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On Controlling Swarm of Moving Agents

On Controlling Swarm of Moving Agents

SIG-FPAI, Mar. 2021, invited talk
https://sig-fpai.org/past/fpai116.html

More Decks by Keisuke Okumura | 奥村圭祐

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Transcript

  1. /123 2 東京工業大学 情報理工学院 博士課程 (2020-,指導教員: Defago Xavier教授) 学振DC1/吉田育英会 ドクター21

    Keisuke Okumura | 奥村圭祐 @_kei18 興味があること 移動エージェント群を大規模に操りたい Multi-Agent Planning / Multi-Robot Coordination / Distributed Algorithms 分野としては? => AI & Robotics - IJCAI / AAAI / ICAPS / AAMAS - ICRA / IROS
  2. /123 4 objective-1 Representation objective-2 Planning Who Plans? Huge Search

    Space Common Knowledge? Cooperation? (increased) Uncertainty Execution Multi-Agent Planning & Execution
  3. /123 5 本日の構成 Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存なな実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  4. /123 8 応用例 YouTube/Mind Blowing Videos Twitter/@knaohiro1 YouTube/StarCraft 倉庫の荷物運搬 [Wuman+

    AI Magagine-08] 航空機の牽引計画 [Morris+ AAAI Workshop-16] 自動駐車 [Okoso+ ITSC-19] ロボットのパターン形成 [Li+ AAMAS-20] 自動運転・交差点の管理 [Dresner&Stone JAIR-08] ビデオゲーム [Silver AIIDE-05] ロボットサッカー [MacAlpine AAAI-15]
  5. /123 9 cooperative pathfinding multi-robot path planning multi-agent path planning

    multi-agent pathfinding ≠ multi-robot motion planning 日本語だと “マルチエージェント経路計画” ? Robotics の人たち AI の人たち 名称
  6. /123 10 目的関数 length: k ring makespan: k+1, sum-of-costs: 2k+3

    時計回り makespan: k+2, sum-of-costs: k+6 反時計回り k > 3 で同時最適化は不可 [Yu&LaValle AAAI-13] 例. 1. last arrival time (aka. makespan) 2. total arrival time (aka. sum-of-costs, flowtime) 3. total distance メジャー 4. max distance
  7. /123 11 複雑性の解析 - 最適化 makespan, sum-of-costs, total distance の最小化は

    NP 困難 [Surynek AAAI-10, Yu&LaValle AAAI-13, Ma+ AAAI-16] 平面グラフ下で makespan, sum-of-costs, total distance, max distance の最小化は NP 困難 [Yu RA-L-15 ] グリッド下で makespan, sum-of-costs の最小化は NP 困難 [Banfi+ RA-L-17] makespan 最小化に関して 4/3 以下の近似解を得ることは NP 困難 [Ma+ AAAI-16] *証明は 3-SAT からの帰着より
  8. /123 12 複雑性の解析 - 実行可能解 有向グラフでは実行可能解を求めること自体が NP 困難 [Nebel ICAPS-20]

    無向グラフでは pebble motion problem の解析より 解があれば O(n^3) 回の動きの実行可能解を生成できる [Kornhauser 84, Röger&Helmert SoCS-12] n: ノード数, タイト 多項式時間で解ける 証明は 3-SAT からの帰着より (綺麗) wikipedia c.f., 15パズルの 最短手数の求解は NP 困難 [Ratner&Warmuth AAAI-86]
  9. /123 15 優先順位付き経路計画: Prioritized Planning シンプル, 速い, そこそこ良い解, 実用的, しかし不完全

    エージェントに優先順位を割当てる 1. 優先順位順に一台ずつ経路計画 自身より高い優先順位をもつエージェントの経路との衝突を避ける 2. どんな順序付けでも解けない 代表例: HCA*: Hierarchical Cooperative A* [Silver AIIDE-05] 衝突を無視した最短経路長 (A* を階層的に利用 )をヒューリスティックとして使用 部分的に利用されることも多い [Wang&Botea JAIR-11, Bnaya&Felner ICRA-14] 準最適・不完全・高速 オリジナル? [Erdmann&Lozano-Perez Algorithmica-87]
  10. /123 16 優先順位の割当の工夫 総当り, 山登り法, ヒューリスティック, 再割当て, 割当自体を探索, etc [Azarm&Schmidt

    ICRA-97, Bennewitz+ Robotics-02, Van Den Berg&Overmars ICRA-05, Andreychuk&Yakovlev AAMAS-18, Ma+ AAAI-19] RPP: Revisit Prioritized Planning [Cap+ T-ASE-15] well-formed なインスタンスであれば完全性を保証 優先順位付き経路計画のチップス 分散的なプランニングとの相性が良い [Velagapudi+ IROS-10, Cap+ T-ASE-15] well-formed ill-formed 他エージェントのスタート・ゴールを 通らない経路が少なくとも一つは存在する
  11. /123 17 ルールベース 二重連結グラフのループ分解を利用: BIBOX [Surynek ICRA-09, Surynek FLAIRS-09] 強連結・二重連結な有向グラフへの拡張

    [Botea&Surynek AAAI-15] 準最適・完全・超高速 グラフを抽象化, いくつかのコンポーネントに分解 [Ryan JAIR-08] 全域木の利用 [Peasgood T-RO-08] Push&Swap, Push&Rotate [Luna&Bekris IJCAI-11, de Wilde+ AAMAS-13] プッシュ操作でエージェントを1台ずつゴールに向かって動かす 必要に応じてスワップ操作で2台のエージェントの位置を入れ替える 次数≥3のノード +空の隣接ノードx2 発展: 並列実行 [Sajid+ SoCS-12], 分散実行 [Wiktor+ IROS-14, Wei+ IEA/AIE-14, Zhang+ DARS-16, Wang&Rubenstein RA-L-20] TASS: Tree-based Agent Swapping Strategy [Khorshid+ SoCS-11] も同じようなアイデア
  12. /123 18 還元ベース 最適・完全 よく知られている問題へ変換して汎用ソルバで解く CSP: 制約充足問題 [Ryan ICRA-10] SAT:

