DYNAMICS CONTROL AND DH PARAMETRIZATION OF · PDF fileDenavit-Hartenberg notation (Fig.1) is...

ELK ASIA PACIFIC JOURNAL OF MECHANICAL ENGINEERING RRESEARCH

ISSN 2394-9368 (Online); EAPJMER/issn. 2394-9368/2016; Volume 2 Issue 2 (2016)

www.elkjournals.com

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DYNAMICS CONTROL AND DH PARAMETRIZATION OF ARISTO XT 6-AXIS

ROBOT USING ROBOANALYZER

Saurabh Chandra

Dept. of Mechanical Engineering

SRMSCET Bareilly, India

[email protected]

Mohd Mujahid Khan

Jamia Milia Islamia

New Delhi

Vijay Kumar

Dept. of Mechanical Engineering,

SRMSCET Bareilly, India

ABSTRACT

Robotic Manipulators are the heart of modern industries and to be seen externally as well in our daily usage. Robotics

is the interdisciplinary advent of all engineering technologies .In this paper; there is a method that will find the end-

effectors DH parameter table as per the need of work envelope. For this purpose, we are using Robo Analyzer

(Software developed by Prof. S. K. Saha, IIT Delhi). There are such other software’s that can control the movement

of a robotic manipulators but Robo Analyzer is a gem for robotic simulation. In Robo Analyzer, the end-effector DH

table can be easily generated. This DH table gives the values that are analytically derived as per the principles of DH

Parametrization. Further, this paper will describe the real time working space simulation of robotic manipulators.

The chief advantage of using this software is that simulation task can be performed under exact conditions as they are

in real time. In this type of Robot simulation, point to point control of robot takes place.

Keywords— DH Parameters, Forward and Inverse Kinematics, Serial Multi-body Dynamics, Robot Enclosed Motion,

Workspace Simulation.

INTRODUCTION

Denavit-Hartenberg notation (Fig.1) is

widely used in the transformation of

coordinate systems of linkages and robot

mechanisms [1]. It can be used to represent the

transformation matrix between links as shown

in the Figure

Figure 1:- Denavit Hartenberg Notation

http://dx.doi.org/10.16962/EAPJSS/issn.2394-9392/2014

http://www.elkjournals.com/

mailto:[email protected]



………………………………………………………………………………………………

IN PREVIOUS FIGURE,

zi-1 and zi are the axes of two revolute

pairs;

θi is the included angle of axes xi-1 and xi;

di is the distance between the origin of the

coordinate system xi-1yi-1zi-1 and the foot

of the common perpendicular;

ai is the distance between two feet of the

common perpendicular;

αi is the included angle of axes zi-1 and zi;

The transformation matrix (Fig.2) will be

𝐻𝑖−0𝑖 ,𝐻𝑖−0

𝑖 =

[

𝑐𝜃𝑖 − 𝑠𝜃𝑖 0 𝑎𝑖−1

𝑠𝜃𝑐𝛼𝑖−1 𝑐𝜃𝑐𝛼𝑖−1 − 𝑠𝛼𝑖−1 − 𝑠𝛼𝑖−1𝑑𝑖

𝑐𝜃𝑠𝛼𝑖−1 𝑐𝜃𝑠𝛼𝑖−1 𝑐𝛼𝑖−1 𝑐𝛼𝑖−1𝑑𝑖

0 0 0 1

]

Figure 2:- Link Transformation Matrix

The above transformation matrix can be

denoted as 𝐻𝑖−0𝑖 (ai,αi,θi, di) for convenience.

DH (Denavit and Hartenberg) parameters [19]

are basically the horoscopic detail of any

motion of robotic manipulators. Jacques

Denavit and Richard Hartenberg proffered

these parameters in 1955[1].These are

basically used to describe the position of a

joint with respect to the base frame but in a

matrix format. When motion of the robotic

manipulator is being taken as a step of cycle

then all these DH tables [20] are multiplied

according to the standard matrix

multiplication method and the final DH table

gives the DH values of end-effector.

As per the properties and orientation of the

links with respect to base frame the following

DH table is to be designed (Fig.3).

Figure 3:- DH Parameter Table

Operation of robot will be under two work

cycle 1- Loading Cycle 2- Unloading Cycle.

Our objective is to find out DH matrix of end-

effector for both the loading cycle and

unloading cycle as well as the respected data

has also been checked for joint value, velocity

and acceleration.

