Funes, P. and Pollack, J. (1997) Computer Evolution of Buildable Objects. Fourth European
Conference on Artificial Life. P. Husbands and I. Harvey, eds., MIT Press. pp 358-367.
knowledge into the program, which would result in familiar
structures, we provided the algorithm with a model of the
physical reality and a purely utilitarian tness function, thus
supplying measures of feasibility and functionality. In this
way the evolutionary process runs in an environment that has
not been unnecessarily constrained. We added, however, a
requirement of computability to reject overly complex struc-
tures when they took too long for our simulations to evalu-
ate.
The results are encouraging. The evolved structures had a
surprisingly alien look: they are not based in common
knowledge on how to build with brick toys; instead, the com-
puter found ways of its own through the evolutionary search
process. We were able to assemble the nal designs manually
and con rm that they accomplish the objectives introduced
with our tness functions.
After some background on related problems, we describe
our physical simulation model for two-dimensional Lego
structures, and the representation for encoding them and
applying evolution. We demonstrate the feasibility of our
work with photos of actual objects which were the result of
particular optimizations. Finally, we discuss future work and
draw some conclusions.
2 Background
In order to evolve both the morphology and behavior of
autonomous mechanical devices which can be manufactured,
one must have a simulator which operates under several con-
straints, and a resultant controller which is adaptive enough
to cover the gap between simulated and real world.
Features of a simulator for evolving morphology are:
¥ Universal - the simulator should cover an in nite gen-
eral space of mechanisms.
¥ Conservative - because simulation is never perfect, it
should preserve a margin of safety.
¥ Ef cient - it should be quicker to test in simulation than
through physical production and test.
¥ Buildable - results should be convertible from a simula-
tion to a real object
Computer Evolution of Buildable Objects
Pablo Funes and Jordan Pollack
Computer Science Department
Volen Center for Complex Systems
Brandeis University
Waltham, MA 02254-9110
{pablo,pollack}@cs.brandeis.edu
Abstract
Creating arti cial life forms through evolutionary
robotics faces a chicken and egg problem: learn-
ing to control a complex body is dominated by
inductive biases speci c to its sensors and effectors,
while building a body which is controllable is con-
ditioned on the pre-existence of a brain.
The idea of co-evolution of bodies and brains is
becoming popular, but little work has been done in
evolution of physical structure because of the lack
of a general framework for doing it. Evolution of
creatures in simulation has been constrained by the
reality gap which implies that resultant objects
are usually not buildable.
The work we present takes a step in the prob-
lem of body evolution by applying evolutionary
techniques to the design of structures assembled out
of parts. Evolution takes place in a simulator we
designed, which computes forces and stresses and
predicts failure for 2-dimensional Lego structures.
The nal printout of our program is a schematic
assembly, which can then be built physically. We
demonstrate its functionality in several different
evolved entities.
1 Introduction
In this paper we report our work in evolution of buildable
designs using Lego
1
bricks. Legos are well known for their
exibility when it comes to creating low cost, handy designs
of vehicles and structures (see [22], for example). Because of
these properties and general availability, Legos constitute a
good ground for one of the rst experiments involving evolu-
tion of computer simulated structures which can be built and
deployed.
Instead of incorporating an expert system of engineering
1. Lego is a registered trademark of the Lego group.

2There are several elds which bear on this question of
physical simulation, including qualitative physics and struc-
tural mechanics, computer graphics, evolutionary design and
robotics.
2.1 Qualitative Physics
Qualitative Physics is the sub eld of AI which deals with
mechanical and physical knowledge representation. It starts
with a logical representation of a mechanism, such as a Heat
Pump [7] or a String [8], and produces simulations, or envi-
sionments, of the future behavior of the mechanism. QP has
not to our knowledge been used as the simulator in an evolu-
tionary design system.
2.2 Computer Graphics.
The work of Karl Sims [19], [20] was seminal in the elds of
evolutionary computation and arti cial life. Following the
work of Ngo and Marks [16], Sims evolved virtual creatures
that have both physical architecture and control programs
created by an evolutionary computation process.
Despite their beautiful realism, Sims organisms are far
from real. His simulations do not consider the mechanical
feasibility of the articulations between different parts, which
in fact overlap each other at the joints, nor the existence of
real world mechanisms that could produce the forces respon-
sible for their movements.
g. 1. Distribution of material for a piece that
optimizes weight and stiffness. From Chapman,
Saitou and Jakiela [3]. (Reproduced with
permission). This strange shape looks like a distant
relative of our evolved Lego objects.
2.3 Structural Mechanics/Structural Topology
The engineering eld of structural mechanics is based on
methods, such as nite element modelling [23] to construct
computable models of continuous materials by approximat-
ing them with discrete networks. These tools are in broad use
in the engineering community, carefully supervised and ori-
ented towards particular product designs, and are often quite
computationally intensive. Applications of genetic algo-
rithms to structural topology optimization ([3], [18]) are
related to our work. This type of application uses genetic
algorithms as a search tool to optimize a shape under clearly
defined preconditions. The GA is required, for example, to
simultaneously maximize the stiffness and minimize the
weight of a piece subject to external loads (fig. 1.).
2.4 Evolutionary Design
Evolutionary Design, that is, the utilization of evolutionary
computation techniques for industrial design, is a new
research area where Peter Bentley s Ph.D. Thesis [2] is
ground-breaking work. Bentley uses a GA to evolve shapes
for solid objects directed by multiple tness measures. His
evolved designs include tables, prisms, even vehicle pro les.
Bentley s search algorithms use combinations of tness
measures ( Size , Mass , No Fragmentation , Flat Upper
Surface , Supportiveness , etc.) that include some physical
constraints, like center of mass positioning or total weight.
Lacking a more complete physical model, he relies on spe-
ci c measures to guide evolution in each case.
2.5 Evolutionary Robotics
Many researchers are working today on the evolution of con-
trol software for real robots. Evolutionary Robotics has
become a eld on its own [15]. Some rely on carefully
designed simulations [4], while others apply evolution
directly in the real robot [6]. Hybrid techniques [13] are a
mixture of the two.
Lund, Hallam and Lee [11], [14] have evolved in simula-
tion both a robot control program and some parameters of its
physical body (sensor number and positioning, body size,
etc.). Their last paper [14] addresses the possibility of co-
evolving a robot controller and auditory morphology for the
task of (cricket) phonotaxis. They contemplate the possibil-
ity of designing a Lego robot simulator.
3 The Physical Model
The resistance of the plastic material (ABS-acrylonitrile
butadiene styrene) of Lego bricks far surpasses the force nec-
essary to either join two of them together or break their
unions. This makes it possible to design a model that ignores
the resistance of the material and evaluates the strain forces
over a group of bricks only at their union areas. If a Lego
structure fails, it will generally do so at the joints, but the
actual bricks will not be damaged.
This characteristic of Lego structures makes their discret-
ization for modelling an obvious step. Instead of imposing an
arti cial mesh for simulation purposes only as in nite ele-
ments, for example these structures are already made of
relatively large discrete units.