    充足可能性問題 [Surynek PRICAI-12, Surynek+ ECAI-16] ILP: 整数計画問題 [Yu&LaValle T-RO-16] ASP: 解集合プログラミング [Erdem+ IJCAI-13]
  13. /123 19 探索ベース 最適・完全 素朴な考え: A* を適応させる 1つの探索ノードを { すべてのエージェントの位置

    } に対応させればいい ただし探索空間が大きすぎて手に負えない Operator Decomposition 中間状態の導入で枝刈り & Independent Detection エージェントのサブセット (最初は1台) に対してソルバをあてる 衝突が検出されたらサブセット同士をマージ [Standley AAAI-10] MAPF 研究の火付け役
  14. /123 20 ICTS: Increasing Cost Tree Search [Sharon+ AIJ-13] EPEA*:

    Enhanced Partial Expansion A* [Goldenberg+ JAIR-14] M* (subdimensional expansion) [Wagner&Choset AIJ-15] その後 現時点で最も研究されている & 使い勝手がいいのが CBS: Conflict-based Search [Sharon+ AIJ-15] などが提案される SOTA は BCP: Branch-and-Cut-and-Price [Lam+ IJCAI-19, Lam&Le Bodic ICAPS-20] 300 エージェントくらいまでなら解ける 次ページ参照
  15. /123 21 CBS: Conflict-based Search[Sharon+ AIJ-15] 最適解! cost: 5 各エージェントが

    “いつ・どこ” を使っていけなのかを探索する 2段階の探索 constraint tree の構築 high-level: low-level: 制約に従う最短経路を探索 t=1 cost: 5 replan stay t=1 cost: 6 replan t=1 t=2 stay cost: 6 replan t=1 t=2 stay cost: 6 replan 衝突の優先順位付け [Boyarski+ IJCAI-15, Boyarski+ AAAI-21] 許容可能なヒューリスティック [Felner+ ICAPS-18, Li+ IJCAI-19] 遅延評価 [Gange+ ICAPS-19] 対称性の解消 [Li+ AAAI-19, Li+ ICAPS-20] 反復深化 [Boyarski+ IJCAI-20] ML とのハイブリッド [Huang+ AAAI-21] 有界準最適ソルバの開発 (E)ECBS [Barer+ SoCS-14, Li+ AAAI-21a] パワフルな拡張が存在, e.g., 他にもたくさんある… 🤔
  16. /123 22 Multi-agent RTT*: サンプリングベース [Čáp+ AAMAS-13] ノードにアノテーションしてエージェントが進むべき方向性をつくる [Wang&Botea ICAPS-08,

    Jansen&Sturtevant AIIDE-08, Cohen+ IJCAI-16] 衝突回避パターンを事前に作っておく [Han&Yu RA-L-20] 深層学習でいい感じの動きを学習させて分散実行 [Sartoretti+ RA-L-19, Damani+ RA-L-21, Li+ IROS-20] 探索ベースの制約を徐々に厳しくすることで Anytime MAPF を実現 [Standley&Korf IJCAI-11, Cohen+ IJCAI-18, Vedder&Biswas AIJ-21] その他のアプローチ などなど
  17. /123 24 Unlabeled/Anonymous MAPF given agents (starts) graph targets solution

    paths without collisions target assignment *実行可能解が常に存在 [Kornhauser 84, Yu&LaValle WAFR-13, Adler+ WAFR-15, Ma+ AAAI-16]
  18. /123 25 Unlabeled/Anonymous MAPF makespan 最適化は最大フロー問題への還元により多項式時間で解ける?! [Yu&LaValle WAFR-13] unlabeled-MAPF インスタンス

    source sink t=0 t=1 time expanded networkに変換 辺の 容量は すべて1 例えば Ford-Fulkerson のアルゴリズムで最大フロー問題を解くと O( エージェント数 x ノード数 x メイクスパン) 最大フロー: 1 実行可能解がない source sink t=0 t=1 t=2 最大フロー: 2 makespan最適な解
  19. /123 26 MAPD: Multi-agent Pickup & Delivery delivery loc. pickup

    loc. given agents graph package 倉庫の荷物運搬を模した問題設定 [Ma+ AAMAS-17] solution paths without collisions task assignment もともとはオンラインの設定だがオフラインの設定も [Liu+ AAMAS-19]
  20. /123 27 Online MAPF [Švancara+ AAAI-19] given agents (出現・消失あり) graph

    goals solution paths without collisions appear => replanning *複雑性の解析 [Ma ICAPS-21] エージェントが動的に出入り
  21. /123 28 大きいエージェント [Thomas+ Intell. Syst.-15, Li+ AAAI-19, Atzmon+ SoCS-19]

    Any-angle MAPF [Yakovlev&Andreychuk ICAPS-17] Multi-Goal MAPF [Surynek AAAI-21] その他の変種たち (un)-labeled MAPFを 一般化: TAPF [Ma+ AAMAS-16] エージェントの遅延に ある程度はロバストな MAPF [Atzmon+ JAIR-20, Atzmon+ ICAPS-20, Shahar+ JAIR-21] 1 2 1, 2 3 4 delay 移動時間に確率を導入 [Peltzer+ CoRR-19] MAPFR : 辺に重みを導入 [Walker+ IJCAI-18] 3 2 連続時間: Continuous MAPF [Andreychuk+ IJCAI-19, Surynek WoMAPF-20, Andreychuk+ AAAI-21] などなど
  22. /123 30 MAPF-POST[Hönig ICAPS-16] 2 moves 2 moves +1 turn

    model: execution: 実ロボットの挙動を無視 MAPF plan を後処理 運動学的制約を満たすスケジュールを生成 A B C D E B C F C D 時間的依存関係を抽出 A B C D E B C F C D 5 0 0 16 25 32 48 29 33 64 最短実現時間を求める E D A B B C … 0 0 0 0 -1 ∞ -2 -1 0 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0 0 -4 -8 -4 ∞ 距離グラフに変換 E D A B B C … [1,∞] source sink [0,0] [0,0] [1,∞] [2,∞] [8,∞] [4,∞] [4,∞] [0,∞] [0,∞ ] [0,∞ ] 動作に要する時間をアノテーション c.f., STN: simple temporal network [Dechter+ AIJ-91] 動作に要する [最小時間, 最大時間] t=1 t=2 t=3 t=4 t=0 入力: MAPF plan A B C F D E
  23. /123 31 Execution Policy[Ma+ AAAI-17] Fully Synchronized Policies Minimum Communication

