Qualitative modeling is the study of how the physical world behaves. These physical models accept partial descriptions of the world and output the possible changes. Current systems assume that the model is static and that physical entities do not effect change into the world. An approach to planning in physical domains and a working implementation which integrates qualitative models with a temporal interval-based planner are described. The planner constructs plans involving physical qualities and their behavioral descriptions

Carnes, James R.

Johannes, James D.

English

NASA Technical Reports Server

N88-16414
QUALITATIVE MODELS FOR PLANNING:
A GENTLE INTRODUCTION
James D. Johannes
James R. Carnes
Computer Science Department
The University of Alabama in Huntsville
Huntsville, Alabama 35899
Phone (205) 895-6255/6088
ABSTRACT
Qualitative Modeling is the study of how the phy-
sical world behaves. These physical models accept par-
tial descriptions of the world and output the possible
chan_es. Current s[stems assume that the model is
statlc, and that physlcal entltles do not effect change
into the world. For instance a certain qualitative
systems can diagnose faulty electrical circuits, but
cannot design plans to rewire circuits to change their
behavior. This paper describes an approach to planning
in physical domains and a working implementation which
integrates qualitative models with a temporal
interval-based planner. The planner constructs plans
involvin_ physical quantities and their behavioral
descriptlons.
!. INTRODUCTION
This paper describes a system for the representation and
solution of dynamic planning problems. The representation of
physical entit_es an qualitative models provides an excellent
forum for storing definitional and behavioral information about.a
particular domain [2,8,10]. This knowledge is easily coupled, _n
the model, with a temporal component permitting the representa-
tion of entity behavior and interaction over time. The temporal
capability is accomplished with the introduction of a time inter-
val into the qualitative knowledge model. Inference mechanisms
that usually run with the detailed qualitative information are
now time-qualified, adding another "dimension" to the knowledge
model [6,10]. The prototype system developed to illustrate these
concepts is described, and, finally, directions for future work
are outlined.
_. QUALITATIVE MODELS
Qualitative models are aptly described by Williams[10] as a
_hysical system with initial conditions whose analysis typically
_nvolves (1) a description of the temporal behavior of the
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system's state variables, in terms of a particular qualitative
representation, and (2) an explanation how this behavior came
about.
In more detail, a physical system consists of a set of state
variables (e.g., force and acceleration) and a system of equa-
tions, parameterized by time, which describe the interactions
between these variables (e.g., f(t) = ma(t)). A qualitative
representation partitions the range of values for a particular
quantity into a set of interesting regions (e.g., positive, nega-
tive, or zero). The particular representation selected depends
on properties of the domain and the goals of the analysis.
The behavior of the system can be viewed in terms of a qual-
itative state diagram, where each state describes the qualitative
value of every state variable in the system. The behavior of the
system over time can be viewed as a particular path through this
state diagram. Each state along this path represents an interval
of time over which the system's state variables maintain their
values. The duration of this interval is dictated by principles
involving continuity and rates of change.[4,6,10]
The system changes state whenever any state variable changes
its qualitative value. The values in the next state are then
determined by (i) identifying those _uantities which cannot
change value !e.g., if q is positive in a particular state and
its derivative is positive or zero then it will remain positive
in the next state), and (2) propagating the effects of those
quantities that are known to change. The qualitative reasoning
system also keeps track of the reason for every deduction in (i)
or (2), using the record, among other things, to generate expla-
nations (e.g., "an increase in force causes the mass to
accelerate").[5,6,10]
Components in a qualitative model may be expressed as an
object containing five elements[3,9]: individual objects involved
in the process, preconditions (outside of the object knowledge)
on the behavior, quantity conditions (inequalities), relations
asserted as object behavior, and influences the behavior has on
quantities.
3. TEMPORAL INTERVALS
The planning system maintains a list of entity qualities or
properties qualified by intervals over which they hold. The
planner uses a time logic[l] to maintain the temporal relation-
ships between intervals. Table 1 shows the possible values for
different relations.
In operator and rules defined within the system, intervals
are represented by symbols starting with '$', while variables are
represented by symbols starting with '?'. The temporal relation
between two intervals is expressed as a disjunction and written
298
in a list (e.g., (:< :>) is used to mean "is before or after").
Different properties or facts about an object are paired with the
same interval over which they hold. Thus, (ON A TABLE) $INTER-
VALI denotes a fact (ON A TABLE) which holds over the time inter-
val $INTERVALI.
Value Description Inverse Description
:< before :> after
:M meets :MI met by
:O overlaps :OI overlapped by
:S starts :SI started by
:F finishs :FI finished by
:D during :DI encloses
:= equals := equals
