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Hybrid topology control: a dynamic leader-based distributed edge-addition and deletion mechanism

Kunal Garg, Xi Yu

Abstract

Coordinated operations of multi-robot systems (MRS) require agents to maintain communication connections to accomplish team objectives. However, maintaining the connections imposes costs in terms of restricted robot mobility, resulting in suboptimal team performance. In this work, we consider a realistic MRS framework in which agents are subject to unknown dynamical disturbances and experience communication delays. Most existing works on connectivity maintenance use consensus-based frameworks for graph reconfiguration, where decision-making time scales with the number of nodes and requires multiple rounds of communication, making them ineffective under communication delays. To address this, we propose a novel leader-based decision-making algorithm that uses a central node for efficient real-time reconfiguration, reducing decision-making time to depend on the graph diameter rather than the number of nodes and requiring only one round of information transfer through the network. We propose a novel method for estimating robot locations within the MRS that actively accounts for unknown disturbances and the communication delays. Using these position estimates, the central node selects a set of edges to delete while allowing the formation of new edges, aiming to keep the diameter of the new graph within a threshold. We provide numerous simulation results to showcase the efficacy of the proposed method.

Hybrid topology control: a dynamic leader-based distributed edge-addition and deletion mechanism

Abstract

Coordinated operations of multi-robot systems (MRS) require agents to maintain communication connections to accomplish team objectives. However, maintaining the connections imposes costs in terms of restricted robot mobility, resulting in suboptimal team performance. In this work, we consider a realistic MRS framework in which agents are subject to unknown dynamical disturbances and experience communication delays. Most existing works on connectivity maintenance use consensus-based frameworks for graph reconfiguration, where decision-making time scales with the number of nodes and requires multiple rounds of communication, making them ineffective under communication delays. To address this, we propose a novel leader-based decision-making algorithm that uses a central node for efficient real-time reconfiguration, reducing decision-making time to depend on the graph diameter rather than the number of nodes and requiring only one round of information transfer through the network. We propose a novel method for estimating robot locations within the MRS that actively accounts for unknown disturbances and the communication delays. Using these position estimates, the central node selects a set of edges to delete while allowing the formation of new edges, aiming to keep the diameter of the new graph within a threshold. We provide numerous simulation results to showcase the efficacy of the proposed method.
Paper Structure (12 sections, 1 theorem, 20 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 12 sections, 1 theorem, 20 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem formulation
  4. Proposed method
  5. Communication protocol
  6. Position estimation
  7. Cost estimation
  8. Decision-making
  9. Decision implementation
  10. New central node selection
  11. Simulation results
  12. Conclusions

Key Result

Theorem 1

Assume that the disturbance $d$ in eq: sys closed loop is uniformly bounded as $\|d(t, x)\|\leq d_M$ for all $t\geq 0$, $x\in \mathbb R^n$, for some $d_M\geq 0$. Let $e_d(t) \coloneq \|\phi_{i, 0}(t) - \phi_{i, d}(t)\|$. If $\phi_{i, 0}(0) = \phi_{i, d}(0) = x_{i, r}(0)$, then, under Assumption ass

Figures (3)

  • Figure 1: Hybrid topology control framework: the central node decides the edge to be deleted and the edge to be added to the base graph. Once the new graph is formed, a possibly new central node is chosen. The position uncertainties of each node for the central node are shown through dotted circles.
  • Figure 2: Position estimate, denoted as the shaded region, for 1-hop and 2-hop neighbors in the presence of time delays.
  • Figure 3: Simulation results for A: proposed method, B: centralized method with no delays and no diameter limit, C: centralized method with no diameter limits, and D: distributed method with fixed central node with 20 nodes. In each row, the left figure illustrates the final graph after 3000 iterations, and the right figure plots the number of edges in the graph and the number of stressed edges at each time step.

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • proof