AI_unit IV Full Notes.pdf

Knowledge representation: -
 The task of coming up with a sequence of actions that will achieve a goal is called Planning.
 “Deciding in ADVANCE what is to be done”
 A problem solving methodology
 Generating a set of action that are likely to lead to achieving a goal
 Deciding on a course of actions before acting
 Representation for states and Goals:-
o In the STRIPS language, states are represented by conjunctions of function-free
ground literals, that is, predicates applied to constant symbols, possibly negated.
o For example,
At(Home)^ ¬ Have(Milk)^ ¬ Have(Bananas)^ ¬ Have(Drill)^….
o Goals are also described by conjunctions of literals.
o For example,
At(Home)^Have(Milk)^ Have(Bananas)^ Have(Drill)
o Goals can also contain variables. For example, the goal of being at a store that sells
milk would be represented as
 Representation for actions:-
o Our STRIPS operators consist of three components:
o the action description is what an agent actually returns to the environment in order to
do something.
o the precondition is a conjunction of atoms (positive literals) that says what must be
true before the operator can be applied.
o the effect of an operator is a conjunction of literals (positive or negative) that
describes how the situation changes when the operator is applied.
o Here’s an example for the operator for going from one place to another:
 Op(Action:Go(there),
 Precond:At(here)^Path(here, there),
 Effect:At(there)^ ¬At(here))
 Representation of Plans:-
o Consider a simple problem:
o Putting on a pair of shoes
o Goal RightShoeOn ^ LeftShoeOn
o Four operators:
UNIT IV
Planning
Classical Planning: Definition of Classical Planning, Algorithms for Planning with State-Space
Search, Planning Graphs, other Classical Planning Approaches, and Analysis of Planning
Approaches.
Planning and Acting in the Real World: Time, Schedules, and Resources, Hierarchical
Planning, Planning and Acting in Nondeterministic Domains, Multi-agent Planning.

Op(Action:RightShoe,PreCond:RightSockOn,Effect:RightShoeON)
Op(Action:RightSock , Effect: RightSockOn)
Op(Action:LeftShoe, Precond:LeftSockOn, Effect:LeftShoeOn)
Op(Action:LeftSock,Effect:LeftSockOn)
Given:-
 A description of an initial state
 A set of actions
 A (partial) description of a goal state
Problem:-
 Find a sequence of actions (plan) which transforms the initial state into the goal state.
Application areas:-
 Systems design
 Budgeting
 Manufacturing product
 Robot programming and control
 Military activities
Benefits of Planning:-
 Reducing search
 Resolving goal conflicts
 Providing basis for error recovery
3.1 Planning with State Space Search:
 Planning with state space search approach is used to construct a planning algorithm.
 This is most straightforward approach.
 The description of actions in a planning problem specifies both preconditions and effects.
 It is possible to search in either direction.
 Either from forward from the initial state or backward from the goal
 The following are the two types of state space search ,
o Forward state-space search
o Backward state-space search
 The following diagram shows the Forward state-space search
At(P1,A)
At(P2, A)
Fly(P1,A,B)
Fly(P2,A,B)
At(P1,B)
At(P2, A)
At(P1,A)
At(P2, B)
3.1.1 Forward state-space search:-
 Planning with forward state-space search is similar to the problem solving using Searching.

 It is sometimes called as progression Planning.
 It moves in the forward direction.
 we start in the problems initial state, considering sequence of actions until we find a sequence
that reaches a goal state.
 The formulation of planning problems as state-space search problems is as follows,
o The Initial state of the search is the initial state from the planning problem.
o In general, each state will be a set of positive ground literals; literals not appearing are
false.
o The actions that are applicable to a state are all those whose preconditions are
satisfied.
o The successor state resulting from an action is generated by adding the positive effect
literals and deleting the negative effect literals.
o The goal test checks whether the state satisfies the goal of the planning problem.
o The step cost of each action is typically 1.
 This method was too inefficient.
 It does not address the irrelevant action problem, (i.e.) all applicable actions are considered
from each state.
 This approach quickly bogs down without a good heuristics.
 For Example:-
o Consider an air cargo problem with 10 airports, where each airport has 5 planes and
20 pieces of cargo.
o The Goal is to move the entire cargo form airport A to airport B.
o There is a simple solution to the Problem,
o Load the 20 pieces of cargo into one of the planes at A, then fly the plane to B, and
unload the cargo.
o But finding the solution can be difficult because the average branching factor is huge.
3.1.2 Backward state- space search:-
 Backward search is similar to bidirectional search.
 It can be difficult to implement when the goal states are described by a set of constraints
rather than being listed explicitly.
 It is not always obvious how to generate a description of the possible predecessors of the set
of goal states.
 The main advantage of this search is that it allows us to consider only relevant actions.
 An action is relevant to a conjunctive goal if it achieves one of the conjuncts of the goal.
 The following diagram shows the Backward state-space search
At(P1,A)
At(P2, B)
At(P1,B)
At(P2, A)
Fly(P1,A,B)
Fly(P2,A,B)
At(P1,B)
At(P2, B)

 For example:-
o The goal in our 10-airport cargo problem is to have 20 pieces of cargo at airport B, or
more precisely,
At(C1,B)  At(C2,B)  ……  At(C20,B)
o Now consider the conjunct At(C1,B). working backwards, we can seek actions that
have this as an effect. There is only one unload(C1,p,B), where plane p is unspecified.
o In this search restriction to relevant actions means that backward search often has a
much lower branching factor than forward search.
 Searching backwards is sometimes called regression planning.
 The principal question is:- what are the states from which applying a given action leads to the
goal?
 Computing the description of these states is called regressing the goal through the action.
 consider the air cargo example;- we have the goal as,
At(C1,B)  At(C2,B) …… At(C20,B)
and the relevant action Unload(C1,p,B), which achieves the first conjunct.
 The action will work only if its preconditions are satisfied.
