Building a Temporal Graphplan

1
Building a Temporal Graphplan

• Richard Smiley

2
Graphplans Strengths

• Speed
• Combines planning and scheduling
• Has a rudimentary concept of time
• Demonstrably optimal plans

3
Graphplans Concept of Time

• Each action is assumed to take one timestep
• Doesnt correspond to real world
• Example Logistics domain

4
The Problem

• Make Graphplans timesteps correspond to
  real-world time
• Each timestep corresponds to a chunk of time
• Need to preserve proper mutex relations
• Some actions have effects that take effect
  immediately and actions that take effect some
  time in the future

5
The delay effect

• Format (delay timesteps fact fact_params)
• (operator FLY-AIRPLANE
• (params
• (ltairplanegt AIRPLANE)
• (ltloc-fromgt AIRPORT)
• (ltloc-togt AIRPORT))
• (preconds
• (at ltairplanegt ltloc-fromgt))
• (effects
• (delay 0 at ltairplanegt ltloc-togt)))
• Will make (at plane1 LAX) true in 4 timesteps

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The Algorithm

• for each delay fact at a timestep
• 1) If timesteps is 0, insert the corresponding
  fact into the next timestep.
• 2) If timesteps is nonzero, insert another delay
  into the next timestep (connected with delay
  operator), with the timesteps parameter
  decremented by one.

7
Some complicating issues

• Noops must not be applied to delay facts
• Different operator parameters should create
  different delays
• Premature termination of search (number of facts
  stays the same)
• Proper mutex propagation

8
Results

• Exponential increase in number of tried actions
• Still, favorable results for small domains