    Policies wait 時間的依存関係をチェック 1 2 1 2 3 4 => 保持, GO arrival time: 3 arrival time: 2 *あとで重要 1 2 1 2 3 4 Planning Execution 実行時のロボット通信を仮定 いかなる遅延に対しても MAPF plan の実行を保証
  24. /123 33 そのほか個人的ピックアップ 利己的なエージェント [Bnaya SoCS-13] 環境もプランニングの対象にしてしまう [Bellusci+ AAMAS-20] 説明可能な

    MAPF [Almagor&Lahijanian, AAMAS-20] 組合せオークションとの融合 [Amir+ AAAI-15] あと船のモデルとか…(即座に止まれない) Algorithm Selection: MAPF インスタンスの特徴を学習, 適切なソルバを選択 [Kaduri+ ICAPS-20, Ren+ AAMAS-21]
  25. /123 35 本日の構成 Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存な実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  26. /123 36 MAPF を柔軟に解くアルゴリズム Priority Inheritance with Backtracking for Iterative

    Multi-agent Path Finding Keisuke Okumura, Manao Machida, Xavier Défago & Yasumasa Tamura IJCAI-19
  27. /123 37 最適化はNP困難 [Surynek AAAI-10, Yu&LaValle AAAI-13, Yu RA-L-15, Ma+

    AAAI-16, Banfi+ RA-L-17] 許容できる時間でなるべく効率的な解を求める 柔軟なアルゴリズムを設計できないだろうか? 狙い +できれば分散化もしたい +エージェント間の交渉はなるべく局所的に 実用では繰り返し&オンライン・リアルタイムで 大規模な問題を解く必要あり [Ma+ AAMAS-17, Svancara+ AAAI-19]
  28. /123 38 PIBT Priority Inheritance with Backtracking [Okumura+ IJCAI-19] 繰り返し

    MAPF を解く 高速 & スケーラブル 分散化との相性◦ 500 agents within 50ms Applicable to Multi-agent Pickup & Delivery [Ma+ AAMAS-17] 準最適
  29. /123 39 locations at t=1 t=2 t=3 repeat one-timestep prioritized

    planning high low mid How PIBT works – 1/8 … 1 2 3 4 5 6 7 8 9 decision order time-window
  30. /123 41 How PIBT works – 3/8 high low mid

    as high priority inheritance [Sha+ IEEE Trans Comput-90]
  31. /123 42 high low mid How PIBT works – 4/8

    1 3 2 decision order … …
  32. /123 43 How PIBT works – 5/8 high as high

    as high as high as high stuck
  33. /123 44 How PIBT works – 6/8 invalid valid re-plan

    re-plan valid You can move invalid You must re-plan, I will stay introduce backtracking
  34. /123 45 Proof sketch. highest as high as high このサイクルは必ず探索される

    すべての隣接ノードを探索 次に行きたい場所 サイクルの 最後のノード invalid valid ローテーションは常に成功! How PIBT works – 7/8 現在地 補題: 二重連結グラフ等では最高優先順位のエージェントが任意の隣接ノードに移動可能
  35. /123 46 補題: 二重連結グラフ等では最高優先順位のエージェントが任意の隣接ノードに移動可能 How PIBT works – 8/8 定理:

    (reachability) すべてのエージェントが有限時間で目的地に到達する +動的な優先順位割当 まだゴールに到着していないエージェントが高い優先度をもつようにする いつか最高優先順位をもつ => 補題の適用
  36. /123 48 One-shot MAPF lak503d (194x194) 25 repetitions timeout: 60sec

    sum-of-costs: RPP ECBS << PIBT <<<< Push&Swap makespan: PIBT << RPP ECBS <<<< Push&Swap runtime: PIBT Push&Swap << RPP << ECBS code: https://kei18.github.io/mapf-IR/ agents sum-of-costs / lower bound makespan / lower bound agents success rate (%) within 60 sec runtime (sec) PIBT [Okumura+ IJCAI-19] ECBS [Barer+ SoCS-14] Push&Swap [Luna&Bekris IJCAI-11] RPP [Cap+ T-ASE-15] prioritized planning rule-based search-based sub-opt. 1.05
  37. /123 49 MAPD: Multi-Agent Pickup & Delivery (task) frequency service

    time TP [Ma+ AAMAS-17] PIBT [Okumura+ IJCAI-19] runtime (sec) 50 agents 500 tasks 100 repetitions PIBT のタスク割当: フリーのエージェントは一番近いタスクに向かう (PIBT は MAPD を必ず解くことを保証)
  38. /123 51 ハイライト – PIBT PIBT: Priority Inheritance with Backtracking

    繰返し・オンラインの状況で大規模に使える なるべく分散化・局所化できそうなアルゴリズムが欲しい 狙い 手法 ターゲット MAPF-like な問題設定 課題 経路の効率向上, c.f., 次のトピック ちゃんと分散化する, c.f., 次の次のトピック
  39. /123 53 本日の構成 Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存な実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  40. /123 54 MAPF に対する逐次改善法 Iterative Refinment for Real-Time Multi-Robot Path

