Walking Robot Bio-inspired by Insect’s Locomotion for Carbon

Dioxide Diagnostic Indexed in the Air

Santiago Noriega Álvarez, María Camila Rojas and Hernando Leon-Rodriguez

Electronic Department, Faculty of Engineering, El Bosque University, Bogota, Colombia

Keywords: Robot’s Simulation, Spider Motion, Quadruped Robots.

Abstract: The spiders, in comparison with the majority of others animals, it has the ability to access all kind of

environment where others animals or even the humans can’t. Those attributes of the spiders are taken into

this project in order to design and develop a quadruped spider robot with the ability to move in all kind of

directions and perform pre-set motions programs such as ascend, descend, obstacles avoiding and gas

detections. The paper is presented the dynamic and kinematics model with the purpose of understand how,

mathematically the quadruped animal and spiders walk. In this sense we studied the movement of a real

spider in order to define a suitable bio-mimetic locomotion model. In additions walking simulations were

implemented and the gas detection results are presented.

1 INTRODUCTION

In the recent years, human want to reproduce all

kind of movement bioinspired by the nature, given

back some successful results. The effort on try to

understanding and analyse the locomotion behaviour

allowed novel mathematical models. All this models

can be used in robotics for certain task instead of

risk human lives. This kind of biomimetic

replication can be employed in, as example, land

mines task, exploration task and even underwater

inspection (Zhao, 2017) Another important

application of these robots is the incursion in

dangerous environments, like contaminated places,

or hostile landmarks.

In quick evaluation into the subject at the macro-

scale Boston Dynamic’s is one research institution

or business company that design and produce a huge

variety of robots, especially quadruped ones.

(Raibert, 2008). The most popular one is Big Dog; it

is employing entirely in exploration duties.

Other approaches of walking robots

biomimetically inspired at mili-scale are based in the

insects like spider locomotion. The spider robot was

built around 90’s where researches started to

innovate the whole world with their robots. (Shoval,

1999) Now, is a big market built hexapod spider

robot, which had the ability of climb all kind of

surfaces.

Nowadays, the majority of information suggests

that the quadruped spider robots are developed by

amateurs or fans whom wants to develop a kind of

open loop control device. Other approaches are

being done by complex close loop control (Lu,

2017) or by using other mechanism for quadruped

walking like parallel mechanism (Wang, 2010), soft

materials (Garabini, 2017) and so on.

Figure 1: Quadruped robot design.

This paper presents a basic approach of one

quadruped robot with its different attributes and

characteristics showing in figures 1 and 2. Several

historical contributions had been developed by other

researches incorporating cameras, sensors, geo-

localization and so on. (Semini, 2010) This project is

a particular bio inspired robot that carry onboard gas

480

Álvarez, S., Rojas, M. and Leon-Rodriguez, H.

Walking Robot Bio-inspired by Insect’s Locomotion for Carbon Dioxide Diagnostic Indexed in the Air.

DOI: 10.5220/0006912804800486

In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 2, pages 480-486

ISBN: 978-989-758-321-6

sensor to characterize the air in a narrow and/or

constrain areas.

Figure 2: Quadruped robot prototype.

The movement of this robot executed the

mathematical control of forward kinematics and

evaluates the air environment for gas contamination.

2 THE QUADRUPEDS

In order to achieve this project initially observes the

behaviour of the quadruped locomotion in the

animal kind in their natural environment. The

motions and algorithms are well established, like

how they move, avoid obstacles and synchronise its

motion behind. As a result, the majority of the

quadrupeds move in a mammalian form, like a dog

or a horse, as example. This represented to follow its

complex locomotion or used a mixture of sources of

inspiration to meet the quadruped animal movement

and behaviour. On the other hand, the mili-scale

inspired the anatomy for spiders. As a result, the

anatomy, movements and physic shape of insects are

not yet well stables in the robotics field.

3 MOTION ANALYSIS

Initially, it’s important to know that the spider has 7

parts by leg (figure 3). These parts are: coxa,

trochanter, femur, patella, tibia, metatarsus and

tarsus. This spatial arrangement it’s illustrated in the

figure 4. From the original anatomy of the spider,

this project suppresses some leg’s part and

component´s joints. Based in simplification some

spider´s leg part the robot is reduced as follow:

instead of using the Patella part, we linked the femur

and the tibia by a direct joint. The metatarsus and the

tibia were united as a single link or part. Similarly,

we dismiss the tarsus. All of these dismissals were

executed in the robot, however, for kinematic

analysis and simulation we took the entirely system

for a realistic approach resulting to know which

parts can be considering redundant.

