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Resource-Aware Distributed Submodular Maximization: A Paradigm for Multi-Robot Decision-Making

Zirui Xu, Vasileios Tzoumas

TL;DR

This paper introduces the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination, and introduces the notion of Centralization Of Information among non-Neighbors (COIN).

Abstract

Multi-robot decision-making is the process where multiple robots coordinate actions. In this paper, we aim for efficient and effective multi-robot decision-making despite the robots' limited on-board resources and the often resource-demanding complexity of their tasks. We introduce the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination. Particularly, centralization favors globally near-optimal decision-making but at the cost of increased on-board resource requirements; whereas, decentralization favors minimal resource requirements but at a global suboptimality cost. All robots can thus afford our algorithm, irrespective of their resources. We are motivated by the future of autonomy that involves multiple robots coordinating actions to complete resource-demanding tasks, such as target tracking, area coverage, and monitoring. To provide closed-form guarantees, we focus on maximization problems involving monotone and 2nd-order submodular functions. To capture the cost of decentralization, we introduce the notion of Centralization Of Information among non-Neighbors (COIN). We validate our algorithm in simulated scenarios of image covering.

Resource-Aware Distributed Submodular Maximization: A Paradigm for Multi-Robot Decision-Making

TL;DR

This paper introduces the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination, and introduces the notion of Centralization Of Information among non-Neighbors (COIN).

Abstract

Multi-robot decision-making is the process where multiple robots coordinate actions. In this paper, we aim for efficient and effective multi-robot decision-making despite the robots' limited on-board resources and the often resource-demanding complexity of their tasks. We introduce the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination. Particularly, centralization favors globally near-optimal decision-making but at the cost of increased on-board resource requirements; whereas, decentralization favors minimal resource requirements but at a global suboptimality cost. All robots can thus afford our algorithm, irrespective of their resources. We are motivated by the future of autonomy that involves multiple robots coordinating actions to complete resource-demanding tasks, such as target tracking, area coverage, and monitoring. To provide closed-form guarantees, we focus on maximization problems involving monotone and 2nd-order submodular functions. To capture the cost of decentralization, we introduce the notion of Centralization Of Information among non-Neighbors (COIN). We validate our algorithm in simulated scenarios of image covering.
Paper Structure (11 sections, 4 theorems, 9 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 11 sections, 4 theorems, 9 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Distributed Submodular Maximization: A Multi-Robot Decision-Making Perspective
  3. Resource-Aware distributed Greedy ( RAG) Algorithm
  4. Computation, Communication, and Memory Requirements of RAG
  5. Approximation Guarantee of RAG: Centralization vs. Decentralization Perspective
  6. Centralization of Information: A Novel Quantification
  7. Approximation Guarantee of RAG
  8. Evaluation in Image Covering with Robots
  9. RAG vs. State of the Art
  10. The Trade-Off of Centralization vs. Decentralization
  11. Conclusion

Key Result

Proposition 1

Each agent $i$ performs $O(|\mathcal{V}_i||\mathcal{N}^-_i|)$ function evaluations during RAG.

Figures (7)

  • Figure 1: Venn-diagram definition of the set ${\@fontswitch\mathcal{N}}_i^c$ for agent $i \in {\@fontswitch\mathcal{N}}$.
  • Figure 2: Image Covering Setup. (a) A scenario; (b) Agent $i$ and its non-neighbors; (c) ${\smaller \sf coin}\xspace_i$'s upper bound for increasing agent $i$'s communication range.
  • Figure 3: Centralization vs. Decentralization: Resource requirements and coverage performance of RAG for increasing communication range, in an image covering scenario with $10$ robots in a $50\text{ points} \times 50$ points map.
  • Figure : (a) Image covering scenario in a $50\text{ points}$$\times 50$ points map with $10$ agents. The stars are agents' locations, the circles are agents' sensing ranges, and the dots covered points.
  • Figure : (a) Image covering scenario in a $50\text{ points}$$\times 50$ points map with $10$ agents. The stars are agents' locations, the circles are agents' sensing ranges, and the dots covered points.
  • ...and 2 more figures

Theorems & Definitions (17)

  • Remark 1: Resource-aware in-neighborhood selection based on information overlap
  • Remark 2: Resource-aware out-neighborhood selection
  • Definition 1: Normalized and Non-Decreasing Submodular Set Function fisher1978analysis
  • Definition 2: 2nd-order Submodular Set Function crama1989characterizationfoldes2005submodularity
  • Remark 3: Receding-Horizon Control, and Need for Minimal Communication and Computation
  • Remark 4: Directed and Disconnected Communication Topology
  • Proposition 1: Computation Requirements
  • Proposition 2: Communication Requirements
  • Proposition 3: Memory Requirements
  • Remark 5: Near-Minimal Resource Requirements
  • ...and 7 more