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SwarmCVT: Centroidal Voronoi Tessellation-Based Path Planning for Very-Large-Scale Robotics

James Gao, Jacob Lee, Yuting Zhou, Yunze Hu, Chang Liu, Pingping Zhu

TL;DR

This work utilizes centroidal Voronoi tessellation to generate GCs methodically and demonstrates performance improvement while also ensuring consistency and reliability.

Abstract

Swarm robotics, or very large-scale robotics (VLSR), has many meaningful applications for complicated tasks. However, the complexity of motion control and energy costs stack up quickly as the number of robots increases. In addressing this problem, our previous studies have formulated various methods employing macroscopic and microscopic approaches. These methods enable microscopic robots to adhere to a reference Gaussian mixture model (GMM) distribution observed at the macroscopic scale. As a result, optimizing the macroscopic level will result in an optimal overall result. However, all these methods require systematic and global generation of Gaussian components (GCs) within obstacle-free areas to construct the GMM trajectories. This work utilizes centroidal Voronoi tessellation to generate GCs methodically. Consequently, it demonstrates performance improvement while also ensuring consistency and reliability.

SwarmCVT: Centroidal Voronoi Tessellation-Based Path Planning for Very-Large-Scale Robotics

TL;DR

This work utilizes centroidal Voronoi tessellation to generate GCs methodically and demonstrates performance improvement while also ensuring consistency and reliability.

Abstract

Swarm robotics, or very large-scale robotics (VLSR), has many meaningful applications for complicated tasks. However, the complexity of motion control and energy costs stack up quickly as the number of robots increases. In addressing this problem, our previous studies have formulated various methods employing macroscopic and microscopic approaches. These methods enable microscopic robots to adhere to a reference Gaussian mixture model (GMM) distribution observed at the macroscopic scale. As a result, optimizing the macroscopic level will result in an optimal overall result. However, all these methods require systematic and global generation of Gaussian components (GCs) within obstacle-free areas to construct the GMM trajectories. This work utilizes centroidal Voronoi tessellation to generate GCs methodically. Consequently, it demonstrates performance improvement while also ensuring consistency and reliability.
Paper Structure (19 sections, 39 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 19 sections, 39 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. General Form of Objective Function
  4. Brief Introduction of Wasserstein Metric
  5. Problem Formulation In Wasserstein-GMM Space
  6. Path Planning In Wasserstein-GMM Space
  7. Upper Bound of Objective Function
  8. Constrained Optimization in Wasserstein-GMM Space
  9. Gaussian Distribution Based Centroidal Voronoi Tessellation
  10. Traditional Centroidal Voronoi Tessellation
  11. Gaussian Distribution-based CVT
  12. Heuristic Approach for Gaussian-based CVT generation
  13. Numerical Implementation of CVT-Based Path Planning for VLSR Systems
  14. Construction of Gaussian Distribution-based Graph
  15. Path Planning in Gaussian Distribution-based Graph
  16. ...and 4 more sections

Figures (5)

  • Figure 1: The $K=100$ CVT regions are generated with traditional CVT in (a), and the heuristic Gaussian-based CVT result is shown in (b). The blue circles in (b) represent the 95% Gaussian distribution confidence level, and the black polygons are the obstacles in the region.
  • Figure 2: An example graph visual representation generated by swarmCVT (a) and swarmPRM (b) in a region with 500 GCs, where the node is represented by the mean of $\mathbf{G}$, and the line connecting them are $\mathcal{E}$
  • Figure 3: VLSR system must travel from the initial distribution in (a) to the target distribution in (b), avoiding obstacles shown as polygons filled in black. Both the X and Y axes are measured in (km).
  • Figure 4: Extensive comparison between swarmCVT and swarmPRM on (a) all robot average distance traveled, (b) PDF $W_2$ distance displacement, (c) time spent, and (d) energy cost under the different number of Gaussian components generated in the ROI. Each metric is simulated ten times for each value of $K$ Gaussian component.
  • Figure 5: VLSR trajectories from the initial (circles) to target (triangles) obtained by (a) swarmCVT-I, (b) ADOC, (c) swarmCVT-II, and (d) swarmPRM methods.