SINERGI Vol.
No.
June 2018: 69-76 DOAJ:doaj.
org/toc/2460-1217 DOI:doi.
org/10.
22441/sinergi.
ANALYSIS OF KINEMATIC FOR LEGS OF A HEXAPOD
USING DENAVIT-HARTENBERG CONVENTION
Luo Qingsheng1 Julpri Andika2 1Mechatronical Engineering.
School of Mechatronical Engineering.
Beijing Institute of Technology 2Department of Electrical Engineering.
Faculty of Engineering.
Universitas Mercu Buana Jl.
Raya Meruya Selatan.
Kembangan.
Jakarta 11650 Email: luoqsh@bit.
cn, julpri.
andika@mercubuana.
Abstract -- The headway of manipulator robots makes the development of a hexapod quite fast.
Unfortunately, a hexapod is unstable to moving in a regular movement with some values added to programming algorithms.
Various techniques implemented yet to the algorithms, like entering the degree values of each servo.
However, to simplify the implementation of the algorithms, need some equations.
This paper offered a hexapod control system based on Arduino that using Denavit-Hartenberg parameters to produce the equations.
Various experiments have performed.
Based on the experiments the offered system able to simplify the programming algorithms.
Keywords: Manipulator robots.
Hexapod.
Denavit-Hartenberg.
Kinematic Received: March 3, 2018
INTRODUCTION
In this century, the significant progress occurred in the field of robotics.
Many robots created aiming to emulate, help or make things easier for the human.
Robots designed to simplify human tasks or helping to carry out a particular task that cannot be done by a human directly by considerations of time up to security.
The robotic system combines design science, mechanics, electronics, and control (Adriansyah and Amin.
Adriansyah et al.
, 2015.
Munadi et al.
, 2.
Six-legged robot or commonly called Hexapod is one type of walking robot.
Usually, have 12 or 18 servos that serve as the joint of the When compared to a bipedal robot, sixlegged robot configuration has great balance while walking, because leaving only 3 feet in the ground and the rest is in the air, will give a great balance (Yang et al.
, 2.
However, most of the programmers of these six-legged robots did not use the kinematic They used the old way to codes the They make some coding programs that more complicated, lengthy, and a bit difficult to get the servoAos angle or the end-effectorAos distance Some research has done by some researchers such as (Atique & Ahad, 2.
who designed and created a car robot which powered by a foot-shaped tool with 3 degrees of freedom (DOF).
They deduced the kinematics through DH convention and predict the movement of the robotic structure with simulation software then applied to the car robot.
With a foot-shaped tool, the car moves at about 0.
48 feet/second.
The Next, there is (Nookala et al.
, 2.
which analyzes the Revised: April 24, 2018 Accepted: April 24, 2018 robot leg with 3 DOF who assisted with the simulation through the robotic software called Robo Analyzer and MATLAB.
By using Robo Analyzer, they obtained the solution of forwarding and inverse kinematics, then calculated DH parameters theoretically.
The computed matrix was matched with the update matrix in Robo Analyzer.
And also.
MATLAB has obtained forms of a graph which similar to the obtained values in Robo Analyzer.
Then there is (Jianhua, 2.
who designed six arm manipulators like legs with 6 DOF each, so the total is 42 DOF for the sixlegged robot.
The hexapod robot is constructed and could realize the omnidirectional movement.
Then the tripod gait of hexapod is simulated.
The purpose of this research is to produce a kinematic algorithm and then be implemented into each leg of the hexapod so that it can control the end effectorAos distance.
This paper use Denavit-Hartenberg convention to solve kinematic equations from one leg afterward implemented to all legs of hexapod and obtained the error values between the input and the reality.
MATERIAL AND METHOD
Material The hexapod robot (Gao et al.
, 2.
is consists of one body and six legs.
Each leg is consisting of 3 parts, femur, coxa and tibia.
The coxa link is enclosed to the body with a joint named base/coxa joint .
, which could rotate around of the body from the axis plumb to the long and wide side.
The femur link hooked to the coxa by a joint called hip/femur joint .
that plumb to both the coxa and joint 1.
The tibia link is enclosed to the femur link by a tibia joint .
Qingsheng and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod SINERGI Vol.
No.
June 2018: 69-76 The femur and tibia joints were defined using the most robust servo motor because they will hold the body weight.
