在今日快速發展的世界中，多機器人系統已經成為引人矚目的話題，多機器人系統的潛力在於提高效率和韌性。多機器人系統的關鍵問題通常圍繞著任務分配和路徑規劃。然而，大多數研究論文通常僅專注於其中一個問題，而忽略同時處理這兩個關鍵問題。在本論文中，我專注於多機器人的取貨和送貨問題，該問題屬於任務分配的一個子領域。本研究提出一種方法，透過在分派任務給機器人時納入衝突避免機制，來應對取貨和送貨問題。

為了解決這一問題，我採用了基於拍賣的分散式方法作為核心框架。我提出了一種全新的出價策略，其中任務的出價是通過計算執行該任務的時間與不執行該任務的時間進行評估，而路徑的出價是相關任務的出價的平均值。為了計算機器人的最佳路徑，我結合了混合整數線性規劃方法和A*演算法。最終，我成功分配了八個任務並為在一個13x11單位的網格環境中運作的八個機器人生成了無衝突的路徑。

展望未來，我認為還有充分的空間進一步研究系統的探索能力，以發現更高效的解決方案。這個研究方向有潛力在各種現實場景中實現多機器人系統性能的顯著改進。

In today's rapidly evolving world, multi-robot systems have garnered significant attention due to their potential to enhance efficiency and robustness across various domains. Challenges within multi-robot systems revolve around task allocation and path planning, both of which are critical components for optimizing resource utilization. Surprisingly, many research papers have historically treated task allocation and path planning as distinct problems, with limited focus on addressing them simultaneously. In this paper, I hone in on the multi-robot pickup and delivery problem, a branch of task allocation, and propose a method to tackle the pickup-and-delivery problem by incorporating conflict avoidance mechanisms while assigning tasks to agents.

My approach centers on a decentralized auction-based method as the core framework, offering an effective means of resolving task allocation. I introduce a novel bidding strategy where a task's bid is computed by quantifying the time required to complete it with and without the task, while path bids are derived by averaging the bids of associated tasks. To compute optimal robot paths, I deploy a mixed-integer linear programming approach in tandem with A* algorithms. In the end, I successfully assign eight tasks and generate conflict-free paths for eight robots operating in a grid-based environment measuring 13 by 11 units.

Looking ahead, I believe that there is ample room for further research aimed at enhancing the system's exploratory capabilities to uncover even more efficient solutions. This avenue of inquiry has the potential to lead to substantial improvements in the performance of multi-robot systems in diverse real-world scenarios.

摘要i
誌謝iii
Abstract v
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Background Knowledge and Literature Survey 7
2.1 Task Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Path Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Proposed Algorithm 17
3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Pickup and Delivery Allocation Considering Path Planning . . . . . . . . . . . 18
3.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Bundle Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Reach Consensus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.4 Path Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Task Execution Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.4 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Simulation Results and Comparison 35
4.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Simulation Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 Conclusion and Future Works 45
References 47

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