Petri Net Modeling and Simulation of Walking Behaviour

for Design of a Bioinspired Robot Dog

Zuhal Erden

and Macit Araz

Department of Mechatronics Engineering, ATILIM University, Kizilcasar Mah., Incek, Ankara, Turkey

Micro-Electro-Mechanical Systems Research and Application Center, Middle East Technical University, Ankara, Turkey

Keywords: Behavioural Simulation, Petri Net, Bioinspired Design.

Abstract: Research in behavior-based design faces many challenges regarding the aids in conceptual design of

biorobots, representation of a biological system’s behavior in a well formed modeling tool and therefore

providing systematic transformation of this behavior into robot design. This paper reports a research that

focuses on the development of a Petri Net model to represent a biological system’s behavior. The model is

based on real time data collected from an experiment in which a dog is walking on a treadmill with a speed

of 1km/h. The model has the ability of simulating the real time rhythm of dog's walking behavior utilizing

colors and numbers as well as the step-by-step simulation. The aim is to observe the behavior of a walking

dog in time domain as an early stage of conceptual design of a bioinspired robot dog. Main challenge is to

develop a methodology to guide designer towards more creative designs based on bioinspired design ideas.

The presented work is an early attempt to initiate a systematic approach towards the stated goal.

1 INTRODUCTION

Bioinspired design methodology utilizes analogous

biological phenomena to develop solutions for

engineering problems. Inspiring design ideas from

functions, behaviors, structures, materials, and form

of biological systems is a challenging process for

engineers and designers, and it encourages

development of creative designs. However, it is not

a straightforward engineering activity; it requires

high level balanced expertise on both domains.

Moreover, biologists and engineers use different

concepts and terminologies so that there is always

difficulty when biological phenomena are

transformed into engineering domains. Many studies

focus on constructing bioinspired design (BID)

methodologies to eliminate these disadvantages and

help designers to develop creative and innovative

products. Bioinspired conceptual design (BICD)

methodology (Konez-Eroglu et al., 2011a) was

developed for the design of hybrid bioinspired

robots which can be inspired from multiple

biological systems. An important problem in

bioinspired design is that once designers identify a

target biological system to be inspired, they must

obtain necessary knowledge for the solutions

applicable to their design problem. One of the

important types of knowledge is the behavior of the

target system. Rapidly growing experimental

possibilities allow researchers to represent behavior

of biological systems into powerful modeling and

simulation tools. In particular, bioinspired robot

design requires imitating behavior of the biological

target system on a physical robot. Therefore, a deep

understanding of the biological system behavior is of

great importance for designers to extract underlying

behavioral principles and to convert them

systematically into a biorobot design.

This paper presents a case study towards

development of a systematic approach for

converting experimental data of a biological system

behavior to a model framework that can be used in

engineering domain. In this study, a Petri Net model

for walking behavior of a dog is developed based on

an experimental data recorded using a high speed

camera. The model is capable of representing and

simulating the dog’s walking behavior as an 8-state

walking cycle with the associated time periods for

state transitions. The model structure is composed

of a brain-unit and a leg-unit for modularity. A Petri

Net model was developed and simulated using

Artifex graphical modeling and simulation

environment, which is a C++ based software tool.

The model is used to validate the deadlock free

Erden, Z. and Araz, M.

Petri Net Modeling and Simulation of Walking Behaviour for Design of a Bioinspired Robot Dog.

DOI: 10.5220/0005972702170224

In Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2016), pages 217-224

ISBN: 978-989-758-199-1

217

walking behavior of a robot dog at conceptual

design stage.

The paper is organized as follows. Next section

presents a brief overview of the bioinspired design

(BID) methodology with special emphasis on the

importance of behavioral modeling for conceptual

BID. Then, the Petri Net model architecture for the

walking behavior of a dog is explained and

simulation results are given. Finally discussion and

conclusions regarding the current study are provided

together with the intended future research directions.

2 BEHAVIOURAL MODELING IN

BIOINSPIRED DESIGN

Capturing a natural system’s task accomplishment

behavior, and re-creating a qualitatively similar

behavior in an artificial system is one of the most

interesting research issues in the field of robotic

design methodology (Fleischer and Troxell, 1999).

