1. Encoding HTN Planning as a Dynamic CSP Pavel Surynek Charles University, Prague pavel.surynek@seznam.cz A First Step to Application of CP in Planning Domain CP 2005, Doctoral Programme

2.  Traditional planning (STRIPS) Initial world state Set of actions changing the world state (+ conditions under what they can be used) Goal state of the world  Plan = Sequence of actions transforming the initial world state into a goal state of the world Why HTN planning ? NOT easy to incorporate any kind of domain knowledge Location ALocation B Initial state Location ALocation B Goal state Actions CP 2005, Doctoral ProgrammePavel Surynek

3. HTN Planning  Augments the traditional action based model with: Grammar of legal solutions Reduction schemas  Initial state same as in STRIPS  Goal state again same as in STRIPS  But actions are more expressive HTN Planning uses tasks and task networks e.g.: transportPeople:-transportPeopleByBus or transportPeopleByTrain Task Task network Task reduction schema CP 2005, Doctoral ProgrammePavel Surynek

4. transportPeopleByBus :- getIntoBus, travel, getOff | getIntoBus<travel<getOff transportPeopleByBus transportPeople:-transportPeopleByBus or transportPeopleByTrain Details of HTN Planning  Plan = Again sequence of actions (tasks without reduction schemas) transforming initial state into goal state Only the sequences accepted by the grammar are legal plans  reduction of the search space Location ALocation B Initial state Location ALocation B Goal state transportPeopleByTrain transportPeople or getIntoBus and travel getOff getIntoTrain and travel getOff Location ALocation B Goal state Plan #1 Plan #2 CP 2005, Doctoral ProgrammePavel Surynek

5.  For a given HTN planning problem a k-step (hierarchical) CSP model is constructed  Variables are used to encode: Tasks  e.g.: transportPeople{, } Actions  e.g.: getIntoBus{,, …, } World states  e.g.: busAt(time){, } The CSP model: static properties CP 2005, Doctoral Programme Location ALocation B k-moments of execution Always bound with its superior task Pavel Surynek

6. The CSP model: constraints CP 2005, Doctoral Programme  Preconditions and effects of the actions  Initial state  Task constraints are more difficult Constructed hierarchically if getIntoBus = 1 then busAt(1)=Location A and peopleAt(1)=Location A and peopleAt(2)=Bus e.g.: busAt(1)=Location B and trainAt(1)=Location B and peopleAt(1)=Location A e.g.: Pavel Surynek

7. ((Subproblem A) or (Subproblem B)) and transportPeople task is modelled as (if transportPeople=Bus then Subproblem A) and The CSP model: task constraints  Each task constraint is associated with reduction subproblems (Subproblem A) or (Subproblem B) example: transportPeopleByBus :- getIntoBus, travel, getOff | getIntoBus<travel<getOff transportPeopleByTrain :- getIntoTrain, travel, getOff | getIntoTrain<travel<getOff Subproblem A Subproblem B CP 2005, Doctoral Programme (if transportPeople=Train then Subproblem B) (if transportPeople=Bus then Subproblem A) transportPeople Pavel Surynek

8. Dynamic properties of the model  Described model is constructed dynamically as the search proceeds  Depth of the hierarchical model is always limited  When the task variable is instantiated the model is extended with the corresponding subproblems CP 2005, Doctoral ProgrammePavel Surynek Constraint model transportPeople  Bus New constraint model Propagation

9. Conclusions: issues to solve  Amount of model extension after variable instantiation or domain narrowing deeper/larger extension  more constrained model, but larger memory consumption  How to combine constraints via logical conjunctions reification is easy to implement, but provides weak propagation the model uses lot of disjunctive constraints (construct if then), constructive disjunction is more suitable  Experimental evaluation of the proposed encoding ! Pavel SurynekCP 2005, Doctoral Programme