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SwordRiding: A Unified Navigation Framework for Quadrotors in Unknown Complex Environments via Online Guiding Vector Fields

Xuchen Liu, Ruocheng Li, Bin Xin, Weijia Yao, Qigeng Duan, Jinqiang Cui, Ben M. Chen, Jie Chen

TL;DR

This work addresses real-time, robust quadrotor navigation in unknown, cluttered environments by introducing SwordRiding, an online guiding vector field framework built from discrete reference points embedded in an ESDF. The method incrementally constructs GVFs around a discretized trajectory and uses a B-spline-based optimization to generate a smooth, collision-free reference path, yielding a closed-loop navigation system that can adapt to disturbances such as wind or manual perturbations. Comprehensive simulations and real-world experiments demonstrate that the approach achieves real-time performance and enhanced robustness compared with traditional open-loop planners and fixed GVFs. The combination of online field construction, obstacle-aware guidance, and spline-based trajectory shaping provides a practical, flexible solution for high-degree-of-freedom aerial navigation in unknown environments.

Abstract

Although quadrotor navigation has achieved high performance in trajectory planning and control, real-time adaptability in unknown complex environments remains a core challenge. This difficulty mainly arises because most existing planning frameworks operate in an open-loop manner, making it hard to cope with environmental uncertainties such as wind disturbances or external perturbations. This paper presents a unified real-time navigation framework for quadrotors in unknown complex environments, based on the online construction of guiding vector fields (GVFs) from discrete reference path points. In the framework, onboard perception modules build a Euclidean Signed Distance Field (ESDF) representation of the environment, which enables obstacle awareness and path distance evaluation. The system first generates discrete, collision-free path points using a global planner, and then parameterizes them via uniform B-splines to produce a smooth and physically feasible reference trajectory. An adaptive GVF is then synthesized from the ESDF and the optimized B-spline trajectory. Unlike conventional approaches, the method adopts a closed-loop navigation paradigm, which significantly enhances robustness under external disturbances. Compared with conventional GVF methods, the proposed approach directly accommodates discretized paths and maintains compatibility with standard planning algorithms. Extensive simulations and real-world experiments demonstrate improved robustness against external disturbances and superior real-time performance.

SwordRiding: A Unified Navigation Framework for Quadrotors in Unknown Complex Environments via Online Guiding Vector Fields

TL;DR

This work addresses real-time, robust quadrotor navigation in unknown, cluttered environments by introducing SwordRiding, an online guiding vector field framework built from discrete reference points embedded in an ESDF. The method incrementally constructs GVFs around a discretized trajectory and uses a B-spline-based optimization to generate a smooth, collision-free reference path, yielding a closed-loop navigation system that can adapt to disturbances such as wind or manual perturbations. Comprehensive simulations and real-world experiments demonstrate that the approach achieves real-time performance and enhanced robustness compared with traditional open-loop planners and fixed GVFs. The combination of online field construction, obstacle-aware guidance, and spline-based trajectory shaping provides a practical, flexible solution for high-degree-of-freedom aerial navigation in unknown environments.

Abstract

Although quadrotor navigation has achieved high performance in trajectory planning and control, real-time adaptability in unknown complex environments remains a core challenge. This difficulty mainly arises because most existing planning frameworks operate in an open-loop manner, making it hard to cope with environmental uncertainties such as wind disturbances or external perturbations. This paper presents a unified real-time navigation framework for quadrotors in unknown complex environments, based on the online construction of guiding vector fields (GVFs) from discrete reference path points. In the framework, onboard perception modules build a Euclidean Signed Distance Field (ESDF) representation of the environment, which enables obstacle awareness and path distance evaluation. The system first generates discrete, collision-free path points using a global planner, and then parameterizes them via uniform B-splines to produce a smooth and physically feasible reference trajectory. An adaptive GVF is then synthesized from the ESDF and the optimized B-spline trajectory. Unlike conventional approaches, the method adopts a closed-loop navigation paradigm, which significantly enhances robustness under external disturbances. Compared with conventional GVF methods, the proposed approach directly accommodates discretized paths and maintains compatibility with standard planning algorithms. Extensive simulations and real-world experiments demonstrate improved robustness against external disturbances and superior real-time performance.

Paper Structure

This paper contains 23 sections, 1 theorem, 17 equations, 9 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Guiding Vector Field Approach
  3. Constructing Navigation via Guiding Vector Fields
  4. Insights on Tangential and Normal Components
  5. Incremental Guiding Vector Field Navigation
  6. Incremental Construction of Guiding Vector Fields
  7. Reference Trajectory Generation via Optimization
  8. Smoothness cost.
  9. Collision cost.
  10. Results
  11. System Overview
  12. Hardware Architecture
  13. Software Architecture
  14. Initialization Parameters
  15. Simulation Results
  16. ...and 8 more sections

Key Result

Lemma 1

Let $\mathcal{P} \subset \mathbb{R}^n$ be a smooth path, and suppose there exists a mapping operator $\Pi$ that assigns to each point $\xi \in \mathcal{P}$ a pair of normalized vectors $(\boldsymbol{t}(\xi),\boldsymbol{n}(\xi))$, with $\boldsymbol{t}(\xi)$ tangential to $\mathcal{P}$ and $\boldsymbo under standard smoothness and Lipschitz continuity assumptions on $\Pi$ and $k(\xi)$, the correspon

Figures (9)

  • Figure 1: (a) Open-loop architecture based on trajectory planning. (b) Closed-loop architecture based on guiding vector field.
  • Figure 2: Generation details of the incremental GVF method. Left: a quadrotor plans a feasible reference trajectory through the observed free space while avoiding known obstacles. Middle: the optimized trajectory is discretized into a finite set of path points, forming the trajectory space $\mathcal{P}$ embedded within the ESDF representation of the environment. Right: an incremental guiding vector field is synthesized around the discrete trajectory; the resulting field provides local flow directions that guide the robot smoothly along the reference path while ensuring obstacle avoidance.
  • Figure 3: Compact assembly and key component integration.
  • Figure 4: System overview: A: Hardware description. B: Localization and mapping module. C: Navigation module via online guiding vector fields. D: Control module via cascaded PID controller.
  • Figure 5: Simulation experiments: Scenario A: Navigating dense, irregular obstacles. A1: Overview of the flight path. A2-A6: Sequential details of the online vector field-guided planning and avoidance process from start to destination. Scenario B: Navigating a structured environment with rectangular pillars. B1 & B2: Overall flight path. B3 & B4: Zoomed-in views of quadrotor-pillar interactions.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Remark 1
  • Remark 2
  • Remark 3