Timelines with Temporal Uncertainty Alessandro Cimatti Andrea - PowerPoint PPT Presentation

Timelines with Temporal Uncertainty Alessandro Cimatti Andrea Micheli Marco Roveri Embedded Systems Unit Fondazione Bruno Kessler, Trento, Italy amicheli@fbk.eu 18th July 2013 AAAI 2013

Outline Introduction 1 Timelines with Temporal Uncertainty 2 Strong Controllability Bounded-Horizon Encoding 3 Conclusion 4

Outline Introduction 1 Timelines with Temporal Uncertainty 2 Strong Controllability Bounded-Horizon Encoding 3 Conclusion 4

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. 2/9

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. Temporal Uncertainty No Yes Deciding Activities (Temporal Planning) Fixed Activities (Scheduling) 2/9

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. Temporal Uncertainty No Yes Deciding Activities PDDL 2.1, Timelines (Temporal Planning) Fixed Activities (Scheduling) 2/9

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. Temporal Uncertainty No Yes Deciding Activities Timelines with PDDL 2.1, Timelines (Temporal Planning) Temporal Uncertainty Fixed Activities (Scheduling) 2/9

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. Temporal Uncertainty No Yes Deciding Activities Timelines with PDDL 2.1, Timelines (Temporal Planning) Temporal Uncertainty 20 0 7 8 11 16 19 t A s A e Fixed Activities B s B e (Scheduling) 2/9

Temporal Planning (With Temporal Uncertainty) Our setting: Temporal Planning in presence of Temporal Uncertainty, i.e. when some activities cannot be temporally controlled by the plan executor. Temporal Uncertainty No Yes Deciding Activities Timelines with PDDL 2.1, Timelines (Temporal Planning) Temporal Uncertainty 20 20 0 7 8 11 16 19 0 7 8 11 16 19 t t A s A e A s A e Fixed Activities B s B e B s B e (Scheduling) 2/9

Timeline Planning Underlying Idea: Generate a sequence of activities for a set of components according to a Domain Theory that fulfill a set of (temporal) constraints. 3/9

Timeline Planning Underlying Idea: Generate a sequence of activities for a set of components according to a Domain Theory that fulfill a set of (temporal) constraints. Planners HSTS: Muscettola [1993] Europa: Frank and J´ onsson [2003] APSI: Cesta et al. [2009] CNT: Verfaillie et al. [2010] 3/9

Timeline Planning Underlying Idea: Generate a sequence of activities for a set of components according to a Domain Theory that fulfill a set of (temporal) constraints. Planners HSTS: Muscettola [1993] Europa: Frank and J´ onsson [2003] APSI: Cesta et al. [2009] CNT: Verfaillie et al. [2010] Applications: Timeline-based planning is used in many practical applications where temporal constraints are predominant (e.g. Activity Planning & Scheduling for Space Operations). 3/9

Contributions 1 Formalization of Timeline Planning with and without Temporal Uncertainty ◮ Abstract syntax ◮ Problem definition ◮ Formal semantics 4/9

Contributions 1 Formalization of Timeline Planning with and without Temporal Uncertainty ◮ Abstract syntax ◮ Problem definition ◮ Formal semantics 2 Bounded-horizon, strong controllability problem sound and complete encoding in first-order logic. ◮ Directly derived from formal semantics ◮ APSI-derived concrete syntax ◮ Made practical by SMT( LRA ) 4/9

Outline Introduction 1 Timelines with Temporal Uncertainty 2 Strong Controllability Bounded-Horizon Encoding 3 Conclusion 4

Formalization of Timelines (without Temporal Uncertainty) Formalization Satellite Hidden Visible [ 10 , 12 ] [ 10 , 11 ] G D N U I R R I U N D G Device Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible [ 10 , 12 ] [ 10 , 11 ] G D N U I R R I U N D G Device Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 Facts constrain the desired [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] executions (e.g Device.Send2 ∈ [ 30 , ∞ ) ) 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 Facts constrain the desired [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] executions (e.g Device.Send2 ∈ [ 30 , ∞ ) ) Evolution Satellite Hidden Visible Hidden Visible Device Idle Send1 Idle Send2 t 0 10 15 21 33 35 40 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 Facts constrain the desired [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] executions (e.g Device.Send2 ∈ [ 30 , ∞ ) ) Evolution Satellite Hidden Visible Hidden Visible Device Idle Send1 Idle Send2 t 0 10 15 21 33 35 40 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 Facts constrain the desired [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] executions (e.g Device.Send2 ∈ [ 30 , ∞ ) ) Evolution Satellite Hidden Visible Hidden Visible Device Idle Send1 Idle Send2 t 0 11 16 21 33 35 40 5/9

Formalization of Timelines (without Temporal Uncertainty) Formalization Generators describe component behaviors Satellite Hidden Visible Synchronizations describe [ 10 , 12 ] [ 10 , 11 ] inter-component requirements via G D N U I R R I U N D G Quantified Allen Relations Device Send1 Idle Send2 Facts constrain the desired [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] executions (e.g Device.Send2 ∈ [ 30 , ∞ ) ) Evolution Satellite Hidden Visible Hidden Visible Device Idle Send1 Idle Send2 t 0 10 16 20 32 35 40 5/9

Timelines with Temporal Uncertainty Temporal Uncertainty Annotation We annotate the domain values Satellite with controllable or Hidden Visible [ 10 , 12 ] [ 10 , 11 ] uncontrollable flags for both G D N U starting and ending time. R I R I U N D G Device We annotate the Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] synchronizations with contingent or free flag. Evolution 6/9

Timelines with Temporal Uncertainty Temporal Uncertainty Annotation We annotate the domain values Satellite with controllable or Hidden Visible [ 10 , 12 ] [ 10 , 11 ] uncontrollable flags for both G D N U starting and ending time. R I R I U N D G Device We annotate the Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] synchronizations with contingent or free flag. Evolution Satellite Hidden Visible Hidden Visible Device t 0 10 12 15 20 23 30 35 40 6/9

Timelines with Temporal Uncertainty Temporal Uncertainty Annotation We annotate the domain values Satellite with controllable or Hidden Visible [ 10 , 12 ] [ 10 , 11 ] uncontrollable flags for both G D N U starting and ending time. R I R I U N D G Device We annotate the Send1 Idle Send2 [ 5 , 5 ] [ 1 , ∞ ] [ 5 , 5 ] synchronizations with contingent or free flag. Evolution Satellite Hidden Visible Hidden Visible Device Idle Send1 Idle Send2 t 0 10 12 15 20 23 30 35 40 6/9

Outline Introduction 1 Timelines with Temporal Uncertainty 2 Strong Controllability Bounded-Horizon Encoding 3 Conclusion 4

Strong Controllability Bounded-Horizon Encoding Idea: we assume all durations positive and fix (an upper bound of) the maximal number of value changes for each generator withing a given horizon. 7/9