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Collision Avoidance for Non-Cooperative Multi-Swarm Coverage Control with Bounded Disturbance Measurements

Karolina Schmidt, Luis Rodrigues

TL;DR

The paper addresses collision-free coverage by multiple non-cooperative swarms operating in shared spaces under bounded disturbance measurements. It extends the ORCA framework to account for measurement uncertainty via ellipsoidal bounds and Minkowski-sum techniques, ensuring safe velocities even with disturbances. A new multi-swarm coverage algorithm is proposed and demonstrated in 3D UAV/AUV scenarios, achieving locally optimal coverage while maintaining collision avoidance. The work provides formal collision guarantees and practical applicability to real-world, wind- or current-affected environments.

Abstract

This paper proposes a new algorithm for collision-free coverage control of multiple non-cooperating swarms in the presence of bounded disturbances. A new methodology is introduced that accounts for uncertainties in disturbance measurements. The proposed methodology is used to develop an algorithm that ensures collision-free motion in multi-swarm coverage control, specifically for cases where disturbances are present and their measurements are subject to bounded uncertainty. The theoretical results are validated through simulations of multiple swarms that independently aim to cover a given region in an environment with disturbances.

Collision Avoidance for Non-Cooperative Multi-Swarm Coverage Control with Bounded Disturbance Measurements

TL;DR

The paper addresses collision-free coverage by multiple non-cooperative swarms operating in shared spaces under bounded disturbance measurements. It extends the ORCA framework to account for measurement uncertainty via ellipsoidal bounds and Minkowski-sum techniques, ensuring safe velocities even with disturbances. A new multi-swarm coverage algorithm is proposed and demonstrated in 3D UAV/AUV scenarios, achieving locally optimal coverage while maintaining collision avoidance. The work provides formal collision guarantees and practical applicability to real-world, wind- or current-affected environments.

Abstract

This paper proposes a new algorithm for collision-free coverage control of multiple non-cooperating swarms in the presence of bounded disturbances. A new methodology is introduced that accounts for uncertainties in disturbance measurements. The proposed methodology is used to develop an algorithm that ensures collision-free motion in multi-swarm coverage control, specifically for cases where disturbances are present and their measurements are subject to bounded uncertainty. The theoretical results are validated through simulations of multiple swarms that independently aim to cover a given region in an environment with disturbances.
Paper Structure (10 sections, 7 theorems, 84 equations, 4 figures, 1 algorithm)

This paper contains 10 sections, 7 theorems, 84 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Energy-Efficient Coverage Control
  4. Optimal Reciprocal Collision Avoidance (ORCA)
  5. Proposed Method
  6. Disturbance and Measurement Uncertainty
  7. Collision Avoidance with Disturbance Measurements
  8. Application to Multi-Swarm Coverage Control
  9. Simulations
  10. Conclusions

Key Result

Theorem 1

(thesisschmidt, page 24) Consider two agents $A$ and $B$ traveling with velocities $v_A$ and $v_B$, respectively. Let both $v_A$ and $v_B$ be constant for a time horizon $\tau$. Then, $A$ and $B$ collide within the time horizon $\tau$ if and only if Therefore, $A$ and $B$ do not collide if and only if

Figures (4)

  • Figure 1: Geometry of $\mathcal{VO}_{AB}^{\tau}$, adapted from ORCA2011
  • Figure 2: Visualization of $\pi$
  • Figure 3: Positions of the agents of swarm 1 (S1) and swarm 2 (S2) (a) at the beginning and (b) after 5 seconds.
  • Figure 4: Volume of Voronoi cells of each agent (a) and distance between each pair of agents from different swarms (b)

Theorems & Definitions (9)

  • Definition 1
  • Theorem 1
  • Theorem 2
  • Corollary 1
  • Theorem 3
  • Corollary 2
  • Theorem 4
  • Corollary 3
  • Remark 1