CPSC 7373: Artificial IntelligenceLecture 9: Planning

Jiang Bian, Fall 2012University of Arkansas at Little Rock

Planning

• We defined AI to be the study and process of finding appropriate actions for an agent.

• We have looked at problem solving search over a state space.– Given a state space and a problem description, we

can find a solution, a path to the goal. • Problem solving approaches only work when

the environment is deterministic and fully observable.

Problem Solving vs Planning

A Mystery: Why Can't We Walk Straight?

Walking Straight into Circles, by Souman et. al.

Planning vs Execution

• Why we need to interleave planning with execution?– Properties of the environment make it hard

• STOCHASTIC: We don't know for sure what an action is going to do • MULTIAGENT:• PARTIAL OBSERVABILITY:

– Unknown model: lack of knowledge of the world• e.g., we have map or GPS software that's inaccurate or incomplete

– Hierarchical: devils in the details• Instead of planning in the space of world states, we

plan in the space of belief states.

Vacuum Cleaner Example

Search in the state space of belief states rather than in the state space of actual spaces

Sensorless Vaccum Cleaner World

RL

L

R

Partially Observable Vacuum Cleaner

R

[B, Dirty]

[B, Clean]

Suppose we have what's called local sensing, that is our vacuum can see what location it is in and it can see what's going on in the current location, that is whether there's dirt in the current location or not, but it can't see anything about whether there's dirt in any other location.

Observations alone can't introduce a new state

Stochastic Environment

R

[B, Dirty]

[A, Dirty]

[B, Clean]

Action increase uncertainty, Observation decreases uncertainty

Always Maybe

SRS

RSLS

SRRS

SRSRS

Infinite Sequences

• e.g., [S,R,S]

S R B S

A

• e.g., [S, while A:R, S]

CLASSICAL PLANNING

• STATE SPACE: k-Boolean (2^k)• WORLD STATE: Complete assignment• BELIEF STATE: – Complete assignment– Partial assignment– Arbitrary formula

• ACTION SCHEMA – Action(FLY(p, x, y)

• PRECOND: Plane (p) ^ Airport (x) ^ Airport (y) ^ At(p,x)• EFFECT: -At(p,x) ^ At(p,y)

– )

SEARCH in Planning

• Progression Search (Forward search)– Searching in Problem Solving

• Init State -> Goal State

• Regression Search (Backward search)– Goal State -> Init State

• Progression vs Regression– e.g.,

• Action(Buy(b),» PRE: ISBN(b)» EFF: OWN(b))

• GOAL (OWN(0136042597))

• Plan Space Search: Searching in the plan space rather than in the world state space.