 Therefore , any predecessor state must include these preconditions : In(C1,p) At(p,B),
Moreover the subgoal At(C1,B) should not be true in the predecessor state.
 The predecessor description is
In(C1,p)  At(p,B)  At(C2,B)  ……  At(C20,B)
 In addition to insisting that actions achieve some desired literal, we must insist that the
actions not undo any desired literals.
 An action that satisfies this restriction is called consistent.
 From definitions of relevance and consistency, we can describe the general process of
constructing predecessors for backward search.
 Given a goal description G, let A be an action that is relevant and consistent. The
corresponding predecessor is as follows
o any positive effects of A that appear in G are deleted
o Each precondition literal of A is added, unless it already appears
 Termination occurs when a predecessor description is generated that is satisfied by the initial
state of the planning problem.
3.1.3 Heuristics for State-space search:-
Heuristic Estimate:-
 The value of a state is a measure of how close it is to a goal state.
 This cannot be determined exactly (too hard), but can be approximated.
 One way of approximating is to use the relaxed problem.
 Relaxation is achieved by ignoring the negative effects of the actions.
 The relaxed action set, A’, is defined by:
A’ = {<pre(a),add(a),0> | a in A}

Artificial Intelligence CSE/IIIYr/VISem UNIT-III/PLANNING
Building the relaxed plan graph:-
 Start at the initial state
 Repeatedly apply all relaxed actions whose preconditions are satisfied.
o Their (positive) effects are asserted at the next layer.
 If all actions applied and the goals are not
all present in the final graph layer
Then the problem is unsolvable.
Extracting Relaxed solution
 When a layer containing all of the goals is reached ,FF searches backwards for a plan.
 The earliest possible achiever is always used for any goal.
 This maximizes the possibility for exploiting actions in the relaxed plan.
 The relaxed plan might contain many actions happening concurrently at a layer.
 The number of actions in the relaxed plan is an estimate of the true cost of achieving the
goals.
How FF uses the Heuristics:-
 FF uses the heuristic to estimate how close each state is to a goal state
 any state satisfying the goal propositions.

 The actions in the relaxed plan are used as a guide to which actions to explore when
extending the plan.
 All actions in the relaxed plan at layer i that achieve at least one of the goals required
at layer i+1 are considered helpful.
 FF restricts attention to the helpful actions when searching forward from a state.
Properties of the Heuristics:-
 The relaxed plan that is extracted is not guaranteed to be the optimal relaxed plan.
 the heuristic is not admissible.
 FF can produce non-optimal solutions.
 Focusing only on helpful actions is not completeness preserving.
 Enforced hill-climbing is not completeness preserving.
3.2 Partial Order Planning:-
 Formally a planning algorithm has three inputs:
o A description of the world in some formal language,
o A description of the agent’s goal in some formal language, and
o A description of the possible actions that can be performed.
 The planner’s o/p is a sequence of actions which when executed in any world satisfying the
initial state description will achieve the goal.
 Representation for states and Goals:-
o In the STRIPS language, states are represented by conjunctions of function-free
ground literals, that is, predicates applied to constant symbols, possibly negated.
o For example,
At(Home)^ ¬ Have(Milk)^ ¬ Have(Bananas)^ ¬ Have(Drill)^….
o Goals are also described by conjunctions of literals.
o For example,
At(Home)^Have(Milk)^ Have(Bananas)^ Have(Drill)
o Goals can also contain variables. For example, the goal of being at a store that sells
milk would be represented as
 Representation for actions:-
o Our STRIPS operators consist of three components:
o the action description is what an agent actually returns to the environment in order to
do something.
o the precondition is a conjunction of atoms (positive literals) that says what must be
true before the operator can be applied.
o the effect of an operator is a conjunction of literals (positive or negative) that
describes how the situation changes when the operator is applied.
o Here’s an example for the operator for going from one place to another:
 Op(Action:Go(there),
 Precond:At(here)^Path(here, there),
 Effect:At(there)^ ¬At(here))
Representation of Plans:-
o Consider a simple problem:
o Putting on a pair of shoes
o Goal RightShoeOn ^ LeftShoeOn
o Four operators:

Op(Action:RightShoe,PreCond:RightSockOn,Effect:RightShoeON)
Op(Action:RightSock , Effect: RightSockOn)
Op(Action:LeftShoe, Precond:LeftSockOn, Effect:LeftShoeOn)
Op(Action:LeftSock,Effect:LeftSockOn)
 Least Commitment:- The general strategy of delaying a choice during search is called Least
commitment.
 Partial-order Planner:- Any planning algorithm that can place two actions into a plan
without specifying which come first is called a partial order planner.
 Linearization:- The partial-order solution corresponds to six possible total order plans ; each
of these is called a linearization of the partial order plan.
 Total order planner:- Planner in which plans consist of a simple lists of steps.
 A plan is defined as a data structure
o A set of plan steps
o A set of step ordering
o A set of variable binding constraints
o A set of causal links : si
c
sj
”si achieves c for sj”
 Initial plan before any refinements
Start < Finish
Refine and manipulate until a plan that is a solution

 The following diagram shows the partial order plan for putting on shoes and socks, and the
six corresponding linearization into total order plans.


