Task and Path Planning for Multi-Agent Pickup and Delivery Minghua - - PowerPoint PPT Presentation
. Background . . . . . . . . . . Task Assignment . Prioritized Path Planning Hybrid Path Planning Experimental Results Task and Path Planning for Multi-Agent Pickup and Delivery Minghua Liu Hang Ma Jiaoyang Li Sven Koenig
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Minghua Liu Hang Ma Jiaoyang Li Sven Koenig AAMAS May 16, 2019
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Real-World Applications
Aircraft-Towing Vehicles Amazon Warehouse Robots
Agents have to operate in a common environment, continuously attend to pickup and delivery tasks one by one, and plan collision-free paths to execute the tasks.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
A team of agents (ai) have to execute a batch of tasks (ti) in a known environment. Each task: a pickup location (si), a delivery location (gi), and a release time. Each agent: a unique parking location.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
Free Agents
current location → pickup location Task Agents pickup location delivery location
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Multi-Agent Pickup and Delivery (MAPD) Problem
Free Agents
current location → pickup location Task Agents
pickup location → delivery location
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 to execute their tasks. Unlike the traditional multi-agent path fjnding (MAPF) problem, multiple tasks can be assigned to each agent and the agent has to visit multiple locations to execute a task.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Online Version & Offmine Version Online version1: each task becomes known only after its release time. Offmine version: the tasks and their release times are known a priori.
Tasks”. In: AAMAS. 2017, pp. 837–845.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 simplifjed warehouse variant.
TA-Prioritized & TA-Hybrid (offmine)
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 Delivery
Tasks”.
Set Programming”. In: IJCAI. 2017, pp. 1216–1223.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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
.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Goal Ignores collisions and computes one task sequence for each agent.
The task sequence specifjes which tasks are assigned to the agent and in which order the agent should execute them. First construct a directed complete graph for a MAPD instance and then solve a special TSP on it to compute good task sequences.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Constructing the Graph
α2 α3
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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] τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8 τ9
α2 α3
α1 A Hamiltonian cycle can be converted to task sequences, one for each agent.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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] τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8 τ9
α2 α3
α1 Each directed edge has an integer weight w(u, v). The sum of the edge weights of each part is a lower bound on the execution time of the corresponding task sequence. E.g., w(αi, τj) is calculated as the travel time of agent ai from its parking location to the pickup location of its fjrst task tj.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Solving a Special TSP a1 : [t5 t1 t4] a2 : [t6 t2 t9] a3 : [t3 t8 t7] τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8 τ9
α2 α3
α1 Objective: makespan (the largest execution time of all task sequences).
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Prioritized Planning TA-Prioritized uses an improved version of prioritized planning4 to plan collision-free paths for the agents to execute all of their tasks according to their task sequences.
Multiple Robots”. In: IROS. 2005, pp. 430–435.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 the estimated execution times of their task sequences.
estimated execution time
1 2 3
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 the estimated execution times of their task sequences.
estimated execution time
1 2 3
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 the estimated execution times of their task sequences.
estimated execution time
1 2 3
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 the estimated execution times of their task sequences.
estimated execution time
1 2 3
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Original Prioritized Planning
estimated execution time
1 2 3
After a path has been planned for an agent, the paths of all remaining 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Improved Prioritized Planning Original version has already determined the fjxed planning order before it plans a path for an agent. Actual execution time may be longer than the estimated execution time since the agent has to avoid collision with the planned paths of the previous agents. Improvement: in each iteration, it tentatively assumes all remaining agents as the next one and plans a path for each of them, and it then chooses the agent next whose path has the largest (actual) execution time.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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-paths according 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 its current location to its goal location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 parking locations for as long as necessary to avoid collisions with other agents. An agent never moves along its dummy path since the purpose of a dummy path is only to guarantee that the subsequent sub-path for the agent (and its dummy path) exists.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Reserving Dummy Path Not every MAPD instance is solvable.
TA-Prioritized is complete for well-formed5 MAPD instances, a realistic subclass.
On-Line Multi-Robot Trajectory Planning in Well-Formed Infrastructures”. In:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 fjnding (MAPF) problem and anonymous MAPF problem. TA-Hybrid is similar to TA-Prioritized but uses a difgerent path-planning method.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Hybrid Path Planning Plans sub-paths for agents in chronological order.
1 2 3 MAPF instance anonymous MAPF instance
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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-fmow (polynomial).
New Task Agents
→ delivery locations. Cannot swap delivery locations. Uses ICBS 6(exponential).
Multi-Agent Pathfjnding”. In: IJCAI. 2015, pp. 740–746.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid makespan 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 assignment Task Assignment: smaller makespans. Path Planning: scale better. “reserving dummy paths”: smaller makespans.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid makespan 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 planning Task Assignment: smaller makespans. Path Planning: scale better. “reserving dummy paths”: smaller makespans.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Three Inovations
CENTRAL GREEDY1 GREEDY2 TA-ICBS TA-Prioritized TA-Hybrid makespan 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 method Task Assignment: smaller makespans. Path Planning: scale better. “reserving dummy paths”: smaller makespans.
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
TA-Hybrid VS TA-Prioritized TA-Prioritized TA-Hybrid makespan (runtime) 538 (30s) 532 (69s)
Results in the small warehouse.
TA-Prioritized TA-Hybrid makespan (runtime) 669 (1079s) 629 (1298s)
Results in the large warehouse.
Efgectiveness (makespan): TA-Hybrid < TA-Prioritized Effjciency (runtime): TA-Prioritized < TA-Hybrid
Task and Path Planning for Multi-Agent Pickup and Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Background Task Assignment Prioritized Path Planning Hybrid Path Planning Experimental Results
Takeaways Multi-agent pickup-and-delivery (MAPD) problem. Two offmine algorithms: TA-Prioritized and TA-Hybrid. Three innovations:
Task Assignment: one task sequence per agent by solving a special TSP. Path Planning: prioritized path planning and hybrid path planning. Deadlock Avoidance: “reserving dummy paths”.
Smaller makespans and scale better than CENTRAL in simulated warehouses with hundreds of robots and thousands of tasks.
Task and Path Planning for Multi-Agent Pickup and Delivery