Figure 3: Spider’s leg parts.

One important aspect is the amplitude that has every

part of the spider leg. This means, for example, that

the coxa has amplitude of 35 degrees while tibia has

a mobility of 70 degrees. Also, every of the seven

components of the limb, has a different axis of

movement; for example, the trochanter has a

movement in X-Y axis, meanwhile the femur in X-Z

axis. This kind of association and motion, it’s

explained graphically in the figure 4.

Figure 4: Range of movement of the spider.

In order to establish the different joints and links

which constitute the system limb of the spider, it is

defined as follow:

• Body-Coxa joint: joint with three degrees of

freedom (DOFs) ball-and-socket joint.

• Coxa-Trochanter joint: either 3-DOFs ball-and-

socket or a 2-DOFs saddle joint.

• Trochanter-Femur joint: this modeled as a

universal joint with 2-DOFs.

• Femur-Patella joint: Commonly this joint can be

modeled as a hinge joint 1-DOF.

Walking Robot Bio-inspired by Insect’s Locomotion for Carbon Dioxide Diagnostic Indexed in the Air

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• Patella-Tibia joint: There are two options to

model this joint; first as a hinge joint or a

universal joint with very limited joint on Y-Z

axis.

• Tibia-Metatarsus: it is also possible to assume

this joint as a hinge joint, or a universal joint but

with some constraints.

• Metatarsus-Tarsus joint: this joint can be

modeled as a universal joint.

In this case, the claws are the end-effector of the

system. This means that this part of the limb is

whom interacts with the outside.

4 MATHEMATICAL ANALYSIS

As we mentioned previously, there are some

constraints that we applied in the anatomic

development. We applied these modifications in the

mathematical development and we decided to

involve all the possible variables, based on the

following table to produces the most faithful model

and prototype.

Table 1: Limited ranges of angular rotation.

Parts Movements Plane

Coxa 75 Transversal

Femur 140 Sagittal

Tibia 40 Sagittal

4.1 Direct Kinematics

In order to study the direct kinematics of the robot at

first by using the joint variables of contact limbs,

position and orientation of the platform based on

fixed frame are determined.

Figure 5: Coordinate frames of the robot.

Taking into account the figure 5 and knowing OAi

vectors, which are the end points of contact legs, we

can establish the next expression:

rBi=rAi+rMi/Ai+rBi/Mi (1)

In this expression, rBi and rAi represent the position

vector of Bi. In the same way, we needed to

determinate all the parameters of the system in a

graphically mean. In the figure 6 it can be detail

these parameters.

Figure 6: Parameters of the system.

Figure 7: Quadruped walk locomotion.

Suppose that the leg 1, 2 and 3 are standing on the

ground. According to relation (1) the location of

points Bi versus fixed coordinate are determined and

as direction of x axis of P-coordinate system is direct

to B3B1 vector can determine the direction of x-axis

unit vector:

Ex=⟦B3*B1⟧/⟦B3*B1⟧ (2)

In the same way, we can determinate the vector

B3B2 as follow:

Em=⟦B3*B2⟧/⟦B3*B2⟧ (3)

By having this information, we can determinate the

direction of unit vector, normal to the platform

plane. To do this, we first needed to implement the

cross product of the two previous vectors:

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482

z=Em*Ex (4)

In the same way, having the vectors Ex and Ez, it’s

possible to determinate the Ey by the same method:

Ey=Ex*Ez (5)

These three vectors are necessary because we can

establish the matrix of the platform versus fixed

coordinates with the next expression:

(6)

In order to specify the origin of coordinate system,

we can use the equation of the circle in this way:

(7)

(8)

(9)

If we solve the equations system previously

established, we can determinate the position of the

body in the coordinate system.