 Solutions
o solution : a plan that an agent guarantees achievement of the goal
o a solution is a complete and consistent plan
o a complete plan : every precondition of every step is achieved by some other step
o a consistent plan : no contradictions in the ordering or binding constraints. When we
meet a inconsistent plan we backtrack and try another branch
3.2.1 Partial order planning Algorithm:-
The following is the Partial order planning algorithm,
function pop(initial-state, conjunctive-goal, operators)
// non-deterministic algorithm
plan = make-initial-plan(initial-state, conjunctive-goal);
loop:
begin
if solution?(plan) then return plan;
(S-need, c) = select-subgoal(plan) ; // choose an unsolved goal
choose-operator(plan, operators, S-need, c);
// select an operator to solve that goal and revise plan
resolve-threats(plan); // fix any threats created
end
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end
function solution?(plan)
if causal-links-establishing-all-preconditions-of-all-steps(plan)
and all-threats-resolved(plan)
and all-temporal-ordering-constraints-consistent(plan)
and all-variable-bindings-consistent(plan)
then return true;
else return false;
end
function select-subgoal(plan)
pick a plan step S-need from steps(plan) with a precondition c
that has not been achieved;
return (S-need, c);
end
procedure choose-operator(plan, operators, S-need, c)
// solve "open precondition" of some step
choose a step S-add by either
Step Addition: adding a new step from operators that
has c in its Add-list
or Simple Establishment: picking an existing step in Steps(plan)
that has c in its Add-list;
if no such step then return fail;
add causal link "S-add --->c S-need" to Links(plan);
add temporal ordering constraint "S-add < S-need" to Orderings(plan);
if S-add is a newly added step then
begin
add S-add to Steps(plan);
add "Start < S-add" and "S-add < Finish" to Orderings(plan);
end
end
procedure resolve-threats(plan)
foreach S-threat that threatens link "Si --->c Sj" in Links(plan)
begin // "declobber" threat
choose either
Demotion: add "S-threat < Si" to Orderings(plan)
or Promotion: add "Sj < S-threat" to Orderings(plan);
if not(consistent(plan)) then return fail;
end
end
 Partial Order Planning Example:-
o Shopping problem: “get milk, banana, drill and bring them back home”
o assumption
1)Go action “can travel the two locations”
2)no need money
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o initial state : operator start
Op(ACTION:Start,EFFECT:At(Home)  Sells(HWS,Drill)  Sells(SM,Milk),
Sells(SM,Banana))
o goal state : Finish
Op(ACTION:Finish, PRECOND:Have(Drill)  Have(Milk)  Have(Banana)
 At(Home))
o actions:
Op(ACTION:Go(there),PRECOND:At(here),EFFECT:At(there)  ¬At(here))
Op(ACTION:Buy(x),PRECOND:At(store)  Sells(store,x),EFFECT:Have(x))
 There are many possible ways in which the initial plan elaborated
o one choice : three Buy actions for three preconditions of Finish action
o second choice:sells precondition of Buy
• Bold arrows:causal links, protection of precondition
• Light arrows:ordering constraints
 The following diagram shows the,
o partial plan that achieves three of four preconditions of finish
o Refining the partial plan by adding casual links to achieve the sells preconditions of
the buy steps
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 causal links : protected links
a causal link is protected by ensuring that threats are ordered to come before or after the
protected link
 demotion : placed before
promotion : placed after
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 The following diagram shows the partial plan that achieves At Precondition of the three buy
conditions
 The following diagram shows the solution of this problem,
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 The following are the Knowledge engineering for plan,
 Methodology for solving problems with the planning approach
(1) Decide what to talk about
(2) Decide on a vocabulary of conditions, operators, and objects
(3) Encode operators for the domain
(4) Encode a description of the specific problem instance
(5) pose problems to the planner and get back plans
 (ex) The blocks world
o (1) what to talk about
 cubic blocks sitting on a table
 one block on top of another
 A robot arm pick up a block and moves it to another position
o (2) Vocabulary
 objects:blocks and table
 On(b,x) : b is on x
 Move(b,x,y) : move b form x to y
 ¬exist x On(x,b) or x ¬On(x,b) : precondition
 clear(x)
o (3)Operators
Op(ACTION:Move(b,x,y),
PRECOND:On(b,x)  Clear(b)  Clear(y),
EFFECT:On(b,y)  Clear(x)  ¬On(b,x)  ¬Clear(y))
Op(ACTION:MoveToTable(b,x),
PRECOND:On(b,x)  Clear(b),
EFFECT:On(b,Table)  Clear(x)  ¬On(b,x))
3.3 Planning Graph:-
 Planning graphs are an efficient way to create a representation of a planning problem that can
be used to
o Achieve better heuristic estimates
o Directly construct plans
 Planning graphs only work for propositional problems.
 Planning graphs consists of a seq of levels that correspond to time steps in the plan.
o Level 0 is the initial state.
o Each level consists of a set of literals and a set of actions that represent what might be
possible at that step in the plan
o Might be is the key to efficiency
o Records only a restricted subset of possible negative interactions among actions.
 Each level consists of
o Literals = all those that could be true at that time step, depending upon the actions
executed at preceding time steps.
o Actions = all those actions that could have their preconditions satisfied at that time
step, depending on which of the literals actually hold.
 For Example:-
Init(Have(Cake))
Goal(Have(Cake)  Eaten(Cake))
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Action(Eat(Cake),
PRECOND: Have(Cake)
EFFECT: ¬Have(Cake)  Eaten(Cake))
Action(Bake(Cake),
PRECOND: ¬ Have(Cake)
EFFECT: Have(Cake))
 Steps to create planning graph for the example,
o Create level 0 from initial problem state.
o
o
o Add all applicable actions.
o Add all effects to the next state.
o Add persistence actions (inaction = no-ops) to map all literals in state Si to state Si+1.
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o Identify mutual exclusions between actions and literals based on potential conflicts.
 Mutual Exclusion:-
o A mutex relation holds between two actions when:
 Inconsistent effects: one action negates the effect of another.
 Interference: one of the effects of one action is the negation of a precondition
of the other.
 Competing needs: one of the preconditions of one action is mutually exclusive
with the precondition of the other.
o A mutex relation holds between two literals when:
 one is the negation of the other OR
 each possible action pair that could achieve the literals is mutex (inconsistent
support).
 Level S1 contains all literals that could result from picking any subset of actions in A0
o Conflicts between literals that can not occur together
(as a consequence of the selection action) are
represented by mutex links.
o S1 defines multiple states and the mutex links are the constraints that define this set of
states.