    Planning Keisuke Okumura,Yasumasa Tamura & Xavier Défago under review, available at arXiv
  41. /123 55 実用では繰り返し&オンライン・リアルタイムで 大規模な問題を解く必要あり [Ma+ AAMAS-17, Svancara+ AAAI-19] 準最適解なら即座に得られる e.g.,

    [Wang&Botea ICAPS-08, Surynek ICRA-09, Luna&Bekris IJCAI-11, de Wilde+ AAMAS-13, Okumura+ IJCAI-19] 狙い 限られた時間で 解を返すこと + 準最適解を逐次的に改善するのが妥当なアプローチなのでは? いわゆる anytime プランニング にもなる 最適化はNP困難 [Surynek AAAI-10, Yu&LaValle AAAI-13, Yu RA-L-15, Ma+ AAAI-16, Banfi+ RA-L-17]
  42. /123 57 アドホックなルールで修正 [Surynek IJAIT-13] サーチベースのソルバの制約を徐々に厳しくする [Standley&Korf IJCAI-11, Cohen+ IJCAI-18,

    Vedder&Biswas AIJ-21] そもそも初期解得られないかも… 事前にわかっているパターンしか修正できない
  43. /123 59 エージェントのサブセット M を何らかのルールでピックアップ A. M 外のエージェントの経路を固定しながら, M 内に対する部分問題を最適

    MAPF ソルバで解いて解を置き換える B. 2. 以下をひたすら繰り返す コンセプト 1. 準最適 MAPF ソルバで解を得る * M={ すべてのエージェント } としない限り局所解は存在する オリジナルと比較して小さい問題を解くことに => 高速に解の改善が可能
  44. /123 61 アドホックな例: focusing-at-goals original plan refined plan -2 cost

    (お気持ち) あるエージェントが目的地に早く到達することを 妨害しているエージェント群を抽出したい M = { i の目的地を時刻 t で使用しているエージェント, i の理想コスト ≤ t ≤ 実コスト } 非効率な解に対して効果的
  45. /123 62 アグレッシブな例: using-MDD ある程度効率的な解に対して効果的 Multi-valued Decision Diagram [Srinivasan+ ICCAD-90]

    t=0 t=1 t=2 t=3 t=2 までの の MDD t=3までの の MDD stay の経路で のMDD が 更新されたら経路同士が 干渉していることがわかる M = { i の時刻 t までの MDD を 更新するエージェント, i の理想コスト ≤ t < 実コスト } (お気持ち) あるエージェントが目的地に早く到達することを 妨害しているエージェント群を抽出したい 無効な MDD に!
  46. /123 63 いいとこどり: composition ある程度効率的な解に対して効果的 using-MDD 非効率な解に対して効果的 focus-at-goals e.g., focusing-at-goals

    => using-MDD => random 組合わせればいいのでは? (スイッチングは改善の見込みが立たなくなったとき) *他にも色々なルールあり+ありそう
  47. /123 64 Example planning time (sec) cost / lower bond

    random-64-64-20, 300 agents initial solver: PIBT+ (43ms) optimal solver: ICBS [Boyarski+ IJCAI-15] refine rule: composition
  48. /123 65 v.s. Optimal Solutions 1.00 1.05 1.10 1.15 1.20

    1.25 1.00 1.05 1.10 1.15 1.20 1.25 50 instance 50 instance cost / optimal cost init ≤ 3ms 0.1s 1.0s 30 agents random-32-32-20 50 agents random-32-32-10 obtained by CBSH [Li+ IJCAI-19] 740ms for 30 agents, 1743ms for 50 agents initial solver: PIBT+ refine rule: composition refinement solver: ICBS refinement timeout: 100ms
  49. /123 66 v.s. Anytime MAPF Solver initial solver: PIBT+ refine

    rule: composition refinement solver: ICBS refinement timeout: 100ms Iterative Refinement Anytime Focal Search [Cohen+ IJCAI-18] 50 agents 70 agents 90 agents 0 2 4 6 8 10 0 1 2 runtime (sec) sum-of-cost random-32-32-20
  50. /123 67 with Different Initial Solvers refine rule: composition refinement

    solver: ICBS refinement timeout: 500ms 0 10 20 30 40 50 60 70 80 90 1.0 1.1 1.2 runtime (sec) cost / lower bound 300 agents random-64-64-20 PIBT+ WHCA* [Silver AIIDE-05] HCA* [Silver AIIDE-05] ECBS [Barer+ SoCS-14] RPP [Cap+ T-ASE-15] not so different
  51. /123 68 ハイライト – Iterative Refinement 既存の MAPF ソルバの組合せで良い近傍解を得る 1.

    準最適ソルバで初期解を得る 2. 最適ソルバを部分問題にあてて逐次改善 準最適解を逐次的に改善したい 狙い 手法 ターゲット MAPF をリアルタイムで解きたい状況 課題 修正セット M の選択手法の改善, e.g., ML ベース ≥1000 エージェントでも充分に動くがもっと改善できそう
  52. /123 69 本日の構成 Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存な実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  53. /123 70 Time-Independent Planning for Multiple Moving Agents Keisuke Okumura,

    Yasumasa Tamura & Xavier Défago AAAI-21 タイミング非依存な実行ポリシー
  54. /123 71 Planning 1 2 1 2 3 4 Execution

    エージェントが同期的に動くことを仮定
  55. /123 72 不完全な実行 1 2 1 2 3 4 delay

    リアリティギャップ 現実は非同期
  56. /123 73 ロバストな実行ポリシー [Ma+ AAAI-17] Fully Synchronized Policies Minimum Communication

    Policies wait 時間的依存関係をチェック 1 2 1 2 3 4 => 保持, GO arrival time: 3 arrival time: 2
  57. /123 75 1 2 1 2 3 4 1 2

