task and path planning for multi-agent pickup and...
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Task and Path Planning forMulti-Agent Pickup and Delivery
Minghua Liu Hang Ma Jiaoyang Li Sven Koenig
AAMASMay 16, 2019
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Real-World Applications
Aircraft-Towing Vehicles
Figure 3: A small region of a Kiva layout. The green cells represent pod storage locations, the orange ovals the robots (withpods not pictured), and the purple and pink regions the queues around the inventory stations.
Figure 2: A Kiva drive unit and storage pod.
used to move the inventory pods with the correct bins fromtheir storage locations to the inventory stations where a pickworker removes the desired products from the desired bin.Note that the pod has four faces, and the drive unit may needto rotate the pod in order to present the correct face. When apicker is done with a pod, the drive unit stores it in an emptystorage location.
Each station is equipped with a desktop computer thatcontrols pick lights, barcode scanners, and laser pointers thatare used to identify the pick and put locations. Because ev-ery product is scanned in and out of the system, overall pick-ing errors go down, which potentially eliminates the needfor post-picking quality control. In general, every station iscapable of being either a picking station or a replenishmentstation. In practice, pick stations will be located near out-bound conveyors, and replenishment stations will be locatednear pallet drop off points.
The power of the Kiva solution comes from the fact thatit allows every worker to have random access to any inven-tory in the warehouse. Moreover, inventory can be retrievedin parallel. When the picker is filling several boxes at thesame time, the parallel, random access ensures that she isnot waiting on pods to arrive. In fact, by keeping a smallqueue of work at the station, the Kiva system delivers a newpod face every six seconds, which sets a baseline pickingrate of 600 lines per hour.2 Peak rates can exceed 600 linesper hour when the operator can pick more than one item offa pod.3
For a large warehouse, the savings in personnel can besignificant. Consider, for example, what a Kiva implemen-tation of the book warehouse would involve. A busy book-seller may ship 100,000 boxes a day. With existing automa-tion, this level of output would employ perhaps 75 workers
2This statistic is based on single unit picks and has been repro-duced for extended periods in the Kiva test facility.
3This statistic was verified when a small Kiva demonstrationsystem was brought to a drugstore distribution center where opera-tors picked at nearly 700 lines per hour.
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Figure 5: The Kiva demonstration facility.
Acknowledgments
Building a working MVS requires a core set of great me-chanical, electrical, and software engineers. It is yet an-other thing to turn it into a commercial product and managethe manufacture, assembly, and deployment of these sys-tems. We thank the world-class Kiva employees who havebreathed life into this vision.
References
Boutilier, C.; Shoham, Y.; and Wellman, M. P. 1997. Eco-nomic principles of multi-agent systems. Artificial Intelli-gence 94(1):1–6.Butenko, S.; Murphey, R.; and Pardos, P. M., eds. 2003.Cooperative Control: Models, Applications and Algo-rithms. Springer.Gilmour, K. 2003. Amazon warehouse, amazon adventure.Internet Magazine.Hazard, C. J.; Wurman, P. R.; and D’Andrea, R. 2006.Alphabet soup: A testbed for studying resource allocationin multi-vehicle systems. In Proceedings of the 2006 AAAIWorkshop on Auction Mechanisms for Robot Coordination,23–30.Jennings, N. R., and Bussmann, S. 2003. Agent-based con-trol systems: Why are they suited to engineering complexsystems? IEEE Control Systems Magazine 61–73.Jennings, N. R. 1996. Coordination techniques for dis-tributed artificial intelligence. In O’Hare, G. M. P., andJennings, N. R., eds., Foundations of Distributed ArtificialIntelligence. Wiley. 187–210.
Konolige, K.; Fox, D.; Ortiz, C.; Agno, A.; Eriksen, M.;Limketkai, B.; Ko, J.; Morisset, B.; Schulz, D.; Stewart,B.; and Vincent, R. 2004. Centibots: Very large scale dis-tributed robotic teams. In Proceedings of the InternationalSymposium on Experimental Robotics.Lesser, V. R. 1999. Cooperative multiagent systems: Apersonal view of the state of the art. IEEE Transactions onKnowledge and Data Engineering 11(1):133–142.Malone, T. W.; Fikes, R. E.; Grant, K. R.; and Howard,M. T. 1988. Enterprise: A market-like task scheduler fordistributed computing environments. In Huberman, B. A.,ed., The Ecology of Computation. North Holland.Rosenschein, J. S., and Zlotkin, G. 1994. Rules of En-counter. Cambridge: The MIT Press.Simmons, R.; Smith, T.; Dias, M. B.; Goldberg, D.; Hersh-berger, D.; Stentz, A.; and Zlot, R. 2002. A layered archi-tecture for coordination of mobile robots. In Schultz, A.,and Parker, L., eds., Multi-Robot Systems: From Swarmsto Intelligent Automata. Kluwer.Wellman, M. P., and Wurman, P. R. 1998. Market-awareagents for a multiagent world. Robotics and AutonomousSystems 24:115–25.