4.2 Platform Velocity

In order to determinate the velocity of the robot’s

platform its necessary to determine the velocity and

angular velocity of robot platform by using the

position and velocity of joint variables. In order to

specify the direct kinematics of platform velocity

can use (10):

(10)

In the previous expression, OAi represents a vector

was drawn from fix coordinate origin to point “A”

from leg No. i. It’s possible to determinate the

relation between velocity of joint variables and

platform velocity by differentiating from (10). The

result is (11):

(11)

In (11), the first and third element of the equality

represents the absolute angular velocity of femur and

tibia of limb No. i respectively. If we take into

account the symmetry of our robot, (11) can be used

for the other three contact legs. By using the fifth

element of (11), it’s possible establishes Vp. Based

on figure 6:

(12)

Regarding to the figure 6:

(13)

In expression (12) and (13), the first factor in both of

them, indicates the unit vector direct to z-axis of first

coordinate frame of limb No. i. The relation between

the unit vectors of different coordinate frames of

each leg is determined in function of the figure 6 as

follow:

(14)

(15)

(16)

Using the expressions from (12) to (18), we can

determine the values of ωi as follows:

(17)

(18)

In (19) and (20) the S’s and the C’s, means cosines

and sines. In this case, for mathematical simplicity,

que can express all the previous equations as

rotational matrices as follows:

(19)

(20)

(21)

As we mentioned previously, ‘R’ represents the

rotational matrix of platform relative to fix

coordinate frame. In this order R1p is rotation matrix

of first coordinate frame of limb No.i relative to P-

coordinate frame system. This last rotational matrix

is defined as follow:

(22)

In (24) is the number of limbs.

4.3 Direct Kinematics of Non-contact

Leg

Direct kinematics of position for a non-contact limb

it’s similar to the direct kinematics for a serial robot.

Walking Robot Bio-inspired by Insect’s Locomotion for Carbon Dioxide Diagnostic Indexed in the Air

483

As shown in Fig. 7 can write:

(23)

(24)

(25)

(26)

Based on the previous expressions PBi can be

establishing as follows:

(27)

As we did with the contact legs, we wanted to

determinate the velocity of the non-contact limbs, so

the procedure is similar. We first need to

differentiate (25) as follows:

(28)

Using the information from (11):

(29)

(30)

With (30) to (32) we can determinate the velocity of

end point of noncontact legs; as a result, these values

can be specified.

5 SIMULATION AND CONTROL

Figure 8 is showing the conceptual map of robot

control based in arduino controller and Bluetooth

communication system sending and receiving

routine commands from mobile device.

Figure 8: schematic control design of quadruped robot.

Figure 9 is showing the representation of the

forward movements of each axis of the robot using

full platform control and communication. For

motion, 12 servo-actuators were set, 3 for each leg

with torque of 2.2Kg-cm. these servo-motors are

attached directly as a joint of each link-leg. The

supply voltage and current for the robot was a

battery package of 4.8 V and 3000 mA with around

power of 7.5 W approx.

Figure 9: Oscillation motion of each leg in x and y axis.

6 GAS SENSOR EVALUATION

Regarding to the reading of the carbon dioxide

index, an embedded circuit capable of monitoring

various types of gases was implemented. Thanks to

the micro-controller implemented to achieve the

movement of the spider, it was easy to incorporate

the sensor in question. The challenge was to recreate

the characteristic curve of this device through a

function based in the response with different types

of gases, figure 10.

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Figure 10: Gas sensor curve (MQ-4).

Initially, the characteristic curve of the sensor

was expected to have a directly proportional

relationship between the voltage at the output of the

sensor, and the carbon dioxide concentration, as

shown below.

Figure 11: Response profile MQ4, time vs voltage.

The figure 11 shows the output voltage of the

sensor depending of the gas concentration reading

by the sensor. In this order of ideas, a gas source was

arranged next to the sensor; as the gas concentration

increased, so did the voltage. Then it will show a

graph that link the voltage at the output of the

sensor, with the carbon dioxide concentration.

Figure 12 is showing the characterization of the

sensor was achieved through a linear regression

model, obtaining fairly accurate results. An

extremely important aspect to mention is the fact

that currently this issue is still being evaluated and

treated, with the purpose of implementing the sensor

that best shapes itself, and conditioning the signals

of it with the purpose of achieving the best results.

Figure 12: Voltage vs Carbon dioxide concentration.

7 CONCLUSIONS

The project had achieved step by step the design,

development and control of a quadruped walking

robot. The mathematical model helped out the

modelling of the motion´s behaviour of the robot.

The robot has achieved 12 DOF in total, 3 DOF

for each leg, controlled by an Arduino Nano via

remote mobile device. The movement has been

analysed with biomimetic inspirations take from

spider.

The gas sensor MQ4 was an excellent first

approach to the sensing technology because it

allowed characterizing the behaviour of the gas.

Additionally, these results will serve as a foundation

in future research.

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