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 Repeat process until graph levels off:
o two consecutive levels are identical, or
o contain the same amount of literals
(explanation follows later)
 In figure
o rectangle denotes actions
o small square denotes persistence actions
o straight lines denotes preconditions and effects
o curved lines denotes mutex links
3.3.1 Planning Graphs for Heuristic Estimation:-
 PG’s provide information about the problem
o PG is a relaxed problem.
o A literal that does not appear in the final level of the graph cannot be achieved by any
plan.
 H(n) = ∞
o Level Cost: First level in which a goal appears
 Very low estimate, since several actions can occur
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 Improvement: restrict to one action per level using serial PG (add mutex links
between every pair of actions, except persistence actions).
 Cost of a conjunction of goals
o Max-level: maximum first level of any of the goals
o Sum-level: sum of first levels of all the goals
o Set-level: First level in which all goals appear without being mutex
 The following is the GraphPlan Algorithm,
 Extract a solution directly from the PG
function GRAPHPLAN(problem) return solution or failure
graph  INITIAL-PLANNING-GRAPH(problem)
goals  GOALS[problem]
loop do
if goals all non-mutex in last level of graph then do
solution  EXTRACT-SOLUTION(graph, goals, LENGTH(graph))
if solution  failure then return solution
else if NO-SOLUTION-POSSIBLE(graph) then return failure
graph  EXPAND-GRAPH(graph, problem)
 Initially the plan consist of 5 literals from the initial state and the CWA literals (S0).
 Add actions whose preconditions are satisfied by EXPAND-GRAPH (A0)
 Also add persistence actions and mutex relations.
 Add the effects at level S1
 Repeat until goal is in level Si
 EXPAND-GRAPH also looks for mutex relations
o Inconsistent effects
 E.g. Remove(Spare, Trunk) and LeaveOverNight due to At(Spare,Ground)
and not At(Spare, Ground)
o Interference
 E.g. Remove(Flat, Axle) and LeaveOverNight At(Flat, Axle) as PRECOND
and not At(Flat,Axle) as EFFECT
o Competing needs
 E.g. PutOn(Spare,Axle) and Remove(Flat, Axle) due to At(Flat.Axle) and not
At(Flat, Axle)
o Inconsistent support
 E.g. in S2, At(Spare,Axle) and At(Flat,Axle)
 In S2, the goal literals exist and are not mutex with any other
o Solution might exist and EXTRACT-SOLUTION will try to find it
 EXTRACT-SOLUTION can use Boolean CSP to solve the problem or a search process:
o Initial state = last level of PG and goal goals of planning problem
o Actions = select any set of non-conflicting actions that cover the goals in the state
o Goal = reach level S0 such that all goals are satisfied
o Cost = 1 for each action.
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3.3.2 Termination of GraphPlan:-
 Termination? YES
 PG are monotonically increasing or decreasing:
o Literals increase monotonically: - Once a literal appears at a given level, it will appear at
all subsequent levels. This is because of the persistence actions; Once a literal shows
up, persistence actions cause it to say forever.
o Actions increase monotonically:- Once a literal appears at a given level, it will appear at
all subsequent levels. This is a consequence of literals increasing; if the preconditions
of an action appear at one level, they will appear at subsequent levels, and thus will the
action
o Mutexes decrease monotonically:- If two actions are mutex at a given level Ai, then they
will also be mutex for all previous levels at which they both appear.
 Because of these properties and because there is a finite number of actions and literals, every PG
will eventually level off
3.4 Planning and Acting in the Real World:
 In which we see how more expressive representation and more interactive agent architectures
lead to planners that are useful in the real world.
 Planners that are used in the real world for tasks such as scheduling,
o Hubble Space Telescope Observations
o Operating factories
o handling the logistics for military campaigns
3.4.1 Time, Schedules and Resources:
 Time is the essence in the general family of applications called Job Shop Scheduling.
 Such a tasks require completing a set of jobs, each of which consists of a sequence of actions,
where each action has a given duration and might require some resources.
 The problem is to determine a schedule that minimizes the total time required to complete all
the jobs, while respecting the resource constraints.
 For Example:- The following problem is a job shop scheduling.
Init (chassis(C1)  chassis(C2)
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EFFECT: Done (c)  Duration(10))
 The above table shows the Job Shop scheduling problem for assembling two cars.
 The notation Duration (d) means that an action takes d minutes to execute.
 Engine(E1,C1,30) means that E1 is an Engine that fits into chassis C1 and takes 30 minutes
to Install
 The problem can be solved by POP (Partial order planning).
 We must now determine when each action should begin and end.
 The following diagram shows the solution for the above problem
 To find the start and end times of each action apply the Critical Path Method CPM.
 The critical path is the one that is the longest and upon which the other parts of the process
cannot be shorter than.
 At the top, the solution is given as a partial order plan.
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 Engine (E1,C1,30)  Engine (E2,C2,60)
 Wheels (W1,C1,30)  Wheels (W2,C2,15))
Goal (Done(C1)  Done(C2))
Action (AddEngine(e,c,m),
PRECOND: Engine(e,c,d)  chassis(c)   EngineIn(c),
EFFECT: EngineIn(c)  Duration (d))
Action (AddWheels(w,c),
PRECOND: Wheels(w,c,d)  chassis(c),
EFFECT: WheelsOn(c)  Duration (d))
Action (Inspect(c),
PRECOND: EngineIn(c)  WheelsOn (c)  chassis (c),

resources.
Init (chassis(C1)  chassis(C2)
 Engine (E1,C1,30)  Engine (E2,C2,60)
 Wheels (W1,C1,30)  Wheels (W2,C2,15)
 EngineHoists (1)  WheelStations (1)  Inspectors (2))
Goal (Done(C1)  Done(C2))
Action (AddEngine(e,c,m),
PRECOND: Engine(e,c,d)  chassis(c)   EngineIn(c),
EFFECT: EngineIn(c)  Duration (d)
RESOURCE: EngineHoists (1))
Action (AddWheels(w,c),
PRECOND: Wheels(w,c,d)  chassis(c),
EFFECT: WheelsOn(c)  Duration (d),
RESOURCE: WheelStations (1))
Action (Inspect(c),
PRECOND: EngineIn(c)  WheelsOn (c)  chassis (c),
EFFECT: Done (c)  Duration(10),
 The duration of each action is given at the bottom of each rectangle, with the earliest and
latest start time listed as [ES, LS] in the upper left.
