Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent Execution Keisuke Okumura & Xavier Defago Tokyo Institute of Technology, Japan ౦ژ޻ۀେֶ 5PLZP*OTUJUVUFPG5FDIOPMPHZ Jun. 21st – 24th, 2022 virtual conf. (Singapore) ICAPS-22

/39 2 https://kei18.github.io/tswap pattern formation async execution complete & sub-optimal algorithm (TSWAP) for unlabeled multi-agent pathfinding applicable to both offline & online scenarios ≥1000 agents within 1 sec Summary

/39 3 MAPF: Multi-Agent Path Finding given agents (starts) graph goals solution paths without collisions

/39 4 Unlabeled/Anonymous MAPF given agents (starts) graph targets solution paths without collisions target assignment

/39 5 Motivation optimal sub-optimal (scalable) MAPF unlabeled-MAPF MAPP [Wang&Botea JAIR-11] EECBS [Li+ AAAI-21] PIBT [Okumura+ IJCAI-19] … CBS [Sharon+ AIJ-15] M* [Wagner&Choset AIJ-15] BCP [Lam+ COR-22] … reduction to maximum flow [Yu&LaValle WAFR-13] objective: solve large unlabeled-MAPF with sufficiently good quality in small computation time

/39 6 Existing Optimal Algorithm by reducing to maximum flow problem: 𝑂( 𝐴 ⋅ 𝑉 !) * polynomial-time makespan-optimal algorithm exists! [Yu&LaValle WAFR-13] computable but take time (≥1min) fast sub-optimal solver is attractive *assuming |𝐸| = 𝑂(|𝑉|) MAPF benchmarks [Stern+ SOCS-19] 418x530 43,151 257x256 28,178 194x194 14,784 |𝑉|

/39 7 optimal linear assignment collision-free scheduling [Yu&LaValle WAFR-13] Hungarian algorithm: 𝑂( 𝐴 ") [Kuhn 1955] lexicographic bottleneck assignment decoupled path planning [Turpin+ AURO-14] [Sokkalingam&Aneja OAL-98] known best algorithm: 𝑂( 𝐴 #) relying on optimal assignments Existing Sub-optimal & Complete Algorithms TSWAP works with arbitrary initial target assignments & applies to online scenarios

/39 8 Proposed Algorithm: TSWAP compute arbitrary initial target assignment Step 1. repeat one-timestep path planning with target swapping Step 2. 𝑂( 𝐴 ! ⋅ 𝑑𝑖𝑎𝑚 𝐺 ⋅ (𝛼 + 𝛽)) vertex scoring & deadlock resolution algorithm sketch 2000 agents [Yu&LaValle WAFR-13] optimal algorithm TSWAP 56.3 89.8 230.2 0.4 0.4 1.1 1.36 1.17 1.02 runtime (sec) sub-optimality (makespan) lak303d den520d brc202d evaluation example

/39 9 Algorithm Description

/39 10 Why Not Arbitrary Assignment + MAPF? => incomplete! need to swap targets on demand

/39 11 swap targets rotate targets shortest path move shortest path TSWAP repeat one-timestep path planning with target swapping Step 2. stay currently assigned target stay (otherwise)

/39 12 Running Example 1 2 3 planning order: timestep: t

/39 13 Running Example move shortest path timestep: t

/39 14 Running Example timestep: t

/39 15 Running Example swap targets timestep: t

/39 16 Running Example timestep: t

/39 17 Running Example move shortest path timestep: t

/39 18 Running Example timestep: t

/39 19 Running Example timestep: t+1

/39 20 Running Example timestep: t+1 move shortest path stay

/39 21 Running Example timestep: t+1

/39 22 Running Example timestep: t+2 fin.

/39 23 Completeness the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent Proof. Using potential function 0 when all agents are on targets

/39 24 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path

/39 25 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path

/39 26 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path

/39 27 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path

/39 28 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path

/39 29 the shortest path distance from the current location to the target #targets in the shortest path (excluding endpoints) + Σ agent swap targets rotate targets shortest path stay stay move shortest path for each timestep, at least one agent performs one of the three actions for each timestep, the potential function decreases

/39 30 Initial Target Assignment compute arbitrary initial target assignment Step 1. good assignment? => quick & good quality for certain criteria The paper introduces two algorithms using lazy distance (cost) evaluation resulting in good total/maximum traveling time bottleneck assignment 1. quick with acceptable quality: 𝑂( 𝐴 ⋅ ( 𝑉 + |𝐸|)) greedy assignment with refinement 2.

/39 31 Evaluation

/39 32 v.s. Makespan-optimal Alg. 0 200 400 600 0 10 20 30 random-64-64-20 64x64 (3,270) random-32-32-20 32x32 (819) makespan runtime (ms) 110 agents TSWAP (bottleneck) TSWAP (greedy) optimal alg. [Yu&LaValle WAFR-13] TSWAP is scalable for graph size solution quality is comparable scalability for graph

/39 33 v.s. Makespan-optimal Alg. [Yu&LaValle WAFR-13] TSWAP is scalable for #agents (according to assignment algorithms) 0 500 1000 1500 0 5 10 makespan runtime (ms) TSWAP (bottleneck) TSWAP (greedy) optimal alg. 500 agents 2000 agents (extremely dense) random-64-64-20 64x64 (3,270) scalability for #agents

/39 34 Online Planning asynchronous execution

/39 35 How to Model Async Execution? time-independent planning [Okumura+ AAAI-21] agents sequentially perform atomic actions we cannot control execution schedule given: start target graph or Online Planning / Policy completeness: regardless of execution schedules, all targets are eventually occupied

/39 36 Online TSWAP complete! *this is a centralized algorithm algorithm sketch* compute arbitrary initial target assignment 1. offline phase 2. online phase when is activated: same as offline

/39 37 Demo of Time-Independence adaptive to timing uncertainties no synchronous procedure

/39 38 8 Robots Demo

/39 39 Concluding Remarks TSWAP algorithm our approach target simultaneous target assignment & path planning for indistinguishable agents (unlabeled-MAPF) future directions sub-optimal / complete / quick / scalable applicable to both offline & online decentralization offline planning for async execution c.f., OTIMAPP [Okumura+ IJCAI-22] https://kei18.github.io/tswap