$, for $i=1,3,5,7,9$.
  • Figure 3: Course angle based vector field for $\chi^p=0$
  • Figure 4: Illustration of path following by the proposed switched vector field-based guidance.
  • Figure 5: Illustration of path following by the proposed method, vector fieldnelson2007, PLOSkothari2014uav and NLGL ($L_1$) park2007
  • ...and 1 more figures

Theorems & Definitions (13)

  • Proposition 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Remark 2
  • Remark 3
  • Proposition 3
  • proof
  • Proposition 4
  • ...and 3 more