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Distributed Lloyd-Based algorithm for uncertainty-aware multi-robot under-canopy flocking

Manuel Boldrer, Vit Kratky, Viktor Walter, Martin Saska

Abstract

In this letter, we present a distributed algorithm for flocking in complex environments that operates at constant altitude, without explicit communication, no a priori information about the environment, and by using only on-board sensing and computation capabilities. We provide sufficient conditions to guarantee collision avoidance with obstacles and other robots without exceeding a desired maximum distance from a predefined set of neighbors (flocking or proximity maintenance constraint) during the mission. The proposed approach allows to operate in crowded scenarios and to explicitly deal with tracking errors and on-board sensing errors. The algorithm was verified through simulations with varying number of UAVs and also through numerous real-world experiments in a dense forest involving up to four UAVs.

Distributed Lloyd-Based algorithm for uncertainty-aware multi-robot under-canopy flocking

Abstract

In this letter, we present a distributed algorithm for flocking in complex environments that operates at constant altitude, without explicit communication, no a priori information about the environment, and by using only on-board sensing and computation capabilities. We provide sufficient conditions to guarantee collision avoidance with obstacles and other robots without exceeding a desired maximum distance from a predefined set of neighbors (flocking or proximity maintenance constraint) during the mission. The proposed approach allows to operate in crowded scenarios and to explicitly deal with tracking errors and on-board sensing errors. The algorithm was verified through simulations with varying number of UAVs and also through numerous real-world experiments in a dense forest involving up to four UAVs.

Paper Structure

This paper contains 11 sections, 2 theorems, 15 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Contribution and paper organization
  4. Problem description
  5. Proposed Approach
  6. Reshaping the cell geometry $\mathcal{V}_i$
  7. The weighting function $\varphi_i(q)$
  8. Dealing with dynamics and uncertainties
  9. Simulation results
  10. Experimental Results
  11. Conclusions

Key Result

Theorem 1

By imposing the control $\dot{p}_i(\mathcal{A}_i)$ in eq:lb, with $\mathcal{A}_i = \tilde{\mathcal{V}}_i^p \cap \tilde{\mathcal{V}}_i^o \cap \mathcal{S}_i$, collision avoidance is guaranteed at every instant of time.

Figures (8)

  • Figure 1: Deployment of the proposed algorithm in a real-world scenario with $3$ UAVs navigating in a forest.
  • Figure 2: (a) Representation of the Convex Weighted Voronoi Diagram (CWVD) $\mathcal{V}_i^p$ in \ref{['eq:cwvd']} with $\epsilon_p=2$ and $\epsilon_p=1$. Where the green circle is the i--th robot and the cyan circles represent the neighboring robots. (b) Example of $\mathcal{F}_i$ and $\mathcal{A}_i$ cell geometry with $\epsilon_p =\epsilon_o = 2$. Red solid lines indicate the proximity maintenance constraints. Obstacles are represented as grey circles, while the robots are depicted in cyan.
  • Figure 3: Dealing with uncertainties: (a) tracking error case, (b) measurement uncertainty case, (c) combined tracking error and measurement uncertainty. The robots are indicated with the cyan circles. We represent in light yellow the $\mathcal{F}_i$ set, in dark yellow the set $\mathcal{K}_i$, in green the set $\mathcal{Z}_i$, in blue the ellipse of uncertainty $\mathcal{E}_{i,j}$.
  • Figure 4: Simulation results with $N=9$ and $N=16$ robots, with $d_u=1.0$ (m). The images represent example scenarios used for generation of results presented in Table \ref{['tab:simulation']}. Colored circles represent the robots' positions at different time $t$. Red lines represent the proximity maintenance constraints between the robots. Black dots are the obstacles in the scene.
  • Figure 5: Distances between UAVs in the simulations in Figure \ref{['fig:sim']}a and \ref{['fig:sim']}b. The flocking and safety constraints are in magenta. Colored lines indicate the presence of an active flocking constraint between the two robots.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 1: Safety
  • proof
  • Theorem 2: Proximity maintenance or flocking constraint
  • proof
  • Remark 1: Tracking error and measurement uncertainties invariance property