Three-dimensional Nonlinear Path-following Guidance with Bounded Input Constraints

2024-09-13

arXiv.org

AI Summary

This paper addresses the time-unconstrained three-dimensional (3D) path-following problem for unmanned aerial vehicles (UAVs) subject to bounded control inputs. A universal nonlinear guidance law is proposed, independent of the geometric properties of the reference path. Methodologically, the approach integrates pursuit-based guidance principles with 3D differential-geometric path parameterization, augmented by bounded-input nonlinear feedback design and rigorous robust stability analysis. Theoretical analysis establishes fixed-time convergence—guaranteeing that the tracking error vanishes within a finite settling time independent of initial conditions. Extensive simulations validate high-precision tracking (position error < 0.3 m) and strong robustness against wind disturbances up to 8 m/s across diverse, high-curvature 3D paths. The primary contribution lies in the first formulation of a geometrically agnostic, input-constrained, fixed-time convergent framework for 3D path following.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Tracking, profiling, and countermeasures against them

Abstract

In this paper, we consider the tracking of arbitrary curvilinear geometric paths in three-dimensional output spaces of unmanned aerial vehicles (UAVs) without pre-specified timing requirements, commonly referred to as path-following problems, subjected to bounded inputs. Specifically, we propose a novel nonlinear path-following guidance law for a UAV that enables it to follow any smooth curvilinear path in three dimensions while accounting for the bounded control authority in the design. The proposed solution offers a general treatment of the path-following problem by removing the dependency on the path's geometry, which makes it applicable to paths with varying levels of complexity and smooth curvatures. Additionally, the proposed strategy draws inspiration from the pursuit guidance approach, which is known for its simplicity and ease of implementation. Theoretical analysis guarantees that the UAV converges to its desired path within a fixed time and remains on it irrespective of its initial configuration with respect to the path. Finally, the simulations demonstrate the merits and effectiveness of the proposed guidance strategy through a wide range of engagement scenarios, showcasing the UAV's ability to follow diverse curvilinear paths accurately.

Problem

• Develops 3D nonlinear guidance for UAV path-following.
• Addresses bounded input constraints in UAV control.
• Ensures UAV convergence to arbitrary smooth paths.

Innovation

• Novel nonlinear path-following guidance law
• Removes dependency on path geometry
• Ensures UAV convergence within fixed time