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Hybrid Feedback Control for Global Navigation with Locally Optimal Obstacle Avoidance in n-Dimensional Spaces

Ishak Cheniouni, Soulaimane Berkane, Abdelhamid Tayebi

TL;DR

The paper addresses safe, globally convergent autonomous navigation in $n$-dimensional space with multiple spherical obstacles by introducing a hybrid feedback controller that toggles between motion-to-destination and locally optimal obstacle-avoidance modes. The design ensures continuous velocity inputs, forward invariance of the obstacle-free space, and local optimality of avoidance maneuvers, while remaining implementable with range sensors in unknown environments. Theoretical results guarantee GAS to the destination and Zeno-free switching, complemented by sensor-based implementations, 2D/3D simulations, and real-world TurtleBot 4 experiments that demonstrate shorter, smoother trajectories relative to state-of-the-art reactive methods. The work significantly advances practical, scalable navigation in high dimensions, with potential extensions to non-spherical and more complex obstacle geometries.

Abstract

We present a hybrid feedback control framework for autonomous robot navigation in n-dimensional Euclidean spaces cluttered with spherical obstacles. The proposed approach ensures safe and global navigation towards a target location by dynamically switching between two operational modes: motion-to-destination and locally optimal obstacle-avoidance. It produces continuous velocity inputs, ensures collision-free trajectories and generates locally optimal obstacle avoidance maneuvers. Unlike existing methods, the proposed framework is compatible with range sensors, enabling navigation in both a priori known and unknown environments. Extensive simulations in 2D and 3D settings, complemented by experimental validation on a TurtleBot 4 platform, confirm the efficacy and robustness of the approach. Our results demonstrate shorter paths and smoother trajectories compared to state-of-the-art methods, while maintaining computational efficiency and real-world feasibility.

Hybrid Feedback Control for Global Navigation with Locally Optimal Obstacle Avoidance in n-Dimensional Spaces

TL;DR

The paper addresses safe, globally convergent autonomous navigation in -dimensional space with multiple spherical obstacles by introducing a hybrid feedback controller that toggles between motion-to-destination and locally optimal obstacle-avoidance modes. The design ensures continuous velocity inputs, forward invariance of the obstacle-free space, and local optimality of avoidance maneuvers, while remaining implementable with range sensors in unknown environments. Theoretical results guarantee GAS to the destination and Zeno-free switching, complemented by sensor-based implementations, 2D/3D simulations, and real-world TurtleBot 4 experiments that demonstrate shorter, smoother trajectories relative to state-of-the-art reactive methods. The work significantly advances practical, scalable navigation in high dimensions, with potential extensions to non-spherical and more complex obstacle geometries.

Abstract

We present a hybrid feedback control framework for autonomous robot navigation in n-dimensional Euclidean spaces cluttered with spherical obstacles. The proposed approach ensures safe and global navigation towards a target location by dynamically switching between two operational modes: motion-to-destination and locally optimal obstacle-avoidance. It produces continuous velocity inputs, ensures collision-free trajectories and generates locally optimal obstacle avoidance maneuvers. Unlike existing methods, the proposed framework is compatible with range sensors, enabling navigation in both a priori known and unknown environments. Extensive simulations in 2D and 3D settings, complemented by experimental validation on a TurtleBot 4 platform, confirm the efficacy and robustness of the approach. Our results demonstrate shorter paths and smoother trajectories compared to state-of-the-art methods, while maintaining computational efficiency and real-world feasibility.
Paper Structure (28 sections, 7 theorems, 44 equations, 16 figures, 3 tables, 2 algorithms)

This paper contains 28 sections, 7 theorems, 44 equations, 16 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions and Organization of the Paper
  5. Notations and Preliminaries
  6. Problem Formulation
  7. Main Results
  8. Control design
  9. Sets definition
  10. Motion-to-destination mode ($m=0$)
  11. Obstacle-avoidance mode ($m=\pm1$)
  12. Operation mode switching scheme
  13. Safety and stability analysis
  14. Continuity and optimality
  15. Sensor-Based Implementation
  16. ...and 13 more sections

Key Result

Lemma 1

Let $c,v_{-1},v_{1}\in\mathbb{R}^n$ such that $\angle(v_{-1},v_{1})=\psi$ where $\psi\in(0,\pi]$. Let $\varphi_{-1},\varphi_{1}\in[0,\pi]$ such that $\varphi_{-1}+\varphi_{1}<\psi<\pi-(\varphi_{-1}+\varphi_{1})$. Then

Figures (16)

  • Figure 1: (a) Example navigation scenario in a priori unknown environment, showing the robot's trajectory generated by the proposed hybrid feedback control approach (blue) compared to alternative methods. (b) Performance comparison highlighting the path length and computational efficiency of the proposed approach. The proposed approach generates paths similar to our previously proposed quasi-optimal (QO) approach Ishak2023 while avoiding the issue of undesired equilibria in QO approach. The details of this experiment are reported in Section \ref{['experimental_validation']}. The complete experiment can be visualized in the video available online https://youtu.be/KzUNLwQ5lMo.
  • Figure 2: 2D representation of the sets in Section \ref{['section:sets']}.
  • Figure 3: 2D illustration of the flow and jump sets for the motion-to-destination mode associated with obstacle $\mathcal{O}_k,\;k\in\mathbb{I}$.
  • Figure 4: Construction of the control in the obstacle-avoidance mode for a 2D case.
  • Figure 5: 2D illustration of the flow and jump sets for the obstacle-avoidance mode associated with obstacle $\mathcal{O}_k,\;k\in\mathbb{I}$.
  • ...and 11 more figures

Theorems & Definitions (12)

  • Lemma 1: HybBerkaneECC2019
  • Lemma 2
  • Lemma 3
  • proof
  • Theorem 1
  • proof
  • Lemma 4
  • proof
  • Proposition 1
  • proof
  • ...and 2 more