 The difference between these two numbers is the slack of an action
 Action with zero slack are on the critical path, shown with bold arrows.
 At the bottom of the figure the same solution is shown as timeline.
 Grey rectangles represent time intervals during which an action may be executed, provided
that the ordering constraints are respected.
 The unoccupied portion of a grey rectangle indicates the slack.
 The following formula serve as a definition for ES and LS and also as the outline of a
dynamic programming algorithm to compute them:
ES(Start)  0
ES(B)  max A BES(A)  Duration( A)
LS(Finish)  ES(Finish)
LS(A)  min A BLS(B)  Duration( A)
 The complexity of the critical path algorithm is just O(Nb).
 where N is the number of actions and b is the branching factor.
Scheduling with resource constraints:
 Real scheduling problems are complicated by the presence of constraints on resources.
 Consider the above example with some resources.
 The following table shows the job shop scheduling problem for assembling two cars, with
RESOURCE: Inspectors (1))
 The available resources are on engine assembly station, one wheel assembly station, and two
inspectors.
 The notation RESOURCE: means that the resource r is used during execution of an action,
but becomes free again when the action is complete.
 The following diagram shows the solution to the job shop scheduling with resources.
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 The left hand margin lists the three resources
 Actions are shown aligned horizontally with the resources they consume.
 There are two possible schedules, depending on which assembly uses the engine station first.
 One simple but popular heuristic is the minimum slack algorithm.
 it schedules actions in a greedy fashion.
 On each iteration, it considers the unscheduled actions that have had all their predecessors
scheduled and schedules the one with the least slack for the earliest possible start.
 It then updates the ES and LS times for each affected action and repeats.
 The heuristics is based on the same principle as the most-constrained variable heuristic in
constraint satisfaction.
3.4.2 Hierarchical Task Network Planning:
 One of the most pervasive ideas for dealing with complexit y is Hierarchical Decomposition.
 The key benefit of hierarchical structure structure is that, at each level of the hierarchy is
reduced to a small number of activities at the next lower level
 So that the computational cost of finding the correct way to arrange those activities for the
current problem is small.
 A planning method based on Hierarchical Task Networks or HTNs.
 This approach we take combines ideas from both partial-order planning and the area known
as “HTN planning”.
 In HTN planning, the initial plan, which describes the problem, is viewed as very high-level
description of what is to be done. For Example: - Building a House.
 Plans are refined by applying a action decompositions.
 Each action decompositions reduces a high-level action to a partially ordered set of lower-
level actions
3.4.2.1 Representing action decompositions:
 The following diagram shows the decomposition of a Building a house action.
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Land
Start
Get
Permit
Build House
Land House
decomposes to
Construction
Money
Hire
Builder
 In pure HTN planning, plans are generated only by successive action decompositions.
 Therefore the HTN views planning as a process of making an activity description more concrete,
rather than a process of constructing an activity description, starting from the empty activity.
 The action decompositions are represented as, action decompositions methods are stored in a
plan library
 From which they are extracted and instantiated to fit the needs of the plan being constructed.
 Each method is an expression of the form Decompose (a, d).
 It means that an action a can be decomposed into the plan d, which is represented as a partial
ordered plan.
 The following table shows the action descriptions for the house-building problem and a
detailed decomposition for the BuildHouse action.
 The start action of the decomposition supplies all those preconditions of actions in the plan
that are not supplied by other actions, such a things called external preconditions.
 In our example external preconditions are land and money.
 Similarly, the external effects, which are the preconditions of Finish, are all those effects of
actions in the plan that are not negated by other actions.
 Decomposition should be a correct implementation of the action.
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22
Pay
Builder
House
Finish
 Money
Action (BuyLand, PRECOND: Money, EFFECT: Land   Money)
Action (GetLoan, PRECOND: GoodCredit, EFFECT:Money  Mortgage)
Action (BuildHouse, PRECOND: Land, EFFECT: House)
Action (GetPermit, PRECOND: Land, EFFECT: Permit)
Action (HireBuilder, EFFECT: Contract)
Action (Construction, PRECOND: Permit  Contract, EFFECT: HouseBuilt   Permit)
Action (PayBuilder, PRECOND: Money  HouseBuilt, EFFECT:  Money  House   Contract)
Decompose (BuildHouse,
Plan (Steps : {S1: GetPermit, S2: HireBuilder, S3: Construction, S4: PayBuilder}
ORDERINGS: {Start S1 S3 S4 Finish, Start S2 S3},
Links: {Start Land S1, Start Money S4, S1permit S3, S2 Contract S3, S3 HouseBuilt S4,
S4 House Finish, S4  Money Finish}))

 A plan library could contain several decompositions for any given high-level action.
 Decomposition should be a correct plan, but it could have additional preconditions and
effects beyond those stated in the high-level action description.
 The precondition of the high-level action should be the intersection of the external
preconditions of its decomposition.
 In which two other forms of information hiding should be noted as,
 First the high-level description completely ignores all internal effects of the decompositions
 Second the high-level description does not specify the intervals “inside” the activity during
which the high-level preconditions are effects must hold.
 Information hiding of this kind is essential if hierarchical planning is to reduce complexity.
3.4.2.2 Modifying the planner for decomposition:
 In this we will see how to modify the Partial Order Planning to incorporate HTN planning.
 We can do that by modifying the POP successor function to allow decomposition methods to be
applied to the current partial plan P.
 The new successor plans are formed by first selecting some non-primitive action a’ in P and then,
for any Decompose (a, d) method from the plan library such that a and a’ unify with substitution
θ, replacing a’ with d’ = SUBST (θ, d)
 The following diagram shows the decomposition of a high-level action within an existing plan.