    3 4 5 6 delay 遅延が伝搬 典型的な MAPF (遅延なし) 60 agents, solved by PIBT 予期せぬことが起きる可能性大
  58. /123 76 代替手法の提案: Time-Independent Planning time-independent model を定義: 現実を状態遷移系としてモデリング Causal-PIBT:

    PIBT [Okumura+ IJCAI-19] のタイミング非依存化 offline MAPF plan + online execution by Causal-PIBT MAPF with Delay Probabilities [Ma+ AAAI-17] を使って評価 オンライン & 分散的 タイミングの仮定なし
  59. /123 79 agent transition system: 状態遷移系 reality 状態遷移系たちから成る状態遷移系 自発的に状態を遷移させる, e.g.,

    場所, 目的地, モード, 内部変数 エージェントのアトミックなアクションによって状態が遷移 i.e., agents state configuration
  60. /123 82 interaction アトミックに遷移 … … contracted requesting extended if

    unoccupied *通信はブラックボックス扱い 1台ずつアクティベート
  61. /123 84 given agents (starts) graph goals termination execution チャレンジ:

    起こりうるすべての アクション順序に耐えられる エージェントを設計する
  62. /123 86 Toy Example – GREEDY contracted requesting extended if

    unoccupied ゴールに一番近い隣接ノードに 移動を試みる deadlock もっと考える必要あり never back
  63. /123 90 + reset params is activated – 1/5 Details:

    when +cut off parent & child contracted requesting extended if unoccupied
  64. /123 91 priority inheritance high low high low as high

    parent child high low high low as high parent child is activated – 2/5 Details: when contracted requesting extended if unoccupied
  65. /123 92 +cut off parent & child lower priority higher

    priority is activated – 3/5 Details: when contracted requesting extended if unoccupied
  66. /123 93 deadlock resolution ancestor stuck parent child backtracking invalid

    case +prohibit to back to is activated – 4/5 Details: when +prohibit to back to contracted requesting extended if unoccupied
  67. /123 94 stuck child parent &root cut off child +reset

    params is activated – 5/5 Details: when stuck activated cut off parent & child
  68. /123 95 Planning 1 2 1 2 3 4 Execution

    Time-Independent Model Causal-PIBT enhance offline online
  69. /123 97 given agents (starts) graph termination execution goals +

    offline MAPF plan contracted requesting extended if unoccupied MAPF plan になるべく沿うような ノードを次ノードとして選択 MAPF Plan をヒントとして使う ゴールに一番近い隣接ノードに移動を試みる
  70. /123 99 MAPF-DP (with Delay Probabilities) [Ma+ AAAI-17] 1 −

    𝑝! 𝑝 ! success fail 移動の失敗が確率的に起こる世界
  71. /123 100 Time-Independent Model => MAPF-DP 1. extended を確率 1

    − 𝑝! で アクティベート success fail 1 − 𝑝! 𝑝 ! 2. 安定状態になるまで: contracted / requesting をランダムにアクティベート 以下を1タイムステップとみなす
  72. /123 101 upper bound of delay probabilities 𝑝! sum of

    costs x10^3 Fully Synchronous Policies Minimum Communication Policies Causal-PIBT Causal-PIBT +MAPF plan 32x32,20% obstacles 30 agents 100 repetitions MAPF plan by ECBS [Barer+ SoCS-14] Fix Agents
  73. /123 102 agents sum of costs x10^3 Fully Synchronous Policies

    Minimum Communication Policies Causal-PIBT Causal-PIBT +MAPF plan 32x32,20% obstacles upper bound of delay prob. : 0.5 100 repetitions MAPF plan by ECBS [Barer+ SoCS-14] Fix Delay Prob.
  74. /123 103 ハイライト – Time-Independence time-independent planning, Causal-PIBT 現実の非同期性を克服したい 狙い

    手法 ターゲット グラフ上の移動エージェント群 今後の方向性 offline time-independent multi-agent path planning (OTIMAPP) 実ロボットへの適用, c.f., 次のトピック ongoing
  75. /123 104 本日の構成 Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存な実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  76. /123 105 Active Moduler Environment for Robot Navigation Shota Kameyama,

    Keisuke Okumura,Yasumasa Tamura & Xavier Défago to appear at ICRA-21, available at arXiv 環境による計算支援 *supported by NTT Facilities, アセンブリ手伝ってくれたラボメンにも感謝
  77. /123 107 planning representation navigation そもそも“正しく”モデリングできてる? 外部環境≠内部表象 => “Use the

    world as its own model” [Brooks AIJ-91] ノイズ, 予期せぬ障害物, 不完全な実行, ロボット間での表象のずれ, etc
  78. /123 108 内部表象の環境へのオフロード センサー・タグを環境にばら撒くことで実現 初期の自動運転は道路に埋め込まれたデバイスで誘導 c.f., [Bimbraw ICINCO-15] 環境にデプロイされたセンサーネットワークでロボットを誘導 e.g.,

    [Verma+ PerCom-05, Kim&Chong T-ASE-08] 自然界ではスティグマジーという現象がある, e.g., 蟻の行列 ロボットのナビゲーションもよく使われる e.g., [Fujisawa+ Swarm Intell.-14, Khaliq&Saffiotti ICRA-15] 例えば 内部表象が必要ない
  79. /123 113 経路の管理 トポロジの管理 物理レイヤー 簡易的な予約プロトコルで排他制御 +将来的にはアルゴリズム組みたい c.f. Time-Independent Planning

    [Okumura+ AAAI-21] 自己安定な分散ルーティング 複数の分散アルゴリズムを 階層的・並列に実行 *セル内で大量のタスク(e.g., 接続検知)を同時実行 Elements of AFADA
  80. /123 114 Self-Stabilizing /自己安定性 c.f., イントロ本 [Altisen 19] 系の正常状態 系の異常状態

