74.419 Artificial Intelligence 2005/06

Partial Order Planning

Socks & Shoes

Left Sock

Start

Finish

Right Shoe

Left Shoe

Right Sock

Start

Right Sock

Finish

LeftShoe

RightShoe

Left Sock

Start Start Start Start Start

Right Sock

Right Sock

Right Sock

Right Sock

Right Sock

Left Sock

Left Sock

Left Sock

Left Sock

Left Sock

Left Sock

RightShoe

RightShoe

RightShoe

RightShoe

RightShoe

LeftShoe

LeftShoe

LeftShoe

LeftShoe

Finish Finish Finish Finish 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 ca

b

threatb<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, 1998.

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. (AAAI’96 Robot Competition - Meeting Scheduling)

Martina Veloso, MIT (RoboCup)