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Path-Following Guidance for Unmanned Aerial Vehicle with Bounded Lateral Acceleration

Vinay Kathiriya, Saurabh Kumar, Shashi Ranjan Kumar

Abstract

This paper addresses the three-dimensional path-following guidance problem for unmanned aerial vehicles under explicit actuator constraints. Unlike conventional approaches that assume unbounded control inputs or handle saturation heuristically, the proposed method incorporates bounded lateral acceleration directly into the guidance design. A nonlinear guidance framework is developed employing a nested saturation-based control technique. The proposed guidance strategy guarantees bounded control inputs while ensuring exponential convergence of cross-track errors to zero. The formulation is applicable to general smooth paths and is systematically extended from planar to three-dimensional scenarios using a path-tangent coordinate framework. Rigorous stability analysis based on Lyapunov theory establishes convergence and feasibility properties of the closed-loop system. Numerical simulations on representative paths, including straight-line, circular, and sinusoidal paths, demonstrate that the proposed method achieves superior tracking performance, reduced control effort, and robustness against disturbances compared to existing guidance laws. The simplicity of the design and its compatibility with practical actuator limits make it suitable for real-world UAV applications.

Path-Following Guidance for Unmanned Aerial Vehicle with Bounded Lateral Acceleration

Abstract

This paper addresses the three-dimensional path-following guidance problem for unmanned aerial vehicles under explicit actuator constraints. Unlike conventional approaches that assume unbounded control inputs or handle saturation heuristically, the proposed method incorporates bounded lateral acceleration directly into the guidance design. A nonlinear guidance framework is developed employing a nested saturation-based control technique. The proposed guidance strategy guarantees bounded control inputs while ensuring exponential convergence of cross-track errors to zero. The formulation is applicable to general smooth paths and is systematically extended from planar to three-dimensional scenarios using a path-tangent coordinate framework. Rigorous stability analysis based on Lyapunov theory establishes convergence and feasibility properties of the closed-loop system. Numerical simulations on representative paths, including straight-line, circular, and sinusoidal paths, demonstrate that the proposed method achieves superior tracking performance, reduced control effort, and robustness against disturbances compared to existing guidance laws. The simplicity of the design and its compatibility with practical actuator limits make it suitable for real-world UAV applications.

Paper Structure

This paper contains 5 sections, 4 theorems, 93 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Derivation of Guidance Strategy
  4. Performance Evaluations
  5. Conclusions

Key Result

Theorem 1

Consider the system dynamics given in eq:new_dynamics. Let the gains $M_1$ and $M_2$ are where $M_2'>a_{\mathrm{max}}$ is a known bound on the lateral acceleration. For any linear saturation functions $\sigma_1(.)$ and $\sigma_2(.)$ with bounds $M_1$ and $M_2$, respectively, the constrained-input guidance law ensures an exponential convergence of the error, $d$, and its derivative, $\dot d$, to

Figures (13)

  • Figure 1: Illustration of 3D path following problem.
  • Figure 2: Illustration of planar path following problem.
  • Figure 3: Planar generic paths.
  • Figure 4: 3D generic paths.
  • Figure 5: UAV's performance: straight-line path.
  • ...and 8 more figures

Theorems & Definitions (9)

  • Definition 1
  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof