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Planning Integrating Logic and Constraint Reasoning in a Timeline-based Planner Riccardo De Benedictis and Amedeo Cesta Institute of Cognitive Science and Technology National Research Council Rome Italy 25/09/2015 Planning The

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SLIDE 1

Planning

Integrating Logic and Constraint Reasoning in a Timeline-based Planner

Riccardo De Benedictis and Amedeo Cesta

Institute of Cognitive Science and Technology National Research Council Rome – Italy

25/09/2015

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SLIDE 2

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

The Timeline-based Approach

  • A set of relevant features which need to be controlled to
  • btain a desired temporal behavior
  • Physical or logical subsystems which are relevant to a

given planning context

  • The planner/scheduler plays the role of the controller for

these entities

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SLIDE 3

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

The ILOC Reasoning Environment – Objects and Constraints

  • An object-oriented environment for the definition of objects

and constraints among them

  • Every object is an instance of a specific type
  • Primitive types (e.g., bools, ints, reals, etc.)
  • Complex types (e.g., robots, trucks, locations, etc.)
  • Dot notation for addressing objects and enforcing constraints:

<object>.<property>

  • Constraints

π‘š. 𝑦 ≀ 𝑠. 𝑦 Β¬ π‘š. 𝑦 ≀ 5 π‘š. 𝑦 β‰₯ 5 ∧ π‘š. 𝑦 ≀ 10 π‘š. 𝑦 ≀ 5 ∨ π‘š. 𝑦 β‰₯ 10 π‘š. 𝑦 β‰₯ 10 β†’ π‘š. 𝑧 β‰₯ 10 βˆƒπ‘š ∈ π‘€π‘π‘‘π‘π‘’π‘—π‘π‘œπ‘‘: π‘š. 𝑦 β‰₯ 10 βˆ€π‘š ∈ π‘€π‘π‘‘π‘π‘’π‘—π‘π‘œπ‘‘: π‘š. 𝑦 ≀ 100

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SLIDE 4

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

The ILOC Reasoning Environment - Rules

  • First-order Horn clauses
  • At most one positive literal (head of the clause)
  • Any number of negative literals (body of the clause)

𝐼𝑓𝑏𝑒 ⇐ 𝐢𝑝𝑒𝑧

  • The body contains calls to predicates (sub-goals) and

constraints (in any logical combination)

  • No constraints in the head of the clause
  • Rules having the same head are disjunctive
  • First-order resolution
  • Not ordered sub-goaling
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SLIDE 5

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Timeline-based Planning within ILOC

  • Create timeline complex types
  • StateVariable, ReusableResource, ConsumableResource, etc.
  • extendable through inheritance
  • Endow predicates with numerical parameters representing time:
  • starting time
  • ending time
  • duration (duration = end - start)
  • Endow predicates with a scope parameter
  • denotes on which object (e.g., timeline) the formula will appear
  • Extend resolution for managing objects’ inconsistencies
  • add further β€œimplicit” constraints on the formula according to the scope’s type
  • i.e., we provide scheduling capabilities to timelines
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SLIDE 6

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Timeline-based Planning within ILOC

  • Create timeline complex types
  • StateVariable, ReusableResource, ConsumableResource, etc.
  • extendable through inheritance
  • Endow predicates with numerical parameters representing time:
  • starting time
  • ending time
  • duration (duration = end - start)
  • Endow predicates with a scope parameter
  • denotes on which object (e.g., timeline) the formula will appear
  • Extend resolution for managing objects’ inconsistencies
  • add further β€œimplicit” constraints on the formula according to the scope’s type
  • i.e., we provide scheduling capabilities to timelines

class Robot extends StateVariable { … } Going(Location l, Robot scope, real start, real end, real duration) := … At(Location l, Robot scope, real start, real end, real duration) := …

Robot extends StateVariable t

At(l1, sc1, s1, e1, d1) Going(l2, sc2, s2, e2, d2) At(l2, sc3, s3, e3, d3)

𝑓1 ≀ 𝑑2 ∨ 𝑓2 ≀ 𝑑1 ∨ 𝑑𝑑1 β‰  𝑑𝑑2

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SLIDE 7

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Scope Variables and Execution Uncertainty

t

10:00 12:00

Truck 2 Truck 1

11:00 13:00 𝑒0 13:30 15:30 𝑒1 𝑒2

𝑒1. 𝑑𝑒𝑏𝑠𝑒 = 13: 30 𝑒0. π‘’π‘£π‘ π‘π‘’π‘—π‘π‘œ β‰₯ 2: 00 𝑒0. π‘“π‘œπ‘’ ≀ 17: 00

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SLIDE 8

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Scope Variables and Execution Uncertainty

t

10:00 12:00

Truck 2 Truck 1

11:00 13:00 𝑒0 𝑒0 13:30 15:30 𝑒1 𝑒2

𝑒1. 𝑑𝑒𝑏𝑠𝑒 = 13: 30 𝑒0. 𝑑𝑒𝑏𝑠𝑒 β‰₯ 11: 00 𝑒0. π‘’π‘£π‘ π‘π‘’π‘—π‘π‘œ β‰₯ 2: 00 𝑒0. π‘“π‘œπ‘’ ≀ 17: 00