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Amazon Warehouse RobotsAgents have to operate in a common environment, continuously attendto pickup and delivery tasks one by one, and plan collision-free pathsto execute the tasks.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
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A team of agents (ai) have to execute a batch of tasks (ti) in aknown environment.Each task: a pickup location (si), a delivery location (gi), and arelease time.Each agent: a unique parking location.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
Free Agents
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Task Agents
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
Free Agents
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Task Agents
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pickup location → delivery locationTask and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
Assign tasks to agents and plan collision-free paths for them toexecute their tasks.Unlike the traditional multi-agent path finding (MAPF) problem,multiple tasks can be assigned to each agent and the agent has tovisit multiple locations to execute a task.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Objective
Finish executing all tasks as quickly as possible.Makespan: the earliest time step when all tasks have been executed.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Online Version & Offline Version
Online version1: each task becomes known only after its release time.Offline version: the tasks and their release times are known a priori.
1H. Ma et al. “Lifelong Multi-Agent Path Finding for Online Pickup and DeliveryTasks”. In: AAMAS. 2017, pp. 837–845.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
MAPD Algorithms
CENTRAL etc.2 (online)G-TAPF3
Using answer set programming.Scales only to 20 agents or tasks for a simplified warehouse variant.
TA-Prioritized & TA-Hybrid (offline)Scales to hundreds of agents and thousands of tasks.Smaller makespans than CENTRAL.Complete for well-formed MAPD instances.
2Ma et al., “Lifelong Multi-Agent Path Finding for Online Pickup and DeliveryTasks”.
3V. Nguyen et al. “Generalized Target Assignment and Path Finding using AnswerSet Programming”. In: IJCAI. 2017, pp. 1216–1223.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
TA-Prioritized & TA-Hybrid
TA-Prioritized: Improved Prioritized Path Planning
TA-Hybrid: MAPF and anonymous MAPF
2. Plan collision-free paths for agents to finish their assigned tasks.
1. Assign the tasks to agents by solving a special TSP.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Goal
Ignores collisions and computes one task sequence for each agent.a1 : [t5 t1 t4]
a2 : [t6 t2 t9]
a3 : [t3 t8 t7]
The task sequence specifies which tasks are assigned to the agentand in which order the agent should execute them.First construct a directed complete graph for a MAPD instance andthen solve a special TSP on it to compute good task sequences.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Constructing the Graph
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A directed complete graph G′ = (A ∪ T ,E′).Two types of vertices:
αi ∈ A represents agent ai,τi ∈ T represents task ti.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Constructing the Graph
a1 : [t5 t1 t4]
a2 : [t6 t2 t9]
a3 : [t3 t8 t7]⌧1
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A Hamiltonian cycle can be converted to task sequences, one for eachagent.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Constructing the Graph
a1 : [t5 t1 t4]
a2 : [t6 t2 t9]
a3 : [t3 t8 t7]⌧1
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Each directed edge has an integer weight w(u, v).The sum of the edge weights of each part is a lower bound on theexecution time of the corresponding task sequence.E.g., w(αi, τj) is calculated as the travel time of agent ai from itsparking location to the pickup location of its first task tj.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Solving a Special TSP
a1 : [t5 t1 t4]
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Objective: makespan (the largest execution time of all task sequences).
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Prioritized Planning
TA-Prioritized uses an improved version of prioritized planning4 to plancollision-free paths for the agents to execute all of their tasks accordingto their task sequences.
4J. P. Van den Berg and M. H. Overmars. “Prioritized Motion Planning forMultiple Robots”. In: IROS. 2005, pp. 430–435.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
Plan paths for the agents, one by one, in decreasing order of theestimated execution times of their task sequences.
estimated execution time
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
Plan paths for the agents, one by one, in decreasing order of theestimated execution times of their task sequences.
estimated execution time
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
Plan paths for the agents, one by one, in decreasing order of theestimated execution times of their task sequences.
estimated execution time
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
Plan paths for the agents, one by one, in decreasing order of theestimated execution times of their task sequences.
estimated execution time
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
estimated execution time
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After a path has been planned for an agent, the paths of allremaining agents are not allowed to collide with it.Agents with larger estimated execution times have fewer constraints,which may result in a smaller makespan.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Improved Prioritized Planning
Original version has already determined the fixed planning orderbefore it plans a path for an agent.Actual execution time may be longer than the estimated executiontime since the agent has to avoid collision with the planned paths ofthe previous agents.Improvement: in each iteration, it tentatively assumes all remainingagents as the next one and plans a path for each of them, and itthen chooses the agent next whose path has the largest (actual)execution time.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Path Planning for Single Agent
The path of an agent is a concatenation of several sub-pathsaccording to its task sequence.
parking location
pickup location
delivery location
pickup location
delivery location ……
Constructs the path sub-path by sub-path.A* search in the space of location-time pairs (x, t).
