Optimal Multi-robot Task Planning: from Synthesis to Execution (and Back) Francesco Leofante Theory of Hybrid Systems AIMS Lab, Dibris RWTH Aachen University University of Genoa Germany Italy Supervisors: Erika ´ Abrah ´ am and Armando Tacchella At a Glance Motivation Autonomous robots are increasingly used in modern factories How can we provide guarantees and explanations for their behaviors? Project Overview Optimal multi-robot task planning Integration with online execution and monitoring agent Testbed: RoboCup Logistics League Optimization Modulo Theories (OMT) Boolean abstraction SAT solver Input CNF formula ϕ + objective f Theory solver(s) SAT (optimal) or UNSAT constraints C SAT: compute local optimum μ = Opt(f,C ) update ϕ := ϕ ∧ (f μ), ∈{<, >} UNSAT: explanation Optimal Plans with OMT [1, 2] Find optimal reward for bounded executions s 0 a 0 -→ s 1 a 1 -→ ... a p -→ s p+1 over states s 0 ,...,s p+1 executing actions a 0 ,...,a p obtaining rewards r 0 ,...,r p after transitions s i a i -→ s i+1 Encode in linear mixed-integer arithmetic: initial states I (s), transition relation T (s, a, s 0 ) and reward function R(s) Solve an optimal bounded planning problem maximize X 0≤i≤p r i s.t. I (s 0 ) ∧ ^ 0≤i≤p T (s i ,a i ,s i+1 ) ∧ _ 0≤i≤p+1 R(s i ) Online Execution and Monitoring [2, 3] Plans are only as good as the model! Modelling assumptions may be chal- lenged during execution. What happens to our plan? Planner Executive Environment Monitor ✗ RoboCup Logistics League (RCLL) [4, 5] Principles Two teams of three robots each compete on a common field Task: fulfill orders and deliver goods Products consist of colored base, 0 to 3 colored rings, and cap Machines of four different types can be used to maintain and optimize production Order schedule posted by automated referee Complexity and color known at run-time BS RS 1 RS 2 RS 2 CS 2 Base Element (specific color) Base Element (any color) Up to 3 rings (four colors) Top-most cap (two colors) CS Machine Type {BS,DS,CS,RS} Summing up... Developed a domain-specific task planner for the RCLL Integrated it with an online execution and monitoring agent. What did we learn? OMT is expensive... → novel encodings/relaxations needed. What’s next? Implementation of a domain-independent planner based on what we learned with the RCLL Assess the impact of our findings on a broader range of AI planning problems. Stay tuned! References [1] F. Leofante, E. ´ Abrah ´ am, T. Niemueller, G. Lakemeyer and A. Tacchella: On the Synthesis of Guaranteed-Quality Plans for Robot Fleets in Logistics Scenarios via Optimization Modulo Theories. IEEE IRI. (2017) [2] F. Leofante, E. ´ Abrah ´ am, T. Niemueller, G. Lakemeyer and A. Tacchella: Integrated Synthesis and Execution of Optimal Plans for Multi-Robot Systems in Logistics. Information Systems Frontiers. (2018) [3] T. Niemueller, G. Lakemeyer, F. Leofante, E. ´ Abrah ´ am Towards CLIPS-based Task Execution and Monitoring with SMT-based Planning and Optimization. PlanRob@ICAPS. (2017) [4] T. Niemueller, G. Lakemeyer, and A. Ferrein: The RoboCup Logistics League as a Benchmark for Planning in Robotics. PlanRob@ICAPS. (2015) [5]T. Niemueller, E. Karpas, T. Vaquero and E. Timmons: Planning Competition for Logistics Robots in Simulation. PlanRob@ICAPS. (2016) Download this poster

Optimal Multi-robot Task Planning: from Synthesis to ... · Optimal Multi-robot Task Planning: from Synthesis to Execution (and Back) Francesco Leofante Theory of Hybrid Systems AIMS

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Optimal Multi-robot Task Planning:from Synthesis to Execution (and Back)

Francesco Leofante

Theory of Hybrid Systems AIMS Lab, DibrisRWTH Aachen University University of Genoa

Germany Italy

Supervisors: Erika Ábrahám and Armando Tacchella

At a Glance

Motivation

� Autonomous robots are increasingly used in modern factories

� How can we provide guarantees and explanations for their behaviors?