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SLIDE 9

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Scope Variables and Execution Uncertainty

t

10:00 12:00

Truck 2 Truck 1

11:00 13:00 𝑒0 𝑒0 13:30 15:30 𝑒1 𝑒2

𝑒1. 𝑑𝑒𝑏𝑠𝑒 = 13: 30 𝑒0. 𝑑𝑒𝑏𝑠𝑒 β‰₯ 11: 00 𝑒0. π‘’π‘£π‘ π‘π‘’π‘—π‘π‘œ β‰₯ 2: 00 𝑒0. 𝑑𝑒𝑏𝑠𝑒 β‰₯ 12: 00

𝑒0

𝑒0. π‘“π‘œπ‘’ ≀ 17: 00

𝑒0

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SLIDE 10

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Conclusions

  • An uniform schema for
  • Logic Programming (LP)
  • not-ordered subgoaling
  • Constraint Programming (CP)
  • similar to CLP
  • Timeline-reasoning
  • e.g., Scheduling
  • Heuristics
  • Static and Dynamic
  • Different planners
  • VHPOP (partial order approach)
  • OPTIC (TRPG heuristic)
  • COLIN (TRPG heuristic)
  • CPT, TPSHE, ITSAT, LPG, etc… will be added soon!!!

:D

1 10 100 1000 10000 100000 02 04 06 08 10 12 14 16 18 20 22 Execution time (ms)

  • Nr. blocks

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN

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SLIDE 11

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Conclusions

  • An uniform schema for
  • Logic Programming (LP)
  • not-ordered subgoaling
  • Constraint Programming (CP)
  • similar to CLP
  • Timeline-reasoning
  • e.g., Scheduling
  • Heuristics
  • Static and Dynamic
  • Different planners
  • VHPOP (partial order approach)
  • OPTIC (TRPG heuristic)
  • COLIN (TRPG heuristic)
  • CPT, TPSHE, ITSAT, LPG, etc… will be added soon!!!

:D

1 10 100 1000 10000 100000 02 04 06 08 10 12 14 16 18 20 22 Execution time (ms)

  • Nr. blocks

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN 1 10 100 1000 10000 100000 1000000 01 03 05 07 09 15 25 35 45 60 80 100 Execution time (ms)

  • Nr. ceramics

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN

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SLIDE 12

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Conclusions

  • An uniform schema for
  • Logic Programming (LP)
  • not-ordered subgoaling
  • Constraint Programming (CP)
  • similar to CLP
  • Timeline-reasoning
  • e.g., Scheduling
  • Heuristics
  • Static and Dynamic
  • Different planners
  • VHPOP (partial order approach)
  • OPTIC (TRPG heuristic)
  • COLIN (TRPG heuristic)
  • CPT, TPSHE, ITSAT, LPG, etc… will be added soon!!!

:D

1 10 100 1000 10000 100000 02 04 06 08 10 12 14 16 18 20 22 Execution time (ms)

  • Nr. blocks

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN 1 10 100 1000 10000 100000 1000000 01 03 05 07 09 15 25 35 45 60 80 100 Execution time (ms)

  • Nr. ceramics

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN 1 10 100 1000 10000 100000 1000000 10000000 001 003 005 007 009 015 025 035 045 060 080 100 Execution time (ms)

  • Nr. dishes

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN

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SLIDE 13

riccardo.debenedictis@istc.cnr.it AI*IA-2015

Planning

Conclusions

  • An uniform schema for
  • Logic Programming (LP)
  • not-ordered subgoaling
  • Constraint Programming (CP)
  • similar to CLP
  • Timeline-reasoning
  • e.g., Scheduling
  • Heuristics
  • Static and Dynamic
  • Different planners
  • VHPOP (partial order approach)
  • OPTIC (TRPG heuristic)
  • COLIN (TRPG heuristic)
  • CPT, TPSHE, ITSAT, LPG, etc… will be added soon!!!

:D

1 10 100 1000 10000 100000 02 04 06 08 10 12 14 16 18 20 22 Execution time (ms)

  • Nr. blocks

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN 1 10 100 1000 10000 100000 1000000 01 03 05 07 09 15 25 35 45 60 80 100 Execution time (ms)

  • Nr. ceramics

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN 1 10 100 1000 10000 100000 1000000 10000000 001 003 005 007 009 015 025 035 045 060 080 100 Execution time (ms)

  • Nr. dishes

iLoC (AR) iLoC (MR) VHPOP2.2 OPTIC COLIN

Thank you!

Questions?

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