An evolutionary model for 3D agents integrating continuous and plastic development

Most of the current research in generative encodings for artificial creatures has only focused on the final matured genotypes, and doesn’t take into account the developmental process itself. In this paper, we introduce a grammar based approach for generat

An evolutionary model for3D agents integrating continuous and plastic development Artur Matos Takaya Arita Graduate School of Human Informatics Graduate School of Information Science Nagoya University Nagoya University

Nagoya,464-8601,Japan Nagoya,464-8601,Japan

Abstract

Most of the current research in generative encod-ings for arti?cial creatures has only focused on the?-nal matured genotypes,and doesn’t take into account the developmental process itself.In this paper,we introduce a grammar based approach for generating agents with both3D morphology and neural networks that leads to more natural developmental processes than previous approaches.This new model is based on Lindenmayer systems,but with added extensions for dealing with continuous development of limbs,and for simulating chemical interactions between develop-ment and the surrounding environment.This paper includes a detailed description of the model,as well as some results of our preliminary experiments for evolv-ing agents that exhibit walking or other similar behav-iors.

1Introduction

Since Karl Sims’seminal work[5]on virtual crea-tures,signi?cant research has been done for evolving agents with both integrated3D morphology and neu-ral systems.Most of the research currently being done in the?eld has been focusing on generative encod-ings,where the genotype is interpreted as instructions for building the phenotype,instead of directly map-ping traits to it.Regarding these generative encod-ings,two distinct approaches can be observed in the current literature:the?rst one uses formal grammars or high-level structures for representing developmental processes(grammar based approaches),for example, Lindenmayer systems(LSystems).On the other hand, cell chemistry approaches attempt to simulate the low level interactions between cells during development, for instance,gene regulation and targeting.Although at a?rst glance these two approaches appear to be distinct and even opposite to each other,this division is largely arti?cial,and it should be possible to incor-porate concepts from one approach to the other.So in this paper,we present a developmental system that although being grounded on developmental grammars, attempts to bridge between these two approaches,by introducing concepts that can easily be modeled on cell chemistry systems but that are usually not found in the grammar based ones.This new model,based on a previous one by Hornby and Pollack[1],inte-grates two di?erent LSystems:Di?erential LSystems (Prusinkiewicz,Hammel and Mjolsness[4])for mod-eling continuous processes,for instance,elongation of limbs;And Open LSystems(Mech and Prusinkiewicz [2]),for simulating chemical interactions between the developmental process and the environment.

2The3D agents and the environment The agents in our model have both a3D morphol-ogy and a simulated nervous system to control it.The 3D morphology for each agent is made of rectangu-lar parallelepipeds connected by hinge joints,that re-strict the movement of the connecting parts in one degree of freedom.The nervous system actuates on the joints by changing the speed of actuating motors present on each joint.The nervous system is a sim-ple free form neural network,and includes sensors for the environment and joint positions,processing nodes and actuators for the joints.The processing nodes in-clude sigmoids,linear transfer functions and sinusoid oscillators.The nodes in the neural network use stan-dard propagation functions on the incoming connec-tions,that is,the weighted sum of all the connections values,and are constantly active(no activation func-tion is considered).For the sinusoid oscillator,the computed weighted sum of the incoming connections works as frequency modulator for the sinusoid,map-ping the frequency in the interval[0,2π].

The environment simulates all physical interactions, including gravity and collision with objects.A?at ground is also simulated,extending inde?nitely in the XZ plane.The simulation may include other objects

Most of the current research in generative encodings for artificial creatures has only focused on the final matured genotypes, and doesn’t take into account the developmental process itself. In this paper, we introduce a grammar based approach for generat

depending on the behavior that is being evolved.

3The developmental process

Each step for the developmental process is repre-sented by a sequence of commands indicating the mor-phology and neural system for the agent.The com-mands themselves are changed by the LSystem asso-ciated with each agent through developmental time. The commands used are similar to the ones by Hornby and Pollack[1],but extended for allowing continuous values,in order to use di?erential Lindenmayer Sys-tems.The developmental commands for the morphol-ogy work as a turtle constructor,and they include: forward(n)for moving the turtle forward n units in the currently de?ned direction,creating a new stick, and connecting it to the previous existing one by a joint;backward()for moving the turtle cursor back to the parent stick;right(n),up(n),clockwise(n)for al-lowing to control the direction of the turtle,rotating in the speci?ed direction n units,with1corresponding toπ

2]for revolute-1(),and[?π

2

]for revolute-1(),and

revolute-2(),respectively.The twist commands work in a similar way,but for the X axis.The developmen-tal commands for the nervous system work as edge encoding commands,and they are described in table 1.There are also stack commands(push()and pop()), for pushing a retrieving the current state of the turtle and neural constructor,allowing to create branched morphologies.

3.1Representing continuous develop-

ment

DLSystems are based on parametric Lindenmayer systems,but they add a di?erential component for modeling continuous changes.Due to space con-straints,parametric LSystems themselves will not be explained here and we will focus on dLSystems in-stead.For a good introduction to LSystems,the reader is referred to to Prusinkiewicz and Lindenmayer [3].

The?rst major di?erence concerning dLSystems is that development doesn’t occur in discrete steps,in-stead there is a continuous developmental time frame t.As in PLSystems,the development is iterative,but it progresses by an user speci?ed time step,?t.This time step is completely detached from the underlying model,so it is possible to use a di?erent?t in order to observe the developmental process with more or less detail,as desired.

For specifying the changes occurring as t progresses through the developmental space,two di?erent kinds of successors are used.Continuous changes are spec-i?ed by using di?erential equations,that relate the changes in parameters’values to the step?t.Struc-tural changes,or adding new limbs or nodes to the agent are speci?ed by sequence of tokens,as in PLSys-tems.Discrete transitions are applied on the same way as in PLSystems,the token being replaced by the matched sequence.Depending on the time step?T, the LSystem interpreter may need to subdivide the in-terval for taking into account both continuous and dis-crete transitions.An example dLSystem can be seen in?gure1.In this example system,for?T=1,the following sequence,starting fromωwould be derived: B(1),A(0,0);B(2),A(2,1);B(3),B(4),C(2).A smaller?t(for instance0.5),would yield B(1),A(0,0); B(1.5),A(1,0.5),B(2),A(2,1).

ω:B(1)A(0,0)

B(x):x<4→solve dx

dt

=2(3)

solve dy

Most of the current research in generative encodings for artificial creatures has only focused on the final matured genotypes, and doesn’t take into account the developmental process itself. In this paper, we introduce a grammar based approach for generat

ble processes.Another set of commands mirrors ex-actly the same functionality,but are used for modeling maturing processes that are still changing in devel-opmental time.This maturing set of commands has the same name as their matured counterpart,pre?xed by an“m”.This separation is needed most of the times for modeling growing phenomena by using Lin-denmayer Systems as pointed out by Prusinkiewicz, Hammel and Mjolsness[4].

For assuring continuity,the generated rules are al-ways instances of the same template,working as fol-lows:if matched,a maturing command grows linearly, until it reaches a certain threshold.After this thresh-old has been reached,the token is replaced by its ma-tured counterpart,possibly with some more additional tokens added.Only linear di?erential equations are used.Additional constraints may be present depend-ing on the command.An example rule for the mfor-ward(a)command can be seen in?gure2. mforward(x):x<2→solve dx

Most of the current research in generative encodings for artificial creatures has only focused on the final matured genotypes, and doesn’t take into account the developmental process itself. In this paper, we introduce a grammar based approach for generat

Command Description

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