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TR, and TR. are two sets of trajectories of cp and cq for performing the
ma& task !fw.
Type is one of the elements of the following set, (sing&+g-imrtion,
multipeg_insertion, stack. screw, pcsh_and_huist), which is a set of
most common types of mating tasks in industry [SI. This set can be
expanded to accommodate other types of mating tasks.
Stability E [stable, unsrcrble). A stable task will always maintain the
Elationship once established regardless of the orientation of the assem-
bly.
There are three basic elements in an assembly cek assembly machines,
fixtures, and assembly tools. An assembly machine can be a robot or any
mechanism which performs assembly functions. A fixture can be modular
fixture for gend assembly or speciallydesigned fixture for some dedicate
product The planning system described in this paper will deal with logical
design of fixtures rather than physical design of fixtmes. It is assumed that
all logical fixtures can be realized. eitha constructed from modular fixtures
or customized fixtures. In case Some of the fixtures cannot be realized. their
setup costs can simply be assigned to have an in!ini@ value such that the
assembly planner will never select them. A set of tools am also available in
the assembly cell. In this paper it is assumed that the selection of tools can
be done simply by direct mapping from assembly tasks to the tool to be
used according to manuals or experience. A unified representation of the
knowledge of these resources will be presented in Section 2.4. Figure 1 shows an example assembly of six components with its Fcl,
tional model. For this example only translations motionS BIC umsidexd,
thus the trajecmies in TRb and TRh are 3x1 pition vectors.
2.2. Slmullrted World Model
The simulated world model is a dambase which desaibes and kceps
track of the state of the assembly and various resixum (fixlures and took)
by simulating the assembling process. and is updated according to the tasks
that have been perfamed.
An assembled produd. is a set ofumnected components. Then arc two
ways of representing the state of an assembly. The 6rsl rcpreSentatian
describes the state of an assembly through the aonditions of the msks
between components. In this paper we assume that a task is either done or
not done, and thaefore can be wfiiciently described by a predicatG DONE,
where Ti represent a task. Ler - mpnt negation and 5 repm-ent the
disassemblying of Ti, then DONE( Ti ) = TRUE if Ti is not done. The
expressions shown above are called well-formed formulas (or simply for-
mulas). and the assignment of truth value to a well-formed formula acumi-
ing to the condition of tasks is called an inrcrpretation of the formula
Hence, Using the above m, formulas can be constructed to describe