74.419 Artificial Intelligence 2005/06

Partially Ordered Plans - or:

"How Do You Put Your Shoes On?"

Partially Ordered Plans

Partially Ordered Plans - or:

"How Do You Put Your Shoes On?"

Partially Ordered Plans:

• no strict sequence

• partly parallel

• observe threats

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 2

Add causal links to connect effects from actions to matching preconditions for plan.

Causal links specify a partial order.

Recognize threats - the effect of an action A negates the precondition of another action B.

Add threats as partial order to plan: B<A (do B before A).

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.

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 Planning

Hierarchical Planning / Plan Decomposition • hierarchical organisation of 'actions'• complex and less complex (or: abstract) actions• lowest level reflects directly executable actions • 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, cf. ABSTRIPS)

• overall plan must generate effect of complex action

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.

Other Issues in Planning

Disjunctive Preconditions

Conditional Effects change is due to specific condition integrate into partial planning with threats

Disjunctive Effects parallel future worlds to consider

All-Quantified Variables (in preconditions and effects)

only for finite, static Universe of objects

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)

Web Links

RoboCup official web page – www.robocup.org

Active Media Robotics (pioneer, Saphira) – www.activmedia.com

SONY’s RoboDog AIBO – www.aibo.com

PBS Videos –

Robots Alive, 04-09-97 (AAAI’96, Maze/Meeting Scheduling Robot Competition)

Games Machines Play, 05-21-2002 (RoboCup, Seattle 2001)