    1. 正常状態に対して閉じている 2. どんな状態からでもいつか正常状態に遷移 *創始者はダイクストラ [Dijkstra Commun. ACM-74] 初期状態に依存せず, いつか正常状態に落ち着く システムに一時的な故障に対しての耐性を付与 様々な自己安定な分散アルゴリズムが提案されてきた e.g., 全域木の構築, 排他制御, プロセス間の同期
  81. /123 115 AFADA のような分散システムでは “完璧” は見込めない e.g., 接触不良, メッセージロスト, 突然の再起動,

    焦げた匂い (本当にあった話) 正常状態: ルーティングテーブルに従っているロボットはいつか目的地に到着 最初から “一時的な故障” を見込んで 自己安定な分散ルーティングアルゴリズムを採用 実行時にセルが増えても減っても故障しても (ルーティングは) 大丈夫!
  82. /123 116 2つのセルを3往復 確率に従って 正常<=>故障 を遷移 故障時は通れない Single-robot Navigation in

    Dynamic Env. 0 20 40 60 80 100 120 正常状態の時間が 多い 少ない steps AFADA self-nav 30 repetitions
  83. /123 117 ハイライト – Active Modular Environment AFADA; モジュール型環境による計算支援 マルチロボットのインフラとしてはたらく

    内部表象&プランニングをロボットから環境へオフロード 中心的な考え Proof of Concept 課題 内部表象, プランニング, 実行のスムーズな統合 今後の方向性 セル駆動型のロバストな経路計画アルゴリズム 大きいロボットへの対応
  84. /123 119 objective-1 Representation objective-2 Planning Who Plans? Huge Search

    Space Common Knowledge? Cooperation? (increased) Uncertainty Acting Multi-Agent Planning & Acting Multi-agent Planning Multi-robot Coordination Distributed Algorithms
  85. /123 120 ハイライト Multi-Agent Path Finding の紹介 環境による計算支援 Active Modular

    Environment Time-Independent Planning タイミング非依存な実行ポリシー Iterative Refinement Anytime アルゴリズム Priority Inheritance with Backtracking MAPF への柔軟なアプローチ execution planning
  86. /123 124 KO のワーク [Okumura+ 1JCAI-19] Okumura, K., Machida M.,

    Défago, X. & Tamura, Y. “Priority Inheritance with Backtracking for Iterative Multi-agent Path Finding”. Proc. Intel. Joint Conf. on Artificial Intelligence (IJCAI). 2019. [Okumura+ WoMAPF-20] Okumura, K., Tamura, Y. & Défago, X. “winPIBT: Extended Prioritized Algorithm for Iterative Multi-agent Path Finding”. Proc. Workshop on Multi-Agent Path Finidng (WoMAPF). 2020. [Okumura+ 21, preprint] Okumura, K., Tamura, Y. & Défago, X. “Iterative Refinement for Real-Time Multi-Robot Path Planning”. arXiv preprint. 2021. [Okumura+ AAAI-21] Okumura, K., Tamura, Y. & Défago, X. “Time-Independent Planning for Multiple Moving Agents”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2021. [Kameyama+ ICRA-21] Kameyama, S., Okumura, K., Tamura, Y. & Défago, X. “Active Modular Environment for Robot Navigation”. to appear at ICRA-21, arXiv preprint. 2021. 便利サイト: https://kei18.github.io/
  87. /123 125 MAPF のレビュー論文 Ma, H., Koenig, S., Ayanian, N.,

    Cohen, L., Hönig, W., Kumar, T. K., Uras, T., Xu, H., Tovey, C. & Sharon, G. “Overview: Generalizations of Multi-Agent Path Finding to Real-World Scenarios”. Proc. Workshop on Multi-Agent Path Finding (WoMAPF). 2016. Felner, A., Stern, R., Shimony, S. E., Boyarski, E., Goldenberg, M., Sharon, G., Sturtevant, N., Wagner, G. & Surynek, P. “Search- based optimal solvers for the multi-agent pathfinding problem: Summary and challenges”. Proc. Annu. Symp. on Combinatorial Search (SoCS). 2017. Stern, R. “Multi-agent path finding – an overview”. Artif. Intell. (AIJ). 2019. Stern, R., Sturtevant, N., Felner, A., Koenig, S., Ma, H., Walker, T., Li, J., Atzmon, D., Cohen, L., Kumar, T. K. , Boyarski, E. & Barták, R. “Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks”. Proc. Intl. Symp. on Combinatorial Search (SoCS). 2019. Salzman, O., Stern, R. “Research Challenges and Opportunities in Multi-Agent Path Finding and Multi-Agent Pickup and Delivery Problems”. Proc. Intl. Joint Conf. on Autonomous Agents & Multiagent Systems (AAMAS). 2020. 便利サイト: http://mapf.info/
  88. /123 126 応用例 [Wuman+ AI Magagine-08] Wurman, P. R., D'Andrea,

    R., & Mountz, M. “Coordinating hundreds of cooperative, autonomous vehicles in warehouses”. AI magazine. 2008 [Dresner&Stone JAIR-08] Dresner, K., & Stone, P. “A multiagent approach to autonomous intersection management”. J. Artif. Intell. Res. (JAIR). 2008. [Morris+ AAAI Workshop-16] Morris, R., Pasareanu, C. S., Luckow, K. S., Malik, W., Ma, H., Kumar, T. S., & Koenig, S. “Planning, Scheduling and Monitoring for Airport Surface Operations”. Proc. AAAI Workshop: Planning for Hybrid Systems. 2016. [Okoso+ ITSC-19] Okoso, A., Otaki, K., & Nishi, T. “Multi-agent path finding with priority for cooperative automated valet parking”. IEEE Proc. IEEE Intell. Transp. Syst. Conf. (ITSC). 2019 [Li+ AAMAS-20] Li, J., Sun, K., Ma, H., Felner, A., Kumar, T. S., & Koenig, S. “Moving agents in formation in congested environments”. Proc. Intl. Joint Conf. on Autonomous Agents & Multiagent Systems (AAMAS). 2020.
  89. /123 127 MAPF の複雑性について [Surynek AAAI-10] Surynek, P. “An optimization