For the coxa, the joint was determine using servo motor that less strong than femur and tibia joints.
Because in this joint, the servo motor is used as swing part, that means move to the right or left without hold the body The list of components that used in the hexapod has been tested with some lab experiment and simulation to get the suitable Such as to hold the body and all its A metal aluminum board is chosen for the mechanical structure.
The components are listed in Table 1.
The components are described in the Fig.
Table 1.
List of components No.
Components Arduino Mega 2560 MG995 Servo HITEC HS-311 Servo Servo Controller UBEC 5V 8A Battery 3300 mAh Bottom Body Top Body Layer Coxa.
Femur.
Tibia Bracket Amount Arduino Arduino (Supegina & Iklima, 2.
is an open source of single-board micro-controller and could be used in various fields of electronics.
used as the main part that controls all of the components, processes the logic programming to generate the output then sends it to the servos.
Arduino Mega 2560 is chosen based on the total number of its digital input/output pins.
Servo The hexapod requires several servos on its leg construction.
To actuate a robot some motors are needed.
There are two types of a servo motor.
Tower Pro MG995, and HITEC HS-311.
Each servo motor has different stall current.
For Tower Pro MG995 is 1.
5 Ampere (A) each and HITEC HS-311 is 700 mA each.
In one leg used 2 Tower Pro MG995 and 1 HITEC HS-311.
So, in 1 leg will need current supply at least 3.
7 A.
And all the legs will need current consumption around 22.
2 A.
that case, it used 3 UBEC 8A .
otal 24 A) to avoid damaging the servo motors.
Servo Controller The Arduino Mega board.
PWM output is 15 pins and for hexapod robot needs an external servo drive, because it needs 18 pins for a servo, so that is not sufficient to move in.
Through this servo driver, it can drive 16 servos individually over I2C with only two pins.
It allows using the SDA and SCL pins on the Arduino.
UBEC
Universal Battery Elimination Circuit (UBEC) is an electronic circuit which spigot the power of the battery and decreases the voltage to 5 or 6 volts (V).
Figure 1.
Components of Hexapod Mechanic Design The hexapod robot is contained a bottom body, top body, a layer, six coxa brackets, six femur links and six tibia links.
This upper body part in Fig.
1 has a rectangular shape with 175 mm length and 155 mm width, six joint points for the legs and a rectangle hole in the middle that used for the cable of the components line.
The bottom body has the same shape as the upper body, rectangular shape with 175 mm length and 155 mm width, six joint points for the legs.
This additional layer part has hexagon shape with 55 mm length of each side and a hole in the middle with radius 22.
5 mm lengths.
It was made with like acrylic component with the red color.
Coxa bracket is a place for servo one and two holders.
Femur link is a connector for joint 2 .
emur join.
with joint 3 .
ibia join.
with 110 mm total length.
Tibia link is a connector for joint 3 Qingsheng and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod
ISSN: 1410-2331
ibia join.
with the end-effector, with 16.
45 mm entire length from top to bottom.
In the Fig.
2 the offset length is 3.
2 cm from the bottom body to the femur joint.
The length from the center joint of coxa to the center joint of a femur is 3 cm.
And the length from the center joint of a femur to the center joint of the tibia is 8.
5 cm and from the center joint of the tibia to the endeffector is 12.
5 cm.
Figure 2.
The Structure leg of Hexapod Figure 3.
Frame Coordinate Method The electronic hardware system is tested in a virtual environment .
to avoid the In the same way, the robotic structure plays an important role to get the mathematical equation modeling.
It well presents the design summary of the robot dynamics in parametric equations form.
It assists to choose feasibility, set up and settle the design.
Theory of forwarding and inverse kinematics provided the way out a model of the proposed hexapod.
(Akhlaq et al.
, 2.
Kinematics in robotics (Beni, 2.
is a representation shape regarding the geometrical explanation of a robot structure.
From the geometrical equation, it could get the connection between joints spatial geometry concept and endeffector coordinates theory to figure an object The purpose of kinematics is to determine the relative position of a frame to its original coordinates.
Forward kinematics is transforming the joint variable to the end-effector position.
Besides that, inverse kinematics is to transform the end-effector position to the joint variable.
The Denavit-Hartenberg parameters .
lso called DH parameter.