 Where The BuildHouse action is replaced by the decomposition from the above example.
 The external precondition land is supplied by the existing causal link from BuyLand.
 The external precondition Money remains open after the decomposition step, so we add a
new action, GetLoan.
 To be more precise follow the below steps,
o First the action a’ is removed from P.Then for each step S in the decomposition d’
o Second step is to hook up the ordering constraints for a’ in the original plan to the
steps in d’.
o Third and final step is to hook up casual links.
Money Land House
Start Buy Land Build House Finish
Money
Start
Land
Buy Land Get Permit House
Construction
Pay
Builder
Finish
GoodCredit
Get Loan Hide Builder
Money
 This completes the additions required for generating decompositions in the context of the
POP Planner.
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3.4.3 Planning and Acting in Non-deterministic domains:
 So far we have considered only classical planning domains that are fully observable, static
and deterministic.
 Furthermore we have assumed that the action descriptions are correct and complete.
 Agents have to deal with both incomplete and incorrect information.
 Incompleteness arises because the world is partially observable, non-deterministic or both.
 Incorrectness arises because the world does not necessarily match my model of the world.
 The possibility of having complete or correct knowledge depends on how much
indeterminacy there in the world.
 Bounded indeterminacy actions can have unpredictable effects, but the possible effects can
be listed in the action description axioms.
 Unbounded indeterminacy the set of possible preconditions or effects either is unknown or
is too large to be enumerated completely.
 Unbounded indeterminacy is closely related to the qualification problem.
 There are four planning methods for handling indeterminacy.
 The following planning methods are suitable for bounded indeterminacy,
o Sensorleses Planning:-
 Also called as Confront Planning
 This method constructs standard, sequential plans that are to be executed
without perception.
 This algorithm must ensure that the plan achieves the goal in all possible
circumstances, regardless of the true initial state and the actual action outcomes.
 It relies on coercion – the idea that the world can be forced into a given state even
when the agent has only partial information about the current state.
 Coercion is not always possible.
o Conditional Planning:-
 Also called as Contingency planning
 This method constructing a conditional plan with different branches for the
different contingencies that could arise.
 The agent plans first and then executes the plan was produced.
 The agents find out which part of the plan to execute by including sensing
actions in the plan to test for the appropriate conditions.
 The following planning methods are suitable for Unbounded indeterminacy,
o Execution Monitoring and Replanning:-
 In this, the agent can use any of the preceding planning techniques to construct
a plan.
 It also uses Execution Monitoring to judge whether the plan has a provision
for the actual current situation or need to be revised.
 Replanning occurs when something goes wrong.
 In this the agent can handle unbounded indeterminacy.
o Continuous Planning:-
 It is designed to persist over a lifetime.
 It can handle unexpected circumstances in the environment, even if these
occur while the agent is in the middle of constructing a plan.
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 It can also handle the abandonment of goals and the creation of additional
goals by goal formulation.
3.4.4 Conditional Planning:-
 Conditional planning is a way to deal with uncertainty by checking what is actually
happening in the environment at predetermined points in the plan.
 Conditional planning is simplest to explain for fully observable environments
 The partially observable case is more difficult to explain in this conditional planning.
3.4.4.1 Conditional planning in fully observable environments:
 Full observability means that the agent always knows the current state.
 CP in fully observable environments (FOE)
o initial state : the robot in the right square of a clean world;
o the environment is fully observable: AtR 𝖠CleanL𝖠CleanR.
o The goal state : the robot in the left square of a clean world.
 Vacuum world with actions Left, Right, and Suck
 Disjunctive effects: Action (Left, PRECOND : AtR, EFFECT : AtL   AtR)
 Modified Disjunctive effects : Action (Left, PRECOND : AtR, EFFECT : AtL
v AtR)
 Conditional effects: Action(Suck, Precond: , Effect: (when AtL: CleanL) ^
(when AtR: CleanR)
Action (Left, Precond: AtR, Effect: AtL v (AtL ^ when CleanL: !ClearnL)
o Conditional steps for creating conditional plans:
if test then planA else planB
e.g., if AtL ^ CleanL then Right else Suck
o The search tree for the vacuum world is shown in the following figure
o The first two levels of the search tree for the double Murphy vaccum world.
o State nodes are OR nodes where some action must be chosen.
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o Chance nodes, shown as circles, are AND nodes where every outcome must be
handled, as indicated by the arc linking the outgoing branches.
o The solution is shown as bold lines in the tree.
 The following table shows the recursive depth first algorithm for AND-OR graph search.
 The following figure shows the part of the search graph,
 clearly there are no longer any acyclic solutions, and AND-OR-GRAPH-SEARCH would return
with failure, there is however a, cyclic solution, which is keep trying Left until it works.
 The first level of the search graph for the triple Murphy vacuum world, where we have shown
cycles explicitly.
 All solutions for this problem are cyclic plans.
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26

 The cyclic solution is as follows,
Conditional Planning in partially observable environments
 In the initial state of a partially observable planning problem, the agent knows only a certain
amount about the actual state.
 The simplest way to model this situation is to say that the initial state belongs to a state!set
 The state set is a way of describing the agents initial belief state.
 Determine “both squares are clean” with local dirt sensing
o the vacuum agent is AtR and knows about R, how about L?
 The following graph shows part of the AND-OR graph for the alternate double Murphy
vaccum world,
 In which Dirt can sometimes be left behind when the agent leaves a clean square
 The agent cannot sense dirt in other squares.
 Sets of full state descriptions
o { (AtR ⋀ CleanR ⋀ CleanL), (AtR ⋀ CleianR ⋀ ¬CleanL) }
 Logical sentences that capture exactly the set of possible worlds in the belief state.
o AtR ⋀ CleanR
 Knowledge propositions describing the agent's knowledge
 closed-world assumption - if a knowledge proposition does not appear in the list, it is
assumed false.
 Now we need to decide how sensing works.