    variant of multi-robot path planning is intractable”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2010. [Yu&LaValle AAAI-13] Yu, J., & LaValle, S. “Structure and intractability of optimal multi-robot path planning on graphs”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2013. [Yu RA-L-15] Yu, J. “Intractability of Optimal Multi-Robot Path Planning on Planar Graphs”. IEEE Robot. Autom. Lett. (RA- L). 2015. [Ma+ AAAI-16] Ma.,H., Tovey, C., Sharon, G., Kumar, T. S., & Koenig, S. “Multi- agent path finding with payload transfers and the package-exchange robot-routing problem,” Proc. AAAI Conf. on Artificial Intelligence. 2016. [Banfi+ RA-L-17] Banfi, J., Basilico, N., & Amigoni, F. “Intractability of time-optimal multirobot path planning on 2d grid graphs with holes”, IEEE Robot. Autom. Lett. (RA-L). 2017. [Röger&Helmert SoCS-12] Röger, G., & Helmert, M. “Non-optimal multi-agent pathfinding is solved (since 1984)”. Proc. Annu. Symp. on Combinatorial Search (SoCS). 2012. [Kornhauser 84] Kornhauser, D. M., Miller, G., & Spirakis, P. “Coordinating pebble motion on graphs, the diameter of permutation groups, and applications”. Master's thesis at M.I.T. 1984. [Nebel ICAPS-20] Nebel, B. “On the Computational Complexity of Multi-Agent Pathfinding on Directed Graphs”. Proc. Intl. Conf. on Automated Planning and Scheduling (ICAPS). 2020.
  90. /123 128 Prioritized Planning 関連 – 1/2 [Erdmann& Lozano-Perez Algorithmica-87]

    Erdmann, M., & Lozano-Perez, T. “On multiple moving objects”. Algorithmica. 1987. [Silver AIIDE-05] Silver, D. “Cooperative pathfinding”. Proc. AAAI Conf. on Artificial Intelligence and Interactive Digital Entertainment (AIIDE). 2005. [Cap+ T-ASE-15] Čáp, M., Novák, P., Kleiner, A., & Selecký, M. “Prioritized planning algorithms for trajectory coordination of multiple mobile robots”. IEEE Trans. Autom. Sci. Eng. (T-ASE). 2015 [Wang&Botea JAIR-11] Wang, K. H. C., & Botea, A. “MAPP: a scalable multi-agent path planning algorithm with tractability and completeness guarantees”. J. Artif. Intell. Res. (JAIR). 2011 [Bnaya&Felner ICRA-14] Bnaya, Z., & Felner, A. “Conflict-oriented windowed hierarchical cooperative A∗”. Proc. IEEE Intl. Conf. on Robotics and Automation (ICRA). 2014.
  91. /123 129 Prioritized Planning 関連 – 2/2 [Azarm&Schmidt ICRA-97] Azarm,

    K., & Schmidt, G. “Conflict-free motion of multiple mobile robots based on decentralized motion planning and negotiation”. Proc. IEEE Intl. Conf. on Robotics and Automation (ICRA). 1997. [Bennewitz+ Robotics-02] Bennewitz, M., Burgard, W., & Thrun, S. “Finding and optimizing solvable priority schemes for decoupled path planning techniques for teams of mobile robots”. Robot. Auton. Syst. 2002. [Van Den Berg & Overmars ICRA-05] Van Den Berg, J. P., & Overmars, M. H. “Prioritized motion planning for multiple robots”. Proc. IEEE Intl. Conf. on Robotics and Automation (ICRA). 2005. [Andreychuk& Yakovlev AAMAS-18] Andreychuk, A., & Yakovlev, K. “Two techniques that enhance the performance of multi-robot prioritized path planning”. Proc. Intl. Joint Conf. on Autonomous Agents & Multiagent Systems (AAMAS). 2018. [Ma+ AAAI-19] Ma, H., Harabor, D., Stuckey, P. J., Li, J., & Koenig, S. “Searching with consistent prioritization for multi-agent path finding”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2019
  92. /123 130 Conflict-based Search (CBS) とその派生 (他にもいっぱいあります… そして毎年たくさん出る…) - 1/2

    [Shraon+ AIJ-15] Sharon, G., Stern, R., Felner, A., & Sturtevant, N. R. “Conflict-based search for optimal multi-agent pathfinding”. Artif. Intell. (AIJ). 2015. [Boyarski+ IJCAI-15] Boyarski, E., Felner, A., Stern, R., Sharon, G., Betzalel, O., Tolpin, D., & Shimony, E. “ICBS: improved conflict-based search algorithm for multi- agent pathfinding”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2015. [Boyarski+ AAAI-21] Boyarski, E., Felner, A., Le Bodic, P., Harabor, D., Stuckey, P. J., & Koenig, S. “f-Aware Conflict Prioritization & Improved Heuristics for Conflict-Based Search” [Felner+ ICAPS-18] Felner, A., Li, J., Boyarski, E., Ma, H., Cohen, L., Kumar, T. S., & Koenig, S. “Adding heuristics to conflict- based search for multi-agent path finding”. Proc. Intl. Conf. on Automated Planning and Scheduling (ICAPS). 2018. [Li+ IJCAI-19] Li, J., Felner, A., Boyarski, E., Ma, H., & Koenig, S. “Improved Heuristics for Multi-Agent Path Finding with Conflict-Based Search”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2019. [Li+ AAAI-19] Li, J., Harabor, D., Stuckey, P. J., Ma, H., & Koenig, S. “Symmetry-breaking constraints for grid-based multi-agent path finding”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2019 [Li+ ICAPS-20] Li, J., Gange, G., Harabor, D., Stuckey, P. J., Ma, H., & Koenig, S. “New techniques for pairwise symmetry breaking in multi-agent path finding”. Proc. Intl. Conf. on Automated Planning and Scheduling (ICAPS). 2020.
  93. /123 131 Conflict-based Search (CBS) とその派生 (他にもいっぱいあります… そして毎年たくさん出る…) - 2/2