TABLE i: Interval Relations and Inverses[l].
An operator defines an action the object can perform to
change its properties in the world. The planning system uses a
model of action[l] with temporally qualified expresslons describ-
ing operator preconditions and effects. For instance, Figure 1
defines an operator PICKUP which can be applied to an object if
it is clear and resting on something. PICKUP's effects clear the
object's old location. The constraints field is used to restrict
the temporal relations among facts matching with the precondi-
tions and effects.
OPERATOR: pickup
PRECONDITIONS: (clear ?object) $clear-object
(on ?object $surface) Son
EFFECTS: (pickup ?object ?surface) Spickup
(clear ?surface) $clear-surface
CONSTRAINTS: $clear-object (:M) Spickup
Son (:0) $pickup
Son (:M) $clear-surface
FIGURE i: Definition of Operator PICKUP[3].
A rule models temporal laws of the domain. The planning
system uses rules as backward chaining operators for solving
goals, as well as forward chaining, temporally constrained infer-
ence rules. Thus, with the object behavior modeled as rules, the
system can both plan their action and infer their results.
Rule definitions are similar to operator definitions, with
antecedents behaving like operator preconditions, consequents
behaving like operator effects, and consequence constraints
behaving like operator constraints. The additional field, tem-
poral conditions, places preconditions on the temporal relations
among facts matching the antecedents. The time logic supports
temporal intersections, allowing a rule to be inhibited until
299
antecedents are known to intersect (meaning their relation is a
subset of (:S :SI :F :FI :D :DI :O :OI :=)) and to assert conse-
quents over their intersection. Figure 2 demonstrates these
features. Given (ON A B) and (ON B C) whose intervals intersect,
(OVER A C) is asserted during their intersection.[3,9]
RULE
Antecedents: (ON ?x ?y) $on-xy
(ON ?y ?z) $on-yz
Temporal Conditions:
Exists (INTERSECTION $on-xy $on-yz)
called $intersection
Consequents: (OVER ?x ?z) $intersection
Consequent Constraints:
Figure 2: A Temporally Qualified Inference Rule[3].
4. APPLICATION
The constructs of the previous section are part of a simple
temporal planning example to operate on selected objects. Plans
can be generated to "pick-up" A, B, or C. This example is, how-
ever, very different from the typical "blocks world" environment
in two respects, each object have been physicall[ described and
temporally _alified. The physlcal descriptlon portrayed the
objects abillty to placed over one another and even how many may
be stack above each particular object. This aspect of the system
has not been exploited in order to concentrate on temporal plan-
ning which give the intervals in which each object resides over
another object. Figure 3 shows the script generated by the
planner to meet a goal in this simple system.
Goal: PICK-UP A tl
Solution: Apply the rule to see if any objects are over A at tl.
Goal: PICK-UP B
Solution: Apply the rule to see if any objects are over B at tl.
Goal PICK-UP C
Solution: Apply the rule to see if any objects are over C at tl.
Action: pick-up C
Action: pick-up B
Action: pick-up A
FIGURE 3: Output for Goal to Pick Up Object A.
Qualitative models such as those described in this paper
will be necessary for detailed planning operations onboard space
station and for many other space applications. Planning systems
using temporally-qualified structural and behavioral knowledge
will be able to plan the independent actions of IVA or EVA
robots, is needed to function in a dynamic, time-varying,
300
environment[7]. Qualitative systems will also be able to gen-
erate complex plans for multiple experiment packages, using
knowledge of core subsystem properties to keep operations within
established constraints.
5. CONCLUSIONS AN___DDFUTURE DIRECTIONS
Qualitative modeling represents the physical and temporal
information required for dynamic planning applications. Charac-
teristic and behavioral info.rmation descrlbe-an entity in term of
properties which are used in different time qualified rules and
operators to generate plans to achieve desired goals. A simple
example of temporal reasoning about physical objects was
presented, but examples of more sophisticated thermal and electr-
ical systems of entmties have been accomplmshed.
Work of this nature is helpful in developing and evaluating
representations for qualltative modeling and planning, that is
controlling the effects of time, space, and general properties ofphysical objects [6,7] Current efforts in the design of the
space systems are requiring the capture detailed knowledge of
system design[7], so new space systems may incorporate advanced
knowledge-based appllcations, such as plannlng systems driven by
qualitative models• Accordingly, this research will continue to
explore detailed representations within domain and world models,
and investigate different planning strategies for reasoning and
control•
•
•
•
•
•
REFERENCES
Allen, J.F., Maintaining Knowledge About Temporal Intervals,
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Brachman, R.J., R.E. Fikes, and H.J. Levesque, _KRYPTON: A
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Hogge J.C., Compiling Plan Operators fo_r!n_Domains Expressed
in Qualitative Process Theory, AAAI-87, Proceedings of the
Sixth National Conference on Artificial Intelligence, August
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Johannes, J.D., Representation and
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Us__ee o_ff Judgmental
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Qualitative models for planning: A gentle introduction

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