1 Chapter 16 Planning Methods

2 Chapter 16 Contents (1) l STRIPS l STRIPS Implementation l Partial Order Planning l The Principle of Least Commitment l Propositional Planning l SAT Planning

3 Chapter 16 Contents (2) l Planning Graphs l GraphPlan l ADL and PDDL l Probabilistic Planning l Dynamic World Planning l Case-Based Planning l Scheduling

4 STRIPS (1) l Stanford Research Institute Problem Solver. l An operator based planning system. l STRIPS uses wffs in FOPC to describe the world. l For example: l STRIPS was designed to enable a planner to devise plans for a robot to solve problems in the blocks world.

5 STRIPS (2) l STRIPS defines operators as in the following rule schemata: Precondition:AT(r, x) Λ AT(o, x) Delete:AT(r, x) AT(o, x) Add:AT(r, y) AT(o, y) l The preconditions specify what must be true for the operator to be applied. l The delete and add lists specify the changes that will take place after the operator is applied.

6 STRIPS Implementation l STRIPS uses resolution and means- ends analysis to devise plans: l The goal is negated, and the rule schemata are instantiated with objects from the real world. l If the resolution fails, then the goal has been achieved. l Otherwise, a plan is devised.

7 Example 1 l Three blocks – a,b,c l Block a on table, block b is on c l Predicates nOn(x,y) means x is on y nClear(x) means x has no block on top of it nt is the table l Goal On(c,a) get c on a

8 Example 2 l Start state On(a,t) On(b,c) On(c,t) Clear(b) Clear(a) Clear(t)

9 Example 3 l Operators nMoveOnto(x,y) move x onto top y –Preconditions On(x,z) Λ Clear(x) Λ Clear(y) –Delete On(x,z), Clear(y) –Add On(x,y), Clear(z) nmoveOntoTable(x) –Preconditions On(x,y) Λ Clear(x) –Delete On(x,y) –Add On(x,t) Clear(y)

10 Example 4 l Approaches nForward chaining – search forward through the space of possible plans until we find one nBuild tree – first move choices –MoveOnto(a,b) –MoveOnto(b,a) –MoveOntoTable(b)

11 Example 5 l Choose MoveOntoTable(b) nPreconditions On(b,y) Λ Clear(b) matched by instantiating y with c. nApply –Delete: On(b,c) –Add: On(b,t), Clear(c)

12 Example 6 l Current state description On(a,t) On(b,t) On(c,t) Clear(b) Clear(a) Clear(c) Clear(t)

13 Example 7 l Applicable moves MoveOnto(a,b) MoveOnto(a,c) MoveOnto(b,a) MoveOnto(b,c) MoveOnto(c,a) MoveOnto(c,b)

14 Example comments l Continue in this manner until a suitable plan is found l Does not use means-ends analysis l Works only for small problems l Could enhance by using backward chaining – MoveOntoTable(b) has the effect of clearing c, which helps l Used unification and resolution

15 Partial Order Planning (1) l A total order plan specifies the order in which all actions must be carried out. l A partial order plan can specify some actions in parallel – these actions can be carried out in any order relative to each other.

16 Partial Order Planning (2) l A partial order plan can be implemented in one of several ways. l The partial order plan on the left is implemented in one of two ways, shown in the total order plans, center and right:

17 The Principle of Least Commitment l In building a plan there will be some variables and objects that can be ignored, as they are superfluous to the goal of the plan. l Some variables do not need to be instantiated – for example it is preferable, where possible, to use MoveOnto (a, y) than to use MoveOnto (a, b). l This is the Principle of Least Commitment.

18 Propositional Planning (1) l Any STRIPS plan can be expressed in propositional logic. l This will often involve increasing the number of variables.

