Automated Model Generation and Simulation 3

1 Introduction Solving problems about complex physical systems generally involves the creation and execution of models of the physics needed to reason about the problem. Models are normally constructed by the person studying the system. Despite the considerable time and e ort spent, a handcrafted model is often error-prone. Modifying a handcrafted model to solve similar problems about other physical systems is also dicult, and may take more time than building a new model for the systems. The work of this paper is motivated by two goals. The rst goal is to automate the model formulation and simulation process for complex spatial reasoning tasks. In particular, we focus on an important subclass of spatial reasoning
an example)
Di erent forms of these problems require spatial rea-
soning to formulate equations of motion, in particu-
lar the ability to reason explicitly about vector quan-
physical object
primitive object
composite object
Figure 2: 3 blocks connected by 2 springs. The middle block is pulled directly to the side and released.
duplicated.
Consider a spring with one end attached to a xed
point and the other end attached to a block, as illus-
trated in Figure 1a. This harmonic oscillator is a com-
Abstract Understanding or predicting the behavior of a complex physical system requires the construction and execution of a model of the system. Such a model is often handcrafted by the person studying the system, and the modeling process is not formalized to be reusable by others. We describe a method which uses rst principles to automatically create models and simulators for complex motions, and an implemented system called . Oracle Given a description of a problem involving a physical system, Oracle automatically identi es relevant model fragments, instantiates them for the particular entities and physical phenomena in the problem, composes the instantiated fragments to form a model, and executes the model. Knowledge of physical phenomena is represented with general model fragments which can be shared and reused by many models. Experimental results show that the method is capable of generating correct models of several di erent types of physical systems if enough domain knowledge is available.
solid
fluid
rigid body flexible body water
air
spring-block ship system
sailboat
block hull spring sail
Figure 4: Taxonomy of entities for the examples of the paper. Properties of a class are inherited to its subclasses. For example, properties of rigid body are inherited by block and hull.
solve 11998864];
cannot handle the more complex problems we describe
above because they lack this spatial reasoning ability.
Consider, now, predicting the behavior of another
Kyungsook Han and Andrew Gelsey
kshan@ gelsey@ Department of Computer Science Rutgers University New Brunswick, NJ 08903 U. S. A.
to a corner of a block instead of the center of the face?

(2) What if a block attached to a spring is put in arbi-
trary position and orientation before being released? (3)
physical system, a sailboat (Figure 3), which appears
(a)
(b)
Figure 1: (a) The block on a spring is pulled from its equilibrium position and released. (b) The block is pulled and rotated from its equilibrium position and released.
{ moving objects. The second goal is to make the mod-
eling process as general as possible so that common do-
main theories can be shared and reused instead of being
mon textbook example which is often used in qualitative
physics research. It is well known that the oscillator has
one degree of freedom, i.e., displacement of the block
predicting the behavior is not as simple as before. Is
the motion going to be still oscillatory? More interest-
ing questions include: (1) What if a spring is attached
3This research was partially supported by the Advanced Research Projects Agency (ARPA) and National Aeronautics and Space Administration under NASA grant NAG2-645 and by the National Science Foundation through grant CCR9209793.
from its equilibrium position, and its motion is oscilla-
tory on a straight line. However, if you consider a block
and a spring in more general con guration (Figure 1b),
tities and moving frames of reference. Many qualitative
tphheysliicnseaarpphraoramchoensicbyoscAilIlarteosreaprrcohbelresmwh[Ficohrbcuasn, Kuipers, 1986; Struss, 1988; Weld, 1988; Williams,