74.419 Artificial Intelligence 2005/06

Hierarchical Planning

and Other StuffRussell and Norvig, Chapter 11

STRIPS – Plan Schemata

Concrete plans can also be seen as instantiations of Plan Schemata.

Shakey was able to generalize generated concrete plans into such plan schemata.

( plan generalization, learning)

Plan Learning / Plan Abstraction

Shakey generated plan schemata, so-called MACROPs (Macro-Operators), from concrete plans it had constructed earlier (i.e. “it learns plans”).

The learning process is based on describing the plan in a triangle-table (preconditions and effects of sequential actions in rows, actions in columns). Then substitute constants with variables, in a kind of inverse variable binding process with unification. (substitute the same constant with one variable)

Thus, an abstract plan schema is generated from the concrete plan.

Triangle Table

Generate Plan with STRIPS Set up Triangle Table:

left of action: precondition below action: effects (add-list) - record only

literals needed by subsequent actions or as part of the goal clause.

Generalization (abstraction) Substitute constants with variables.

"effect" of start-action initial state

precond. of move(A,B,Fl)

effect of move(A,B,Fl)

precond. of move(B,C,Fl)

precond. of finish

effect of move(B,C,Fl)

Generate Plan Schema

Generalization (abstraction) of concrete plan.

Substitute constants with variables: Fl remains Fl A x B y C z

Abstract Planning

ABSTRIPS

Consider different criticality values of preconditions in planning.

Start with global, abstract plan.

Then refine plan by trying to fulfill preconditions of abstract plan:

• Choose preconditions with highest criticality values first ( = most difficult to achieve).

• Then lower criticality value and continue with planning.

Hierarchical Planning

Principle hierarchical organization of 'actions' complex and less complex (or: abstract) actions lowest level reflects directly executable actions

Procedure planning starts with complex action on top plan constructed through action decomposition substitute complex action with plan of less complex

actions (pre-defined plan schemata; or learning of plans/plan abstraction)

overall plan must generate effect of complex action

Hierarchical Planning

Hierarchical Planning / Plan Decomposition

Plans are organized in a hierarchy. Links between nodes at different levels in the hierarchy denote a decomposition of a “complex action” into more primitive actions (operator expansion).

Example:move (x, y, z)

operatorexpansion pickup (x, y) putdown (x, z)

The lowest level corresponds to executable actions of the agent.

Hierarchical Plan - Example

Travel (source, dest.)

Take-Plane Take-Bus Take-Car

Goto (bus, source) Buy-Ticket (bus) Hop-on (bus) Leave (bus, dest.)

Goto (counter) Request (ticket) Pay (ticket)

Extensions and Modificationsto Basic Planning Methods

ADL - Action Definition Language

ADL Can be seen as extension of the STRIPS language.Contains typing of parameters (sorts).Allows explicit expression of negation.Allows equality of terms in precondition formula.

Example:

Fly (p: plane; from: airport; to: airport; c: cargo)precondition: at(p,to) at(c,to) in(c,p) tofromeffect: at(p,to) at(c,to) at(p,from) at(c,from)

From Russell & Norvig, Chapter 11

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

Other Issues in Planning

Disjunctive Preconditions planning with alternatives

Disjunctive Effects parallel future worlds to consider

All-Quantified Variables (in preconditions and effects) only for finite, static Universe of objects

Conditional Planning action depends on conditions specified concretely only at plan execution time typically based on percepts/sensor information integrate into partial order planning with threats

Real World Agents 1 Consider Sensors and Effectors

perception of environment, e.g. vision ensure correspondence between internal map of

robot and environment, e.g. locating robot low-level body control, e.g. Motion Control (behaviour

routines, e.g. Fuzzy or Neural Network Controller) other sensor information for body control and

environment mapping, e.g. bumpers, radar sensors for other information channels and cognitive

processes, e.g. speech – language

Real World Agents 2 Low-level Processing and Control

Motion Control Audio Recording and low-level analysis

Medium-level Processing Navigation / Route Planning Robot Location

Higher-level Processing Speech Recognition, NLP, ... Strategies, Planning BDI (Belief-Desire-Intention) - Architecture

Real World Agents 3

Multi-Agents Language / Communication

communicating agents Mental Models of other Agents

cooperating agents Strategies

cooperating agents Deontic Systems Trust

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)