(Melek, 2.
are the four parameters related with a particular convention for enclosing the reference frames to the links of a spatial, kinematic chain or robot manipulator.
A Joint offset .
: length of junctions of ordinary on the joint axis.
A Joint angle (): angle between the orthogonal projections of the common normal to the plane normal to the joint axes.
A Link length .
: the range among the common normal to the axis.
A Twist angle (): the angle between the orthogonal projections of the joint axes onto a plane normal to the common normal.
is variable if a joint is revolute, is variable if a joint is prismatic.
For this hexapod, the frame coordinates are represented in the Fig.
After determining the coordinates of each frame .
, y, and .
, the Denavit-Hartenberg (DH) parameters of the link could be determined as shown in Table 2.
Table 2.
Denavit-Hartenberg parameters Link yuycn DH Parameters ycaycn yccycn yco1 ycc1 yco2 yco3 Qingsheng, and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod yuEycn yuE1 yuE2 yuE3 SINERGI Vol.
No.
June 2018: 69-76 Forward Kinematics (Akhlaq et al.
, 2.
describes the relationship of each joint of the robotic legs and in supplementary to that, it also as frames for the positioning and alignment of endeffector.
With the provided values of joint variables could unpack the coordinates.
Homogenous transformation matrix of the hexapod could be defined using the DenavitHartenberg (DH) Convention.
The calculation is as This is a translation by ycc1 .
ffset lin.
and translation by yco1 .
ink lengt.
followed by a rotation around ycU1 and ycs1 axis .
wist angl.
ycaycuyc yuE1
ycycnycu yuE1
1T = [
ycycnycu yuE1 Oeycaycuyc yuE1 yco1 ycaycuyc yuE1 yco1 ycycnycu yuE1 Oeycycnycu yuE2 ycaycuyc yuE2 yco2 ycaycuyc yuE2 yco2 ycycnycu yuE2 ycaycuyc yuE3 Oeycycnycu yuE3 ycaycuyc yuE3 yco3 ycaycuyc yuE3 yco3 ycycnycu yuE3 From this calculation we get:
ycyycu = ycu = ycayuE1 .
uE2 yuE3 )yco3 ycayuE2 yco2 yco1 ) ycyyc = yc = ycyuE1 .
uE2 yuE3 )yco3 ycayuE2 yco2 yco1 ) ycayuE1
[ 01T]Oe1 = [ 0
OeycayuE1
Oeyco1
Oeycc1
0 [ 0 ]Oe1 = [ 01T]Oe1 01T 12T 23T
3T 1T
A A ycyycu ycayuE1 ycyyc ycyuE1 Oe yco1
A A
ycyyc Oeycc1
A A
ycyycu ycyuE1 Oe ycyyc ycayuE1 A A A yca.
uE2 yuE3 )yco3 ycayuE2 yco2 )yco = [A A A yc.
uE2 yuE3 3 ycyuE2 yco2 ] A A A 0 0 0 From this calculation it gets:
Transformation of link 0 to link 3 is the result
of the transformation matrix of each link
0 1 2
3T = 1T 2T 3T
Inverse kinematics are solutions to obtain the joint angle values needed to achieve the desired position using algebraic approach.
Algebraic approach is to perform a decrease kinematics equation described by the matrix From Forward Kinematic Equ.
, if it multiplies both sides with [ 01T]Oe1 Where, 0 [ 0 ]Oe1 = 12T 23T
3T 1T
This is a translation by yco3 .
ink lengt.
followed by a rotation around ycs3 axis .
oint angl.
ycycnycu yuE3
3T = [
It can obtain, that:
This is a translation by yco2 .
ink lengt.
followed by a rotation around ycs2 axis .
oint angl.
ycaycuyc yuE2
ycycnycu yuE2
2T = [
ycyyc = yc = yc.
uE2 yuE3 )yco3 ycyuE2 yco2 ycc1 yuE1 = yaycycaycu2 .
cyyc , ycyycu ) .
All the thetas could be described explicitly in Fig.
4, in this case, because this manipulator is a leg of the hexapod, so the value of 3could is negative due to reach value z C 0 of the endeffector.
Qingsheng and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod
ISSN: 1410-2331
Figure 4.
Leg Manipulator In his book (Jakimovski, 2.
, because it has six legs, compose from more than one servo joints, they described hexapod robots belong to the group of walking robots.