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 There are two choices here,
o Automatic sensing:- Which means that at every time step the agent gets all the
variable percepts
o Active sensing:- Which means the percepts are obtained only by executing specific
sensory actions such as
 CheckDirt
 CheckLocation
Action(Left, PRECOND: AtR,
EFFECT: K(AtL) ⋀¬K (AtR) ⋀ when CleanR: ¬K(CleanR) ⋀
when CleanL: K ( CleanL) ⋀
when ¬ CleanL: K(¬ CleanL)) .
Action(CheckDirt, EFFECT:
when AtL⋀CleanL: K(CleanL) ⋀
when AtL ⋀ ¬CleanL: K (¬CleanL) ⋀
when AtR ⋀ CleanR: K(CleanR) ⋀
when AtR ⋀ ¬CleanR: K(¬CleanR))
3.4.4.2 Execution Monitoring and Replanning:
 An execution monitoring agent checks its percepts to see whether everything is going to
according plan.
 Murphy’s law tells us that even the best-laid plans of mice, men and conditional planning
agents frequently fail.
 The problem is unbounded indeterminacy – some unanticipated circumstances will always
arise for which the agents action description are incorrect.
 Therefore, execution monitoring is a necessity in realistic environments.
 we will consider two kinds of execution monitoring,
o Simple, but weak form called action monitoring – whereby the agent checks the
environment to verify that the next action will work.
o more complex, but more effective form called plan monitoring – in which the agent
verifies the entire remaining plan.
 A replanning agent knows what to do when something unexpected happens, call a planner
again to come up with a new plan to reach the goal.
 To avoid spending too much time planning, this is usually done by trying to repair the old
plan – to find a way from the current unexpected state back onto the plan
 Together Execution Monitoring and replanning form a general strategy that can be applied
to both fully and partially observable environments
 It can be applied to a variety of planning representations as state-space, partial-order and
conditional plans.
 The following table shows a simple approach to state-space planning.
 The planning agent starts with a goal and creates an initial plan to achieve it.
 The agent then starts executing actions one by one.
 The replanning agent keeps track of both the remaining unexpected plan segment plan and
the complete original plan whole-plan
 It uses action monitoring: before carrying out the next action of plan, the agent examines its
percepts to see whether any preconditions of the plan have unexpectedly become unsatisfied.
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28

Function REPLANNING-AGENT(percept) returns an action
Static: KB, a Knowledge base (includes action descriptions)
Plan, a plan, initially []
Whole-plan, a plan, initially []
Goal, a goal
TELL(KB,MAKE-PERCEPT-SENTENCE(percept,t))
Current  STATE-DESCRIPTION(KB,t)
If plan = [] the
whole-plan  plan  PLANNER(current,goal,KB)
If PRECONDITIONS(FIRST(plan)) not currently true in KB then
Candidates  SORT(whole-plan, ordered by distance to current)
Find state s in candidates such that
Failure repair  PLANNER(current,s,KB)
Continuation  the tail of whole-plan starting at s
Whole-plan  plan  APPEND(repair, continuation)
 If they have, the agent will try to get back on track by replanning a sequence of actions that
should take it back to some point in the whole-plan.
 The following table has an agent that does action monitoring and replanning
 It uses a complete state-space planning algorithm called PLANNER as a subroutine.
 If the preconditions of the next action are not met, the agent loops through the possible point
p in whole-plan, trying to find one that PLANNER can plan a path to.
 This path is called repair.
 If PLANNER succeeds in finding a repair, the agent appends repair and the tail of the plan
after p, to create the new plan.
 The agent then returns the first step in the plan.
Return POP(plan)
 The following diagram shows the schematic illustration of the process.
 The illustration of process is also called as Plan Monitoring.
 The replanner notices that the preconditions of the first action in plan are not satisfied by the
current state.
 It then calls the planner to come up with a new subplan called repair that will get from the
current situation to some state s on whole-plan.
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whole-plan
plan
S P E G
Continuation
repair
O
 Before execution, the planner comes up with a plan, here called whole-plan, to get from S to
G.
 The agent executes the plan until the point Marked E.
 Before executing the remaining plan, it checks preconditions as usual and finds that it is
actually in state O rather than state E.
 It then calls its planning algorithm to come up with repair, which is a plan to get from O to
some point P on the original whole-plan.
 The new plan now becomes the concatenation of repair and continuation.
 For example:-
o Problem of achieving a chair and table of matching color
 The agents PLANNER should come up with the following plan as,
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 If: the agent constructs a plan to solve the painting problem by painting the chair and table
red. only enough paint for the chair
 Plan monitoring
o Detect failure by checking the preconditions for success of the entire remaining plan
o Useful when a goal is serendipitously achieved
 While you’re painting the chair, someone comes painting the table with the
same color
o Cut off execution of a doomed plan and don’t continue until the failure actually
occurs
 While you’re painting the chair, someone comes painting the table with a
different color
 If one insists on checking every precondition, it might never get around to actually doing
anything
 RP - monitors during execution
3.4.4.3 Continuous Planning
 Continuous planning agent
o execute some steps ready to be executed
o refine the plan to resolve standard deficiencies
o refine the plan with additional information
o fix the plan according to unexpected changes
 recover from execution errors
 remove steps that have been made redundant
 Goal ->Partial Plan->Some actions-> Monitoring the world -> New Goal
 The continuous planning agent monitors the world continuously, updating its world model
from new percepts even if its deliberations are still continuing.
 For example:-
o use the blocks world domain problem
o The action we will need is Move(x, y), which moves block x onto block y, provided
that both are clear.
o The following is the action schema,
Action (Move(x, y),
PRECOND: Clear(x)  Clear(y)  On(x ,z),
EFFECT: On(x, y Clear(z)   Clear(y)   On(x, z))
o Goal: On(C, D)  On(D ,B)
o Start is used as the label for the current state
o The following seven diagram shows the continuous planning agent approach towards
the goal
o Plan and execution
o Steps in execution:
 Ordering - Move(D,B), then Move(C,D)
 Another agent did Move(D,B) - change the plan
 Remove the redundant step
 Make a mistake, so On(C,A)
 Still one open condition
 Planning one more time - Move(C,D)
 Final state: start -> finish
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 The sequences of states as the continuous planning agent tries to reach the goal state On(C,
D)  On(D ,B) as shown in (d).
