Cooperative Task Assignment - EXCELLABUST...Find a conflict free assignment of tasks to robots, such...

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Cooperative Task AssignmentDonato Di Paola

Institute of Intelligent Systems for Automation National Research Council

Talk Outline

Cooperative Mission Planning and Task Assignment

The Multi-Robot Task Assignment Problem

Decentralized Task Assignment Algorithms

Task Allocation in Complex Scenarios

Cooperative Mission Planning and Task Assignment

The big picture Cooperative Multi-Robot Systems

Heterogeneous robots

Local sensing

Communication Network

The big picture Cooperative Multi-Robot Systems

Local sensing

Communication Network

Achieve Global Objectives

The role of task assignment Mission Control Architecture

Planning Task Assignment

Task Execution

Mission Actions

The role of task assignment Mission Control Architecture

Planning Task Assignment

Task Execution

Mission ActionsTasks

Robots

The Multi-Robot Task Assignment Problem

The Task Assignment Problem

J = {1, . . . ,m}

Given a set of robot

Given a set of tasks

David W. Pentico, Assignment problems: A golden anniversary survey, European Journal of Operational Research, Volume 176, Issue 2, 16 January 2007, Pages 774-793

J = {1, . . . ,m}

GoalFind a conflict free assignment of tasks to robots, such that the global cost (score) is minimized (maximized)

Taxonomy of Task Assignment problems

G. A. Korsah, A. Stentz, and M. B. Dias. A comprehensive taxonomy for multi-robot task allocation. International Journal of Robotics Research, 32(12):1495–1512, 2013.

Mathematical formulation for MR-ST-IA

Objective Function

Assignment Constraints

Objective Function

Robot capacity constraint

Objective Function

Conflict-free constraint

Objective Function

Conflict-free constraint

Assignment variables

Objective Function

8i 2 I

8j 2 J

Objective Function

8i 2 I

8j 2 J

Cost Matrix Solution: minimized global cost

Example

Objective Function

8i 2 I

8j 2 J

Cost Matrix Solution: minimized global cost

Example

Optimal solutiont1 assigned to r2 t2 assigned to r3 t3 assigned to r1

Optimal valueCost = 13

Mathematical formulation for MR-ST-TA

Objective Function

Assignment ConstraintsmX

xij Lt 8i 2 I

xij 1 8j 2 J

Objective Function

xij Lt 8i 2 I

xij 1 8j 2 J

Objective Function

xij Lt 8i 2 I

xij 1 8j 2 J

Centralized Approach

Centralized Vs Decentralized approaches

Optimal SolutionWell-studied problems

ConsPros

Not robust against failures

ConsPros

Decentralized Approach

Robust to failuresScale with the size of the robotic network

ConsPros

Decentralized Approach

Robust to failuresScale with the size of the robotic network

Sub-Optimal solution

Decentralized Task Assignment Algorithms

Consensus Based Bundle Algorithm

H.-L. Choi, L. Brunet, J. P. How, Consensus-Based Decentralized Auctions for Robust Task Allocation, IEEE Transactions on Robotics, Vol. 25, No. 4, pp. 912-926, August 2009

Decentralized Task Assignment The CBBA

Consensus Based Bundle Algorithm

It solves MR-ST-TA problems

Decentralized algorithm (leverages the consensus theory)

Iterative algorithm (known number of iteration for convergence)

Performance guarantee

H.-L. Choi, L. Brunet, J. P. How, Consensus-Based Decentralized Auctions for Robust Task Allocation, IEEE Transactions on Robotics, Vol. 25, No. 4, pp. 912-926, August 2009

Synchronized communication

Decentralized Task Assignment The CBBA

CBBA: The two phases approach

Each robot does

Bundle Construction Phasethe robot assigns to itself the tasks with the maximum score, until the bundle if full

Each robot does

Communicationthe robot exchanges information with its neighbors

Each robot does

Conflict Resolution PhaseThe assigned tasks are already assigned to other robots?

if the previous check is true

the robot maintains the tasks with the higher score

Each robot does

Conflict Resolution PhaseThe assigned tasks are already assigned to other robots?

