Artificial Intelligence 2005/06 Partial Order Planning

Socks & Shoes Left Sock Start Finish Right Shoe Left Shoe Right Sock Start Right Sock Finish Left Shoe Right Shoe Left Sock Start Right Sock Right Sock Right Sock Right Sock Right Sock Left Sock Left Sock Left Sock Left Sock Left Sock Left Sock Right Shoe Right Shoe Right Shoe Right Shoe Right Shoe Left Shoe Left Shoe Left Shoe Left Shoe Finish Left Shoe on Right Shoe on Left Sock on Right Sock on Partial Order Plan: Total Order Plans:

Partially Ordered Plans Partially Ordered Plans - or: "How Do You Put Your Shoes On?" Partially Ordered Plans: no strict sequence partly parallel observe threats

Resource Constraints in Planning Resources physical quantities, e.g. money, fluids etc. time Integrate Measures into Action Description and Planning representation of physical quantities and reasoning / calculation, e.g. for buy-action: effect: cash := cash – price (x) time system / time logic, e.g. go-to-action: effect: time := time + 30 (Minutes) Backtracking on Constraint Violation

Least Commitment Strategy Partially Instantiated Plans Least Commitment Strategy In general, make as little concrete as possible, i.e. leave things undetermined until you have to determine them and become concrete. Partially Instantiated Plans During planning, variables have not necessarily to be instantiated immediately. Instantiation can wait, until binding becomes necessary

Partial Order Planning 1 Start with a rough plan and refine iteratively. First plan consists only of start and finish actions: start - T as precondition, initial world state as effect finish - goal as precondition, NIL as effect Select actions to achieve sub-goals separately, quasi in parallel partial-order plan Fulfill open preconditions (sub-goals), until no more unsatisfied preconditions are left (last one is T of start)

Partial Order Planning - Causal Links Add causal links to connect effects from actions to matching preconditions for plan, e.g. move(A,B,x) has effect clear(B) clear(B) is precondition for move(B,y,z) Causal links specify a partial order.

effect of move (A,y,B) is on(A,B) is precondition for finish (goal state) causal link

Partial Order Planning - Threats Recognize threats - the effect of an action A destroys the precondition of another action B, e.g. move(A,x,B) destroys clear(B)(in DELETE-list) clear(B) is precondition for move(B,y,z) thus, move(B,Fl,C) has to be done before move (A,Fl,B) Add threats as partial order to plan: b<a (do b before a).

effect of a = move(A,Fl,B) includes DEL Clear(B) precond of c = move(B,Fl,C) includes Clear(B) threat! c<a c a b threat b<c

Partial Order Planning - Threats partial order plan = set of action strings (partial plans) Problem: Detect and resolve threats, i.e. conflicts between actions – where the precondition of one action is deleted by another action – by choosing an adequate ordering of actions: if action b is a threat to action a, then a<b, i.e. a has to occur before b. (see also Russell/Norvig textbook, The POP Planner)

Partial Order Planning - Overall Use plan transformation operators to refine the partial plan and construct a complete plan: add an action (operator), reorder actions (operators), instantiate actions (operators). A partial order plan consists of a set of action sequences (partial plans; action strings) which together achieve the complete set of goal literals. Threats induce an additional partial order of these action sequences.

Additional References Nils J. Nilsson: Artificial Intelligence – A New Synthesis. Morgan Kaufmann, San Francisco, Konolidge, K. and K. Myers: The Saphira Architecture for Autonomous Mobile Robots (Robot Soccer Class Project) Guzzoni, D. et al.: Many Robots Make Short Work. (AAAI96 Robot Competition - Meeting Scheduling) Martina Veloso, MIT (RoboCup)