19 Propositional Planning (2) l Any STRIPS plan can be expressed in propositional logic. l This will often involve increasing the number of variables. For example: Clear (x) On (x, y) l These predicates can be represented as propositions: X 1 is equivalent to Clear (A) X 2 is equivalent to Clear (B) X 3 is equivalent to On (A, B) X 4 is equivalent to On (B, A)

20 Propositional Planning (3) l States can be represented as an assignment of truth values to the propositions: X 1 Λ ¬X 2 Λ X 3 Λ ¬ X 4 l This state can be represented in STRIPS notation as: Clear (A) Λ ¬Clear (B) Λ On (A, B) Λ ¬On (B, A) l The following sentence represents all states in which A is clear and B is not clear: X 1 Λ ¬X 2

21 Propositional Planning (4) l Actions can also be represented as the preconditions and the results of the action. l We use the notation ¬X 1 ’ to indicate that X 1 ’ is no longer true after the action. l Hence, an action might be: X 1 Λ X 2 Λ ¬X 3 Λ ¬X 4 Λ X 1 ’ Λ ¬X 2 ’ Λ X 3 ’ Λ ¬X 4 ’ l This action is MoveOnto (A, B). l This is a simple example, but propositional planning can lead to very complex expressions being used. l The advantage of using propositional planning is that automated systems can be built to manipulate the plans. l Requires n 2 variables for n blocks

22 Satisfiability (SAT) Planning l The satisfiability problem, of determining whether a given propositional logic sentence is satisfiable or not, is NP- Complete. l A number of efficient methods have been developed for devising plans by determining the satisfiability of propositional logic expressions. l Methods are either systematic, which involve checking all possible assignments of truth values, or stochastic.

23 Planning Graphs (1) l Even-numbered levels represent states. Odd-numbered levels actions. l Level 0 contains the propositions that represent the start state. The arrows from level 0 to level 1 show how those propositions match the preconditions of the actions in level 1. l All possible actions are shown in the graph.

24 Planning Graphs (2) l The partial planning graph shown includes persistence actions (things which do not change) as lines with squares on. l The heavy black lines show mutexes: nTwo propositions joined by such a line are mutually exclusive, and cannot both be used in the same plan.

25 Planning Graphs (3) l The planning graph for even a simple problem can be extremely complex. l By producing a complete planning graph for a problem, it can be determined whether a plan is possible, and the plan itself can also be derived. l Algorithms such as GraphPlan can be used to extract the plan.

26 GraphPlan l Problems are expressed in STRIPS notation. l GraphPlan iteratively builds a planning graph, starting from the initial state and working towards the goal state. l All applicable operators are applied at each level to produce the next level. l When the propositions necessary for the goal are included in the current level, and they are not mutex, a possible solution may have been reached.

27 ADL l Another method for representing planning problems. l ADL – Action Description Language: nMore expressive than STRIPS. nAllows quantified expressions such as: x.P(x) Λ ¬ Q(x) nPreconditions can include disjunctions. nAllows conditional effects – effects of actions that are dependent on other factors.

28 Probabilistic Planning l Thus far we have assumed that all actions are deterministic. l In fact, some actions are non- deterministic – their effects can vary. l It is possible to extend situation calculus to deal with non- deterministic actions.

29 Dynamic World Planning l Our discussion so far has assumed the world is static. l In fact, the world is dynamic – things outside of the control of the planner change. l Execution monitoring is used to monitor the execution of plans: nIf something changes during execution, replanning may be necessary. l Another approach is conditional planning – this includes every possible outcome in the plan.

30 Case-Based Planning l Case-based planning involves storing each plan that is devised. l Plans (and partial plans) can be re-used later to solve other, similar problems. l Example: CHEF. A system that is used to devise recipes for Chinese food given a set of ingredients. l If presented with a set of ingredients it has not seen before, it is able to use similar sets of ingredients it has seen before to devise a new recipe.

31 Scheduling l Scheduling is like planning, but also takes into account the length of time each action takes to execute. l Job-shop scheduling involves allocating machinery to a set of tasks. l The scheduler plans when each task will start, and how long it will take. l Scheduling can be treated as planning with constraints, where the constraints specify how long tasks will take.