This notebook describes the planning.py module, which covers Chapters 10 (Classical Planning) and 11 (Planning and Acting in the Real World) of Artificial Intelligence: A Modern Approach. See the intro notebook for instructions.
We'll start by looking at PDDL and Action data types for defining problems and actions. Then, we will see how to use them by trying to plan a trip from Sibiu to Bucharest across the familiar map of Romania, from search.ipynb. Finally, we will look at the implementation of the GraphPlan algorithm.
The first step is to load the code:
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from planning import *
To be able to model a planning problem properly, it is essential to be able to represent an Action. Each action we model requires at least three things:
Planning actions have been modelled using the Action class. Let's look at the source to see how the internal details of an action are implemented in Python.
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%psource Action
It is interesting to see the way preconditions and effects are represented here. Instead of just being a list of expressions each, they consist of two lists - precond_pos and precond_neg. This is to work around the fact that PDDL doesn't allow for negations. Thus, for each precondition, we maintain a seperate list of those preconditions that must hold true, and those whose negations must hold true. Similarly, instead of having a single list of expressions that are the result of executing an action, we have two. The first (effect_add) contains all the expressions that will evaluate to true if the action is executed, and the the second (effect_neg) contains all those expressions that would be false if the action is executed (ie. their negations would be true).
The constructor parameters, however combine the two precondition lists into a single precond parameter, and the effect lists into a single effect parameter.
The PDDL class is used to represent planning problems in this module. The following attributes are essential to be able to define a problem:
View the source to see how the Python code tries to realise these.
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%psource PDDL
The initial_state attribute is a list of Expr expressions that forms the initial knowledge base for the problem. Next, actions contains a list of Action objects that may be executed in the search space of the problem. Lastly, we pass a goal_test function as a parameter - this typically takes a knowledge base as a parameter, and returns whether or not the goal has been reached.
Now lets try to define a planning problem using these tools. Since we already know about the map of Romania, lets see if we can plan a trip across a simplified map of Romania.
Here is our simplified map definition:
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from utils import *
# this imports the required expr so we can create our knowledge base
knowledge_base = [
expr("Connected(Bucharest,Pitesti)"),
expr("Connected(Pitesti,Rimnicu)"),
expr("Connected(Rimnicu,Sibiu)"),
expr("Connected(Sibiu,Fagaras)"),
expr("Connected(Fagaras,Bucharest)"),
expr("Connected(Pitesti,Craiova)"),
expr("Connected(Craiova,Rimnicu)")
]
Let us add some logic propositions to complete our knowledge about travelling around the map. These are the typical symmetry and transitivity properties of connections on a map. We can now be sure that our knowledge_base understands what it truly means for two locations to be connected in the sense usually meant by humans when we use the term.
Let's also add our starting location - Sibiu to the map.
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knowledge_base.extend([
expr("Connected(x,y) ==> Connected(y,x)"),
expr("Connected(x,y) & Connected(y,z) ==> Connected(x,z)"),
expr("At(Sibiu)")
])
We now have a complete knowledge base, which can be seen like this:
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knowledge_base
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We now define possible actions to our problem. We know that we can drive between any connected places. But, as is evident from this list of Romanian airports, we can also fly directly between Sibiu, Bucharest, and Craiova.
We can define these flight actions like this:
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#Sibiu to Bucharest
precond_pos = [expr('At(Sibiu)')]
precond_neg = []
effect_add = [expr('At(Bucharest)')]
effect_rem = [expr('At(Sibiu)')]
fly_s_b = Action(expr('Fly(Sibiu, Bucharest)'), [precond_pos, precond_neg], [effect_add, effect_rem])
#Bucharest to Sibiu
precond_pos = [expr('At(Bucharest)')]
precond_neg = []
effect_add = [expr('At(Sibiu)')]
effect_rem = [expr('At(Bucharest)')]
fly_b_s = Action(expr('Fly(Bucharest, Sibiu)'), [precond_pos, precond_neg], [effect_add, effect_rem])
#Sibiu to Craiova
precond_pos = [expr('At(Sibiu)')]
precond_neg = []
effect_add = [expr('At(Craiova)')]
effect_rem = [expr('At(Sibiu)')]
fly_s_c = Action(expr('Fly(Sibiu, Craiova)'), [precond_pos, precond_neg], [effect_add, effect_rem])
#Craiova to Sibiu
precond_pos = [expr('At(Craiova)')]
precond_neg = []
effect_add = [expr('At(Sibiu)')]
effect_rem = [expr('At(Craiova)')]
fly_c_s = Action(expr('Fly(Craiova, Sibiu)'), [precond_pos, precond_neg], [effect_add, effect_rem])
#Bucharest to Craiova
precond_pos = [expr('At(Bucharest)')]
precond_neg = []
effect_add = [expr('At(Craiova)')]
effect_rem = [expr('At(Bucharest)')]
fly_b_c = Action(expr('Fly(Bucharest, Craiova)'), [precond_pos, precond_neg], [effect_add, effect_rem])
#Craiova to Bucharest
precond_pos = [expr('At(Craiova)')]
precond_neg = []
effect_add = [expr('At(Bucharest)')]
effect_rem = [expr('At(Craiova)')]
fly_c_b = Action(expr('Fly(Craiova, Bucharest)'), [precond_pos, precond_neg], [effect_add, effect_rem])
And the drive actions like this.
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#Drive
precond_pos = [expr('At(x)')]
precond_neg = []
effect_add = [expr('At(y)')]
effect_rem = [expr('At(x)')]
drive = Action(expr('Drive(x, y)'), [precond_pos, precond_neg], [effect_add, effect_rem])
Finally, we can define a a function that will tell us when we have reached our destination, Bucharest.
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def goal_test(kb):
return kb.ask(expr("At(Bucharest)"))
Thus, with all the components in place, we can define the planning problem.
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prob = PDDL(knowledge_base, [fly_s_b, fly_b_s, fly_s_c, fly_c_s, fly_b_c, fly_c_b, drive], goal_test)
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