Thus a new robot design methodology has been

emerged so as to develop behavior based robot

architectures. Behavior based robotic architectures

can be developed systematically using bioinspired

design (BID) methodologies. Bioinspired design

(BID) needs a systematic method for transformation

and it uses analogical reasoning approach in which

the source domain is the biological domain while the

target domain is engineering (Mak and Shu,

2004;Wilson, 2008;Tsujimoto et al., 2008; Nelson et

al., 2009; Helms et al., 2009). There are two

approaches in BID studies with respect to starting

point of the design; problem-based BID (PB-BID)

and solution-based BID (SB-BID). PB-BID starts

with an engineering problem in engineering domain

whereas SB-BID begins with a biological system in

biology domain.

Modeling the behavior of a biological system is a

challenging topic within the framework of

developing a systematic Bioinspired Conceptual

Design (BICD) process model (Konez-Eroglu et al,

2011a) given in Figure 1. The suggested BICD

process is developed to provide design concepts of

bioinspired robots, biorobots. Based on the existing

literature (Webb and Consi, 2001; Bar-Cohen, 2006;

Meyer and Guillot, 2008), bioinspired robots can be

defined briefly as follows;

Biorobots, biologically inspired (bioinspired)

robots or biomimetic robots, emulate the functions

and performance of biological systems, look like

inspiration model and behave similar to the original

model. Biorobots can be decomposed under

sensoric, motoric and cognitive sub-systems.

This definition is structured in a semantic

network representation (Konez-Eroglu et al., 2011b)

shown in Figure 2, so as to clarify the relationships

between various concepts. Among these concepts,

“behavior” is the main concern of the current study.

Behavior, which can implement different functions,

is a sequential change of states over time with

respect to change in the internal state of the body or

in the environment.

In the BICD methodology, one of the important

problems is to collect information about the behavior

of a biological system and develop a model to

represent the behavior. Then, the model can be used

to transform the biological system’s behavior

systematically into engineering system’s

(biorobot’s) behavior. Behavioral modeling is

described as one of the modeling approaches in

engineering design methodology and defined as a

channel category of the design knowledge stream

(Horvath, 2004). It is an important method in

engineering design to establish a framework for

developing virtual prototypes (Shen et al., 2005).

Behavioral models and their software

implementations allow designers to represent design

artifacts as technical systems and to analyze

compare and evaluate their possible behavior at an

early design stage in a short time. In a previous

research, Discrete Event System Specification

(DEVS) and Petri Net formalism were used for

modeling the operational behavior of educational

robots during conceptual design (Erden, 2010; Erden

2011).

Behavior of the robot was defined as composed

of states and state transitions independent of any

physical embodiment. Quadruped walking behaviour

has been investigated in various research studies

(Griffin et al., 2004; Pongas et al., 2007). In the

BICD process, behavioral modeling of a biological

system is based on observing states of the system

behavior and understanding how transitions occur

between the states. In this study, an experiment has

been conducted to observe walking behavior of a

dog to determine states and state transitions.

Behavioral model is developed using Petri Net

formalism (Peterson, 1977; Murata, 1989) with the

Artifex graphical modeling and simulation

environment as the software tool. We selected to use

Petri Nets in this study due to the simplicity of

describing states and state transitions graphically as

well as due to the possibility of translation into

mathematical-logical expressions. These advantages

also lead several researchers to model robot

behaviours using Petri Nets (Kobayashi et al., 2002;

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Figure 1: PB-BICD and SB-BICD phases in BICD (Konez-Eroglu et.al, 2011a).

Figure 2: A semantic network representation of a biorobot (Konez-Eroglu et.al, 2011b).

Guangtao et al., 2003; Serhan et al., 2008;

Vladareanu et al., 2011).

3 PETRI NET MODEL

ARCHITECTURE FOR A

DOG’S WALKING

BEHAVIOUR

This section includes detailed information on the

Petri Net model developed for the representation and

simulation of the walking behavior of a dog in the

Artifex software environment. The aim is to

observe and systematically represent walking

behavior of a dog in time domain.