Distributed in two different groups located on the two opposite sides of the robotAos body, the legs of the robot are usually symmetrically.
The scheme design of hexapod robots is often inspired by locomotion systems of insects such as cockroaches or insects.
One servo per joint could manipulate the joints, providing 3 DOF .
egrees of freedo.
for each leg, total 18 DOF.
One servo .
oxa/hip.
connects entire leg to the chassis through a vertical axis, allowing the leg to rotate sideways concerning the body.
The two other servos .
emur and tibi.
manipulate the other joints of the leg with rotation about horizontal axes.
The schematic diagram for the hexapod is as shown in Fig.
Servo controllers with PWM used to control the position of the servos.
RESULTS AND DISCUSSION
In this section, is implementing the inverse kinematic into each leg of hexapod and obtained the angle values of each joint.
The angle values were automatically set into the program.
We only need to put the values of x, y, and z coordinate.
We tried one by one of each position and get the value of error.
The error is the difference value between desired and test value.
We simulated these to all the legs.
First, we need to assemble the mechanic design and components in Fig.
Figure 6.
Hexapod Robot Based on Fig.
2, it gets the DH parameters that shown in Table 3.
Figure 5.
Schematic Diagram of the Hexapod The function each part of the diagram is as follows.
Battery 7.
4V/2600 mAh is used as power supply for 3 UBECs 5V/8A and Arduino.
Arduino Mega 2560 is used as a control system for the Hexapod UBEC 5V/8A is used to regulate the voltage down to the necessary 5 or 6 volts for the servos with 8A current each UBEC.
Servo motors are used as joint to connect between links in the legs.
Table 3.
Denavit-Hartenberg Parameter of The Hexapod Link yuycn DH Parameters ycaycn yccycn yuEycn yuE1 yuE2 yuE3 For the test, it chooses 7 points each position .
, y, z coordinate.
for one leg, all is in centimeter and the results are listed in Table 4 to Table 9.
Qingsheng, and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod SINERGI Vol.
No.
June 2018: 69-76 Table 4.
Test for Leg 1 Post Desire Test Error Desire Test Error Desire Test Error Leg 1 Values .
Values .
Table 5.
Test for Leg 2 Post Desire Test Error Desire Test Error Desire Test Error Leg 2 Table 6.
Test for Leg 3 Post Desire Test Error Desire Test Error Desire Test Error Leg 3 Values .
Table 7.
Test for Leg 4 Post Desire Test Error Desire Test Error Desire Test Error Leg 4 Values .
Qingsheng and J.
Andika.
Analysis of Kinematic for Legs of a Hexapod
ISSN: 1410-2331
Table 8.
Test for Leg 5 Post Desire Test Error Desire Test Error Desire Test Error Leg 5 Values .
Table 9.
Test for Leg 6 Post Desire Test Error Desire Test Error Desire Test Error Leg 6 From Leg 1 .
n Table .
the error values lie from 1 to 0.
2 cm.
From Leg 2 (Table .
the error values lie from 0.
1 to 0.
3 cm.
From Leg 3 (Table .
the error values lie from 0.
1 Ae 0.
3 cm.
From Leg 4 (Table .
the error values lie from 0.
1 Ae 0.
3 cm.
From Leg 5 (Table .
the error values lie from 0.
Ae 0.
2 cm.
From Leg 1 (Table .
the error values lie 1 Ae 0.
4 cm.
CONCLUSION
The hexapod robot was constructed and kinematic equations with DH parameters were The results of implementation inverse kinematic to each leg are shown in the result.
the leg 1, 2, 3 and 4 the range of error value is 1 Ae 0.
3 cm, leg 5 is from 0.
1 Ae 0.
2 cm and leg 6 is from 0.
1 Ae 0.
4 cm.
The accuracy of this method is more than 90% where the error value lies on 0.
1 to 0.
4 cm.
This means that the inverse kinematics of the legs is correct.
This range of error caused by some human error, such as in the assembly part is not equilibrium from one link to another, and also the measurement of constraint value of each servo is not accuracy from 0 degrees to 180 degrees.
ACKNOWLEDGMENT
We thank our colleagues from Beijing Institute of Technology and Universitas Mercu Buana who provided insight and expertise that greatly assisted the research.
Values .
REFERENCES