if the previous check is true

the robot maintains the tasks with the higher score

T1 T2 T3 T4 T5

Bundle Construction PhaseIteration 1

CBBA: An example

T1 T2 T3 T4 T5

CBBA: An example

T1 T2 T3 T4 T5

CBBA: An example

T1 T2 T3 T4 T5

Conflict !!!One or more tasks (T1 and T3) are assigned to more than one robot

CBBA: An example

T1 T2 T3 T4 T5

Conflict Resolution PhaseIteration 1

CBBA: An example

COMMUNICATION

T1 T2 T3 T4 T5

CBBA: An example

COMMUNICATION

T1 T2 T3 T4 T5

CBBA: An example

Conflict Removal

T1: score of R1 > score of R2 T3: score of R1 > score of R3

COMMUNICATION

T1 T2 T3 T4 T5

CBBA: An example

Conflict Removal

COMMUNICATION

T1 T2 T3 T4 T5

CBBA: An example

Conflict Removal

T1 T2 T3 T4 T5

CBBA: An example

T1 T2 T3 T4 T5

CBBA: An example

T1 T2 T3 T4 T5

CBBA: An example

Conflict !!!One or more tasks (T2) are assigned to more than one robot

T1 T2 T3 T4 T5

CBBA: An example Iteration 2Conflict Resolution Phase

COMMUNICATION

T1 T2 T3 T4 T5

Conflict Removal

T2: score of R2 > score of R2

COMMUNICATION

T1 T2 T3 T4 T5

Conflict Removal

T2: score of R2 > score of R2

T1 T2 T3 T4 T5

Assignment CompletedAll the tasks are assignedNo conflictsMaximization of score

Task Assignment in Complex Scenarios

Problem Setting

Open challenges

Multi Robot Transportation Problems with Capacity

Task Assignment

Multi-Robot Routing

Balancing of vehicle within the given area

Each robot picks up a task in a location

Load capacity constraint

Distributed coverage of a given area

Multi Robot Transportation Problems with Capacity Problem Setting

Maximize a Network Score

subject to

Routing Constraints }

subject to

Routing Constraints

Assignment constraints

subject to

Routing Constraints

Balancing constraints

subject to

Routing Constraints

Balancing constraints

NP-Hard

Decentralized Assignment with Load Balancing 2 Phases Iterative Algorithm

A. Acquaviva, D. Di Paola, A. Rizzo, Decentralized Optmization-based Load Balancing in Mobility On-Demand Systems, in preparation

Each robot does

Auction Phasethe robot assigns to itself the pair (task,route) with the max score

Each robot does

Balancing PhaseThe starting or the destination area is balanced?

if the previous check is false and the robot is one of those exceeding the area capacity

the robot drops the assignment

Each robot does

Balancing PhaseThe starting or the destination area is balanced?

if the previous check is false and the robot is one of those exceeding the area capacity

the robot drops the assignment

Results Simulation Setup

Simulated City from citibike web site

Real Statistics

Subset of stations of the NY citibike bike sharing system

Rate of arrival of customers

Average number of vehicle at a given station

Average travel time for a given pair of stations

Results

Optimality (6 stations and 30 vehicles)

Convergence 10 stations and 50 vehicles

Always DLB > 70% OPT

20 30 40 50 60 70 80 905000

Number of Customers

0 50 100 1500

Number of Customers

70%OPT

Conclusions

Conclusions Solving Task Assignment in Multi-Robot Systems

Composed by 2 or more phases

Hierarchical Iterative Algorithms

Local decision/evaluation

Decentralized Auction/ElectionNearest neighbors communication

Conclusions Solving Task Assignment in Multi-Robot Systems

Composed by 2 or more phases

Hierarchical Iterative Algorithms

Local decision/evaluation

Decentralized Auction/ElectionNearest neighbors communication

Communications with time delays

Open Issues

Protocols for secure communications

Asynchronous communications

Malicious / Misbehaving robot

Cooperative Task AssignmentDonato Di Paola

Institute of Intelligent Systems for Automation National Research Council

Cooperative Task Assignment - EXCELLABUST...Find a conflict free assignment of tasks to robots, such...

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