A high speed camera was used in the observation

phase of the study. A Photron Fastcam MC-2 Color

10K high speed camera (512 x 512 pixel) with

Navitar TV zoom 8.5 - 51 mm lens and two

Megaman 60 W cold lighters were used. A terrier

type dog with a mass of 3.7 kg was used in the

experiment. The dog walked freely on a treadmill.

The experimental set-up is shown in Figure 3. Since

the camera consists of one head, two dimensional

video images were obtained. The dog’s walking

behavior was recorded with 1000 fps with 376 x 484

pixel resolution videos. TEMA Motion 2D

software program was used to analyze the dog’s

walking behavior and obtain the time data.

Time data for the Petri Net model was collected

with an experiment in which the dog’s walking

speed is 1km/h. Walking period is divided into tours

as shown in Figure 4. A tour is the time duration in

which all legs take one complete step with 8-states

represented by UP and DOWN positions of the legs.

Duration of each tour is 704 ms and Figure 4

represents time data for 3-tours.

Petri Net Modeling and Simulation of Walking Behaviour for Design of a Bioinspired Robot Dog

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Figure 3: Experimental set-up for recording a dog’s walking behavior.

Figure 4: Walking dog stepping schedule obtained from the experiment.

Figure 5: Top level Petri Net model of the dog’s walking behavior.

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In the Petri Net model architecture (Figure 5),

five objects are used to represent behavior of the

dog's body organs that contribute its walking; these

are a brain unit and four leg units (a left foreleg, a

left hind leg, a right foreleg and a right hind leg).

The model has the ability of simulating the real time

rhythm of dog's walking by means of different

colors (as blue and red) and states (numbers); as well

as the step-by-step simulation in virtual time. During

the simulation, the brain unit counts the number of

tours and expresses that by a state (number) and

color of the related leg unit. Behavior of each leg

unit is simulated in real time such that DOWN

position is represented by the number “0” and color

“blue” and UP position is represented by the

number “1” and color “red”. Each object in Figure 5

is modeled with an associated Petri Net. Linksets are

used to connect the leg units in the model

architecture with the brain unit. Petri Net models of

the brain unit and left foreleg are shown in Figure 6

and Figure 7, respectively.

Brain Unit (Figure 6) contains a place

(START_BRAIN) and a transition (CONVEY)

alongside eight columns of components (places and

transitions). The place START_BRAIN contains an

initial token which operates as a starting signal in the

brain and is propagated throughout the eight

columns of components which represent the brain

cells.Brain columns include two transitions, one

normal place, one input place (represented by two

concentric circles) and two output places

(represented as a triangle inside a circle). Input and

output places have the task of communicating with

other units (legs) in the model. Each two brain

columns operate as the control mechanism of one

leg, one for the UP position of the leg and one for

the DOWN position. Each position has an active

period and an inactive period. It means for instance

for the DOWN position, the leg is on the ground

during the active period and it is lifted during the

inactive period. DOWN and UP positions are

exactly converse of each other on the time domain.

Each position (DOWN or UP) has an initial delay

alongside the active and inactive durations. In the

Brain Unit, initial delays are set in the upper

transitions and the active period durations are

inserted in the lower transition while the durations

for inactive periods are set in a transition in the Leg

Unit. The black diamonds at the bottom part of

Figure 6 are Portsets which are used to connect the

brain to other units (legs) through Linksets. Linksets

are like multi-wire cables and the portsets are like

the terminals that those cables are connected. All the

input and output places connecting the brain to each

leg are linked to the related portset. This procedure

is repeated in each unit as well.

Similar to the Brain Unit, Petri Net model for the

Leg Units are composed of two main parts to

represent DOWN and UP positions. As an example,

Petri Net model of the left foreleg is given in Figure

7. The right side models DOWN and the left side

models UP position of the leg. Each part consists of

three transitions, one normal place, two input places

and one output place. Inactive period duration of the

leg position is set in the upper transition and the two

lower transitions have the duty of conveying the

Figure 6: Petri Net for the Brain Unit.

