Robust Planning using Constraint Satisfaction Techniques

1
Robust Planning using Constraint Satisfaction
Techniques
Daniel Buettner and Berthe Y. Choueiry
Constraint Systems Laboratory Department of
Computer Science and Engineering, University of
Nebraska-Lincoln buettnerchoueiry_at_cse.unl.edu

• Modern Planning Systems The fastest of todays
  planners are nonsystematic and rely on some type
  of stochastic search. There are other planners
  that can guarantee completeness and some form of
  optimality, and these planners descend from
  GraphPlan. This work is in the latter camp, as
  we wish are interested in optimal solutions.
• Methodology We are developing new CSP
  techniques to solve planning problems that
• Exploit the structure of planning graphs
• Exploit interchangeability in planning problems
• Goals Our work has two main objectives
• Find robust plans which make use of
  interchangability
• Improve the performance of solution extraction in
  planning problems

Abstract We investigate the automatic conversion
of a planning problem to a binary constraint
satisfaction problem (CSP). This conversion
allows us to use standard constraint processing
(CP) techniques to find solutions to the planning
problem. Of particular interest is the detection
of dynamic symmetry during solution extraction on
the CSP. This will allow bundles of solutions to
be found, where each bundled solutions has
interchangeable values for one or more variables
in the CSP.

• Definitions
• A Constraint Satisfaction Problem (CSP) is a
  triple P (V, D, C), where
• V V1, V2,..., Vn, a set of variables.
• D DV1, DV2,..., DVn, the set of variable
  domains.
• C Ci, Cj,k,..., Ci,j,...,m,..., Cn, a set of
  constraints on variables in V.
• A Planning Problem is a problem in which an agent
  capable of performing certain actions finds
  itself in some known world, needing to achieve
  certain goals. More formally, a planning problem
  should specify
• The initial state of the world (as a set of
  facts).
• A description of the agents goals (as a set of
  facts).
• A description of the actions that the agent can
  carry out. Actions are described by their
  preconditions and effects. The preconditions of
  an action are a set of facts that must be true
  before an action can be performed. The effects
  can be divided into an add list and a delete
  list, where the add list contains facts made true
  by the action and the delete list contains facts
  that are made false by the action.

• Experience
• Summer intern at Honeywell where I worked on an
  industrial scheduling system.
• Summer intern at NASA Ames where I worked on a
  GraphPlan based planning system.

This illustrates the planning graph as
constructed by GraphPlan. A planning graph
consists of alternating layers of facts and
actions. The first entries in a planning graph
are the facts found in the initial state of the
planning problem. The next layer is the set of
actions whose preconditions exist in the initial
state (thus making the actions applicable). Of
note is a pseudo-action called a noop that has
one fact as its precondition and that same fact
as an effect. These noop actions ensure that
once a fact becomes true, it is present at all
future levels in the planning graph. To extend
the planning graph from a given fact layer, all
applicable actions are generated and they form
the next action layer. The effects of these
actions form the next fact layer. GraphPlan
starts with the initial conditions and extends
the planning graph until all goal are found (and
are non-mutex) at the highest fact layer. At
this point, a search is launched to see if a
valid plan exists in the planning graph. If a
solution is found, it is output. Otherwise the
planning graph is extended one more layer and a
search is again launched. This continues until a
valid plan is found or the problem is found to be
unsolveable.
Problem Reformulation The conversion of a
planning problem to a CSP is completely
automated. The planning graph generated by the
GraphPlan algorithm is used as the basis for this
conversion. Early attempts at using CP
techniques with planning required that each
planning problem be hand encoded, a complex and
sometimes difficult task.
Variables Each fact present in the planning
graph for a particular planning problem is
converted to a CSP variable.

• Constraints
• Activity Constraints When a particular action
  is chosen to support some fact, the preconditions
  of that action must be true. The activity
  constraints force the variables representing each
  precondition to take some value other than
  NOTHING.
• Fact Mutex Constraints These simple
  constraints are placed between facts that
  GraphPlan has marked as mutex. These constraints
  say that at least one of the variables must have
  the value NOTHING. These constraints prevent the
  planner from, for example, trying make (FACT) and
  (NOT FACT) true at the same time.
• Mutex Constraints These constraints are used
  to model mutexes that exist between pairs of
  actions. As actions are the domain values in
  this formulation, the constraints must exist
  between facts which have mutex actions supporting
  them. The constraints explicitly forbid
  particular pairs of actions from being
  simultaneously assigned to the fact variables
  involved in the constraint.

Domains The set of actions supporting each fact
becomes the domain, with the addition of a
special value called NOTHING.
Constraints Mutexes between facts and actions
must be enforced, as well as activity constraints
that are used to model the preconditions of
actions. In detail

• References
• Minh?Binh?Do?and?Subbarao?Kambhampati??Planning?as
  ?constraint?satisfaction??Solving?the?
  planning?graph?by?compiling?it?into?CSP??Artificia
  l?Intelligence???????????? -??????????.
• Avrim?Blum?and?Merrick?Furst??Fast?planning?throug
  h?planning?graph?analysis??In?Proceedings?of?the??
  ?th?International?Joint?Conference?on?Artificial?I
  ntelligence? ?IJCAI??????pages????? - ???????????

This work is supported by the CAREER Award
0133568 from the National Science Foundation.