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Polygonal Cone Control Barrier Functions (PolyC2BF) for safe navigation in cluttered environments

Manan Tayal, Shishir Kolathaya

TL;DR

The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments.

Abstract

In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning algorithms, they often face challenges in convergence rates and handling dynamic infeasibilities. Alternative techniques like collision cones struggle to accurately represent complex obstacle geometries. This paper introduces a novel category of control barrier functions, known as Polygonal Cone Control Barrier Function (PolyC2BF), which addresses overestimation and computational complexity issues. The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments. The efficacy of this approach is further demonstrated through PyBullet simulations on quadruped (unicycle model), and crazyflie 2.1 (quadrotor model) in cluttered environments.

Polygonal Cone Control Barrier Functions (PolyC2BF) for safe navigation in cluttered environments

TL;DR

The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments.

Abstract

In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning algorithms, they often face challenges in convergence rates and handling dynamic infeasibilities. Alternative techniques like collision cones struggle to accurately represent complex obstacle geometries. This paper introduces a novel category of control barrier functions, known as Polygonal Cone Control Barrier Function (PolyC2BF), which addresses overestimation and computational complexity issues. The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments. The efficacy of this approach is further demonstrated through PyBullet simulations on quadruped (unicycle model), and crazyflie 2.1 (quadrotor model) in cluttered environments.
Paper Structure (6 sections, 2 theorems, 20 equations, 6 figures)

This paper contains 6 sections, 2 theorems, 20 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Polygonal Cone Control Barrier Functions (PolyC2BF)
  4. Polygonal Cone CBF (PolyC2BF)
  5. Simulations
  6. Conclusions

Key Result

Theorem 1

The proposed CBF candidate eqn:PolyC3BF with $p_{\rm{rel}},v_{\rm{rel}}$ defined by eq:positionvectorunicycle, eq:velocityvectorunicycle is a valid CBF defined for the set $\mathcal{D}$.

Figures (6)

  • Figure 1: Disadvantages of Collision Cones: Collision Avoidance in cluttered environment (left) and against a long wall (right)
  • Figure 2: Polygonal Collision Cone using vertices of the polygonal obstacles
  • Figure 3: Construction of Polygonal Cone to avoid polygonal obstacle
  • Figure 4: Construction of Polygonal Cone for an Aerial Vehicle
  • Figure 5: Navigation in a cluttered environment using PolyC2BF in case of Quadruped
  • ...and 1 more figures

Theorems & Definitions (8)

  • Definition 1: Extended class-$\mathcal{K}$ functions
  • Definition 2: Control barrier function (CBF)
  • Definition 3: Collision Cone CBFs C3BF-UGVC3BF-UAV
  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof