### Statically Stable Assembly Sequence Generation and Structure Optimization for a Large Number of Identical Building Blocks

Abstract

This work develops optimal assembly sequences for
modular building blocks. The underlying concept is
that an automated device could take a virtual shape
such as a CAD file, and automatically decide how to
physically build the shape using simple, identical
building blocks. This entails deciding where to place
blocks inside the shape and generating an efficient
assembly sequence that a robot could use to build
the shape. The blocks are defined in a general,
parameterized manner such that the model can be
easily modified in the future.
The primary focus of this work is the development of
methods for generating assembly sequences in a
time-feasible manner that ensure static stability at
each step of the assembly. Most existing research
focuses on complete enumeration of every possible
assembly sequence and evaluation of many possible
sequences. This, however, is not practical for systems
with a large number of parts for two reasons: (1) the
number of possible assembly sequences is exponential
in the number of parts, and (2) each static stability
test is very time-consuming. The approach proposed
here is to develop a multi-hierarchical rule-based
approach to assembly sequences. This is accomplished
by formalizing and justifying both high-level and
mid-level assembly rules based on static considerations.
Application of these rules helps develop assembly
sequences rapidly. The assembly sequence is developed
in a time-feasible manner according to the geometry
of the structure, rather than evaluating statics along
the way. This work only evaluates the static stability
of each step of the assembly once. The behavior of the
various rules is observed both numerically and through
theory, and guidelines are developed to suggest which
rules to apply.
A secondary focus of this work is to introduce methods
by which the inside of the structure can be optimized.
This structure optimization research is implemented by
genetic algorithms that solve the multi-objective
optimization problem in two dimensions, and can be
extended to three dimensions.