 The start state is (a).
 At (b), another agent has interfered, putting D on B.
 At (c), the agent has executed Move(C, D) but has failed, dropping C on A instead.
 It retries Move(C, D), reaching the goal state (d).
 The initial plan constructed by the continuous planning agent.
 The plan is indistinguishable, so far, from that produced by a normal POP.
 After someone else moves D onto B, the unsupported links supplying Clear(B) and On(D, G)
are dropped, producing this plan.
 The link supplied by Move(D, B) has been replaced by one from Start, and the new-
redundant step Move(D, B) has been dropped.
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 After Move(C, D) is executed and removed from the plan, the effects of the Start step reflect
the fact that C ended up on A instead of the intended D.
 The goal precondition On(C, D) is still open.
 The open condition is resolved by adding Move(C, D) back in.
 After Move(C, D) is executed and dropped from the plan, the remaining open condition
On(C, D) is resolved by adding a causal link from the new start step.
 Now the plan is completed.
 From this example, we can see that continuous planning is quite similar to POP.
 On each iteration, the algorithm finds something about the plan that needs fixing a so-called
plan-flaw and fixes it.
 The POP algorithm can be seen as a flaw-removal algorithm where the two flaws are open
preconditions and causal conflicts.
 On the other hand, the continuous planning agent addresses a much broader range of flaws as
follows,
o Missing goals
o Open precondition
o Causal conflicts
o Unsupported links
o Redundant actions
o Unexecuted actions
o Unnecessary historical goal
 The following table shows the continuous-POP-Agent algorithm
Return action
 It has a cycle of “perceive, remove flaw act”
 It keeps a persistent plan in its KB, and on each turn it removes one ,flaw from the plan.
 It then takes an action and repeats the loop.
Function CONTINUOUS-POP-AGENT (percept) returns an action
Static: plan, a plan, initially with just Start, Finish
Action  NoOp (the default)
EFFECTS [Start] = UPDATE(EFFECTS [Start], percept)
REMOVE-FLAW (plan) // possibly updating action
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 It is a continuous partial-order planning agent.
 After receiving a percept the agent removes flaw from its constantly updated plan and then
returns an action.
 Often it will take many steps of flaw-removal planning, during which it returns NoOp, before
it is ready to take a real action.
3.4.4.4 Multiagent Planning
 So far we have dealt with single-agent environments
 Multiagent environments can be cooperative or competitive.
 For example:-
o the problem is team planning in double tennis.
 Plans can be constructed that specify actions for both players on the team
 Our objective is to construct plans efficiently.
 To do this we need requires some form of coordination, possibly achieved by
communication.
 The following table shows the double tennis problem,
 In the above table, Two agents are playing together and can be in one of four locations as
follows,
o [Left, Baseline]
o [Right, Baseline]
o [Left, Net]
o [Right, Net]
 The ball can be returned if exactly one player is in the right place.
Cooperation: Joint goals and plans
 An agent (A, B) declares that there are two agents, A and B who are participating in the
plan.
 Each action explicitly mentions the agent as a parameter, because we need to keep track of
which agent does what.
 A solution to a multiagent planning problem is a joint plan consisting of actions for each
agent
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 A joint plan is a solution if the goal will be achieved when each agent performs its assigned
actions.
 The following plan is a solution to the tennis problem
o PLAN 1 :
 A : [Go(A,[Right, Baseline]),Hit(A, Ball)]
 B : [NoOp(B),NoOp(B)].
 If both agents have the same KB, and if this is the only solution, then everything would be
fine; the agents could each determine the solution and then jointly execute it.
 Unfortunately for the agents, there is another plan that satisfies the goal just as well as the
first
o PLAN 2:
 A : [Go(A, [Left, Net]), NoOp(A)]
 B : [Go (B,[Right,baseline]),H it(23, Ball)]
 If A chooses plan 2 and B chooses plan 1, then nobody will return the ball.
 Conversely, if A chooses 1 and B chooses 2, then they will probably collide with each other;
no one returns the ball and the net may remain uncovered.
 So the agents need a mechanism for coordination to reach the same joint plan
Multibody Planning:
 concentrates on the construction of correct joint plans, deferring the coordination issue for the
time being, we call this Multibody planning
 Our approach to multibody planning will be based on partial-order planning
 we will assume full observability, to keep things simple
 There is one additional issue that doesn’t arise in the single-agent case; the environment is no
longer truly static.
 Because other agents could act while any particular agent is deliberating.
 Therefore we need synchronization
 We will assume that each action takes the same amount of time and that actions at each point
in the joint plan are simultaneous.
 At any point in time, each agent is executing exactly one action.
 This set of concurrent actions is called a joint action.
 For example, Plan 2 for the tennis problem can be represented as this sequence of joint
actlons:
Coordination Mechanisms:
 The simplest method by which a group of agents can ensure agreement on a joint plan is to
adopt a convention prior to engaging in joint activity.
 A convention is any constraint on the selection of joint plans, beyond the basic constraint that
the joint plan must work if all agents adopt it
 For example
o the convention "stick to your side of the court" would cause the doubles partners to
select plan 2
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o the convention "one player always stays at the net" would lead them to plan 1
 In the absence of an applicable convention, agents can use communication to achieve
common knowledge of a feasible join plan
 For example:
o a doubles tennis player could shout "Mine!" or "Yours!" to indicate a preferred joint
plan.
Competition:
 Not all multiagent environments involve cooperative agents
 Agents with conflicting utility functions are in competition with each other
 One example: chess-playing. So an agent must
(a) recognize that there are other agents
(b) compute some of the other agent's possible plans
(c) compute how the other agent's plans interact with its own plans
(d) decide on the best action in view of these interactions
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