    [Gange+ ICAPS-19] Gange, G., Harabor, D., & Stuckey, P. J. “Lazy CBS: Implicit conflict-based search using lazy clause generation”. Proc. Intl. Conf. on Automated Planning and Scheduling (ICAPS). 2019. [Huang+ AAAI-21] Huang, T., Dilkina, B., & Koenig, S. “Learning to Resolve Conflicts for Multi-Agent Path Finding with Conflict-Based Search”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2021 [Boyarski+ IJCAI-20] Boyarski, E., Felner, A., Harabor, D., Stuckey, P. J., Cohen, L., Li, J., & Koenig, S. “Iterative-Deepening Conflict-Based Search”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2020. [Barer+ SoCS-14] Barer, M., Sharon, G., Stern, R., & Felner, A. “Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem”. Proc. Annu. Symp. on Combinatorial Search (SoCS). 2014. [Li+ AAAI-21a] Li, J., Ruml, W., & Koenig, S. “EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2021.
  94. /123 132 他の主流な探索ベースの optimal なソルバたち [Standley AAAI-10] Standley, T. “Finding

    optimal solutions to cooperative pathfinding problems”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2010. [Sharon+ AIJ-13] Sharon, G., Stern, R., Goldenberg, M., & Felner, A. “The increasing cost tree search for optimal multi-agent pathfinding”. Artif. Intell. (AIJ). 2013. [Goldenberg+ JAIR-14] Goldenberg, M., Felner, A., Stern, R., Sharon, G., Sturtevant, N., Holte, R. C., & Schaeffer, J. “Enhanced partial expansion A*”. J. Artif. Intell. Res. (JAIR). 2014 [Wagner&Choset AIJ-15] Wagner, G., & Choset, H. “Subdimensional expansion for multirobot path planning”. Artif. Intell. (AIJ). 2015. [Lam+ IJCAI-19] Lam, E., Le Bodic, P., Harabor, D. D., & Stuckey, P. J. “Branch-and-Cut-and-Price for Multi-Agent Pathfinding”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2019. [Lam&Le Bodic ICAPS-20] Lam, E., & Le Bodic, P. “New valid inequalities in branch-and-cut-and-price for multi-agent path finding”. Proc. Intl. Conf. on Automated Planning and Scheduling (ICAPS). 2020.
  95. /123 133 帰着ベースの optimal なソルバたち [Ryan ICRA-10] Ryan, M. “Constraint-based

    multi-robot path planning”. Proc. IEEE Intl. Conf. on Robotics and Automation (ICRA). 2010 [Surynek PRICAI-12] Surynek, P. “Towards optimal cooperative path planning in hard setups through satisfiability solving”. Pacific Rim Intl. Conf. on Artificial Intelligence (PRICAI). 2012. [Surynek+ ECAI-16] Surynek, P., Felner, A., Stern, R., & Boyarski, E. “Efficient SAT approach to multi-agent path finding under the sum of costs objective”. Proc. European Conf. on Artificial Intelligence (ECAI-16). 2016 [Yu&LaValle T-RO-16] Yu, J., & LaValle, S. “Optimal multirobot path planning on graphs: Complete algorithms and effective heuristics”. IEEE Trans. on Robotics (T-RO). 2016 [Erdem+ IJCAI-13] Erdem, E., Kisa, D., Oztok, U., & Schüller, P. “A general formal framework for pathfinding problems with multiple agents”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2013.
  96. /123 134 ルールベースな sub-optimal なソルバたち [Ryan JAIR-08] Ryan, M. R.

    K. “Exploiting subgraph structure in multi-robot path planning”. J. Artif. Intell. Res. (JAIR). 2008. [PeasgoodT-RO-08] Peasgood, M., Clark, C. M., & McPhee, J. “A complete and scalable strategy for coordinating multiple robots within roadmaps”. IEEE Trans. on Robotics (T-RO). 2008. [Surynek ICRA-09] Surynek, P. “A novel approach to path planning for multiple robots in bi-connected graphs”. Proc. IEEE Intl. Conf. on Robotics and Automation (ICRA). 2009. [Surynek FLAIRS-09] Surynek, P. “Towards Shorter Solutions for Problems of Path Planning for Multiple Robots in Theta- like Environments”. Florida Artif. Intell. Res. Soc. Conf. (FLAIRS). 2009. [Botea+Surynek AAAI-15] Botea, A., & Surynek, P. “Multi-agent path finding on strongly biconnected digraphs”. Proc. AAAI Conf. on Artificial Intelligence (AAAI). 2015. [Khorshid+ SoCS-11] Khorshid, M. M., Holte, R. C., & Sturtevant, N. R. “A Polynomial-Time Algorithm for Non-Optimal Multi-Agent Pathfinding”. Proc. Annu. Symp. on Combinatorial Search (SoCS). 2011. [Luna&Bekris IJCAI-11] Luna, R., & Bekris, K. E. “Push and swap: Fast cooperative path-finding with completeness guarantees”. Proc. Intl. Joint Conf. on Artificial Intelligence (IJCAI). 2011. [de Wilde+ AAMAS-13] de Wilde, B., ter Mors, A. W., & Witteveen, C. “Push and rotate: cooperative multi-agent path planning”. Proc. Intl. Joint Conf. on Autonomous Agents & Multiagent Systems (AAMAS). 2013. [Sajid+ SoCS-12] Sajid, Q., Luna, R., & Bekris, K. E. “Multi-Agent Pathfinding with Simultaneous Execution of Single-Agent Primitives.” Proc. Annu. Symp. on Combinatorial Search (SoCS). 2012
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