Project Overview

� Optimal multi-robot task planning

� Integration with online execution and monitoring agent

� Testbed: RoboCup Logistics League

Optimization Modulo Theories (OMT)

Boolean abstraction

SAT solver

Input CNF formula ϕ

+

objective f

Theorysolver(s)

SAT (optimal)or

UNSAT

constraints C

SAT: compute local optimum µ = Opt(f, C)update ϕ := ϕ ∧ (f ./ µ), ./∈ {}

UNSAT: explanation

1

Optimal Plans with OMT [1, 2]

Find optimal reward for bounded executions s0a0−→ s1

a1−→ . . . ap−→ sp+1

� over states s0, . . . , sp+1� executing actions a0, . . . , ap

� obtaining rewards r0, . . . , rp after transitions siai−→ si+1

Encode in linear mixed-integer arithmetic:

� initial states I(s), transition relation T (s, a, s′) and reward function R(s)

Solve an optimal bounded planning problem

maximize∑

0≤i≤pri s.t. I(s0) ∧

∧0≤i≤p

T (si, ai, si+1)

∧ ∨

0≤i≤p+1R(si)

Online Execution and Monitoring [2, 3]

� Plans are only as good as the model!

� Modelling assumptions may be chal-lenged during execution.

� What happens to our plan?

Planner Executive Environment

Monitor

X7

1

RoboCup Logistics League (RCLL) [4, 5]

Principles

� Two teams of three robots each compete ona common field

� Task: fulfill orders and deliver goods

� Products consist of colored base, 0 to 3 col-ored rings, and cap

� Machines of four different types can be usedto maintain and optimize production

� Order schedule posted by automated referee

� Complexity and color known at run-time

BS RS 1 RS 2 RS 2 CS 2

Base Element(specific color)

Base Element(any color)

Up to 3 rings(four colors)

Top-most cap(two colors) CS

Machine Type{BS,DS,CS,RS}

Summing up...

� Developed a domain-specific task planner for the RCLL

� Integrated it with an online execution and monitoring agent.

What did we learn?

OMT is expensive. . .→ novel encodings/relaxations needed.

What’s next?

� Implementation of a domain-independent planner based on what we learned with the RCLL

� Assess the impact of our findings on a broader range of AI planning problems.

Stay tuned!

References

[1] F. Leofante, E. Ábrahám, T. Niemueller, G. Lakemeyer and A. Tacchella: On the Synthesis of Guaranteed-QualityPlans for Robot Fleets in Logistics Scenarios via Optimization Modulo Theories. IEEE IRI. (2017)

[2] F. Leofante, E. Ábrahám, T. Niemueller, G. Lakemeyer and A. Tacchella: Integrated Synthesis and Execution ofOptimal Plans for Multi-Robot Systems in Logistics. Information Systems Frontiers. (2018)

[3] T. Niemueller, G. Lakemeyer, F. Leofante, E. Ábrahám Towards CLIPS-based Task Execution and Monitoring withSMT-based Planning and Optimization. PlanRob@ICAPS. (2017)

[4] T. Niemueller, G. Lakemeyer, and A. Ferrein: The RoboCup Logistics League as a Benchmark for Planning inRobotics. PlanRob@ICAPS. (2015)

[5] T. Niemueller, E. Karpas, T. Vaquero and E. Timmons: Planning Competition for Logistics Robots in Simulation.PlanRob@ICAPS. (2016)

Download this poster