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Completeness
There might not exist a collision-free sub-path for an agent from itscurrent location to its goal location.
stimestep = 0
timestep = 2
timestep = 1
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Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Reserving Dummy Path
A dummy path is a path to the parking location of the agent,through which agents can always move to and stay in their parkinglocations for as long as necessary to avoid collisions with otheragents.An agent never moves along its dummy path since the purpose of adummy path is only to guarantee that the subsequent sub-path forthe agent (and its dummy path) exists.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Reserving Dummy Path
Not every MAPD instance is solvable.
a1s1 a2 g1
TA-Prioritized is complete for well-formed5 MAPD instances, arealistic subclass.
5M. Čáp, J. Vokřı́nek, and A. Kleiner. “Complete Decentralized Method forOn-Line Multi-Robot Trajectory Planning in Well-Formed Infrastructures”. In:ICAPS. 2015.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
TA-Prioritized plans paths for agents one by one.Powerful algorithms for multi-agent path finding (MAPF) problemand anonymous MAPF problem.TA-Hybrid is similar to TA-Prioritized but uses a differentpath-planning method.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Plans sub-paths for agents in chronological order.
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MAPF instance
anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning
Free Agents
→ pickup locations.May swap pickup locations.Uses min-cost max-flow(polynomial).
New Task Agents
→ delivery locations.Cannot swap delivery locations.Uses ICBS 6(exponential).
6E. Boyarski et al. “ICBS: Improved Conflict-Based Search Algorithm forMulti-Agent Pathfinding”. In: IJCAI. 2015, pp. 740–746.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Completeness
Also uses “reserving dummy paths”.TA-Hybrid is complete for well-formed MAPD instances.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Settings
CENTRAL and three other strawman MAPD algorithms.Small warehouse: 500 tasks, 10 ∼ 50 agents.Large Warehouse: 2000 tasks, 60 ∼ 180 agents.
21× 35 grid with 50 agents 33× 46 grid with 180 agents
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybridmakespan 600 598 566 timeout 538 532
Results in the small warehouse.CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid
makespan timeout 808 662 timeout 669 629
Results in the large warehouse.w/ our task assignment
w/ greedier task assignmentTask Assignment: smaller makespans.Path Planning: scale better.“reserving dummy paths”: smaller makespans.
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybridmakespan 600 598 566 timeout 538 532
Results in the small warehouse.CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid
makespan timeout 808 662 timeout 669 629
Results in the large warehouse.w/ our path planning
w/ other path planningTask Assignment: smaller makespans.Path Planning: scale better.“reserving dummy paths”: smaller makespans.
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybridmakespan 600 598 566 timeout 538 532
Results in the small warehouse.CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid
makespan timeout 808 662 timeout 669 629
Results in the large warehouse.w/ “reserving dummy paths”
w/ existing deadlock avoidance methodTask Assignment: smaller makespans.Path Planning: scale better.“reserving dummy paths”: smaller makespans.
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
TA-Hybrid VS TA-Prioritized
TA-Prioritized TA-Hybridmakespan (runtime) 538 (30s) 532 (69s)
Results in the small warehouse.
TA-Prioritized TA-Hybridmakespan (runtime) 669 (1079s) 629 (1298s)
Results in the large warehouse.
Effectiveness (makespan): TA-Hybrid < TA-PrioritizedEfficiency (runtime): TA-Prioritized < TA-Hybrid
Task and Path Planning for Multi-Agent Pickup and Delivery
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Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Takeaways
Multi-agent pickup-and-delivery (MAPD) problem.Two offline algorithms: TA-Prioritized and TA-Hybrid.Three innovations:
Task Assignment: one task sequence per agent by solving a specialTSP.Path Planning: prioritized path planning and hybrid path planning.Deadlock Avoidance: “reserving dummy paths”.
Smaller makespans and scale better than CENTRAL in simulatedwarehouses with hundreds of robots and thousands of tasks.
Task and Path Planning for Multi-Agent Pickup and Delivery