Petri Net Modeling and Simulation of Walking Behaviour for Design of a Bioinspired Robot Dog

221

brain command to the leg during the initial delay and

active period duration. The upper transition also

contains some C++ codes to set the illustrating

colors and states (numbers) of the model.

4 MODEL SIMULATION

Figure 5 shows the top level page of the Petri Net

model for the dog’s walking behavior in Artifex

Model Editor environment. All units in the model

architecture are illustrated at this level. Figure 8

illustrates a screenshot from the simulation

environment of the software. The figure depicts the

model at instant 1848 ms in the 3

tour. As for the

legs, One and Red express the UP position, while

Zero and Blue express the DOWN position. Numbers

and colors at the brain simply count the tour number.

Simulation can be carried out both step-by-step in

virtual time and also in real time. Four measures,

one for each leg, are defined in the model. These

measures allow the designer to monitor the

summation of time durations for which each leg is

on the ground (DOWN position) during the total

time of walking which is a specified number of tours

the dog takes. It also let the user to observe the

initial delay and final time gap of the DOWN

position of the leg. It should be noted that the initial

delays are given for the model only, because the

model has to set the legs at the beginning and there

is no such a delay in dog’s nature. Table I shows

total time durations for which each leg is on the

ground for 10 tours.

The results and data collected from these

measurements provide a more realistic and detailed

viewpoint for the designer before stepping into the

stage of designing and manufacturing a prototype of

a robot. In a parallel research study, experimental

data for the walking behavior has been used

manually to design and construct a demonstrative

Figure 7: Petri Net for the left foreleg.

Figure 8: Screenshot of the graphical simulation of the dog’s walking behavior.

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Table 1: Time data for a measurement session.

Beginning (ms) End (ms) Duration (ms)

Right Foreleg 652 6988 4400

Left Foreleg 288 6624 4160

Right Hind Leg 416 6752 4520

Left Hind Leg 100 6436 3400

Tour Numbers: 10 Total Duration: 7040 (704 each tour)

prototype of a bioinspired robot dog. In the starting

setting periods for legs, one can observe the total

duration that each leg is on the ground and the

instant that a leg steps up just before the end of each

run. Therefore, these measures are used in the design

and manufacturing process for checking and

modifications as well as in the processor

programming at the manufacturing stage.

5 CONCLUSIONS

Development of a model to represent and simulate

the behavior of a biological system is a challenging

research topic for the analysis of biological systems

during the implementation of the Bioinspired

Conceptual Design (BICD) methodology for design

and manufacturing of biorobots. As a case study,

this paper presents the development of a Petri Net

model for a walking behavior of a terrier dog. The

model is based on an experimental data for the states

and state transitions during walking. States are

represented as various combinations of up or down

positions of the dog’s legs. Model development and

simulation has been done successfully using

Artifex modeling and simulation environment.

Four user defined measures have been developed to

test the possibility of performance analysis based on

the Petri Net model. These measures are not used for

any evaluation, since the present study mainly

focuses on developing a structured and formal

representation of an unstructured and informal

natural behavior with a well-known modeling tool.

This case study shows that behavior of a biological

system can be represented as a Petri Net model for

simulation. Future research will be directed towards

Petri Net model development for various biological

system behaviors in different case studies and

establishment of a generalized behavioral modeling

method for BICD using Petri Nets. Another future

work includes performance analysis of the model

based on user defined measures.

ACKNOWLEDGEMENTS

This research is conducted with the support of

ATILIM University Research Grant (Project NO:

ATU-BAP-1011-07, Project Title: “Behavior Based

Modeling at Conceptual Robot Design and Desktop

Design of Educational Robots”) and TUBITAK-The

Scientific and Technological Research Council of

Turkey (Project No: TUBITAK 109M379, Project

Title: “Development of biomimetic design

methodology with reverse engineering in cognitive

recognition and control of biomimetic robots”. This

is a joint project between Department of

Mechatronics Engineering, ATILIM University,

Turkey and University of Craiova, Romania).

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