A BRIEF LITERATURE REVIEW

A very short but effective literature review of

Kinematic Analysis of a robot and Robotic

Simulators is being presented here:-

Grasp dexterity is defined as the ability of a

grasp to achieve one or more useful secondary

objectives while satisfying kinematic

relationship (between joint and Cartesian

spaces) as the primary objective. This

definition is based on the fact that grasp is a

kinematically redundant system. To achieve

dexterous manipulation, many studies of

multi fingered hands have been carried out.

Salisbury has described some of the basic

Join

t i

Link

Lengt

h

(ai-1)

Link

Twis

t

(αi-1)

Link

Offse

t

(di)

Link

Rotatio

n

(θi)

1 0 0 0 θ1

2 L1 0 0 θ2

3 L2 0 0 θ3

4 L3 0 0 θ4

5 L4 0 0 θ5

6 L5 0 0 0




………………………………………………………………………………………………

issues of interest [2], Kerr and Roth [3],

Yoshikava Et. Al and other have proposed

schemes to solve for internal grasping forces

suspect to friction and other constants [4],

Nakamura gives a good overview of

mathematical tools for redundant

manipulation [5], Yoshikawa et al. have

developed control strategies for dexterous

hands [6]. Jamaludin jalani worked on to

develop a new method to capture the

parameters from robot fingers by using Robo

Realm tool. [7].

Studies by khurshid, Ghafoor and Malik

worked on enhancing robotic grasping and

fine manipulation using soft fingertip. The

ability to create stable, encompassing grasps

with subsets of fingers is greatly increased by

using soft fingertips that deform during

contact and apply a larger space of frictional

forces and moments than their rigid

counterparts [8].

Currently many researchers are actively

working on this type of task which can offer

universal gripping system with dexterous

approach in the operations. The design

concepts discussed while developing Gifu

Hand, [9] narrates towards biomimetic

approach. Issues related to the use of tendon /

cables for gripping actions are discussed in

this study. Also remedy is provided by using

the linkages for mechanical grasping.

Another similar effort by making provision of

multimodal sensors placed on / in a soft

surface of the tip of the gripper finger. [9] They

have proposed a design for tactile sensing to

embed as many receptors as possible

randomly in soft material so as to provide

different kinds of sensing modalities. In a

study by J. L. Bank, [10] feedback about the

content of its surroundings is suggested in

order to exhibit flexibility for embedding

adaptability in the system.

A paper by G. S. Gupta Et. Al. provides the

information on the design and development of

a low-cost control rig to intuitively

manipulate an anthropomorphic robotic arm

using a bilateral master–slave control

methodology. [11]. Further patterns of hand

motion during grasping and the influence of

sensory guidance is experimented by M.

Santello Et. Al. [12] this widens the scope of

biomimetic action analysis by experimenting

for grasping with the conditions such as, the

memory guided movements, virtual

imagination and physical object handling,

with the help of 15 DOF hand.

Biorobotics is another term which also

reflects the similar logic for total robotic

action with robot gripper as a subset.

Associated parameters like Hand kinematics,

Finger joint actuators, Drive chain

components, Number and location of sensors

are discussed with biomechanical design

strategies by J N Marcincin ET. al. [13] For

initial and final conditions of grasping, human

unconsciously changes the grasp strategy




………………………………………………………………………………………………

according to the size of object even if they

possess same geometry. It is termed as the

grasp planning for the scale dependent grasp.

The grasp patterns thus observed in human

grasping are applied with couple of grasp

procedures to multi-fingered robot hands by

T. Shirai et. al. [14]

A concept for integrating the control system

of an anthropomorphic robot hand into the

control system of an entire humanoid robot

was presented by D. Osswald [15]. Grasp

taxonomy was developed on the basis of the

objects and actions in the intended

environment that can be used to describe the

grasp patterns.

Ohol and Kajale have also worked on the

biometric approach to design a multi-fingered

Robotic Gripper [16].

A robotics simulator is used to create

embedded applications for a robot without

depending physically on the actual machine,

thus saving cost and time. In some case, these

applications can be transferred on the real

robot (or rebuilt) without modifications. The

term robotics simulator can refer to several

different robotics simulation applications. For

example, in mobile robotics applications,

behavior-based robotics simulators allow

users to create simple worlds of rigid objects

and light sources and to program robots to

interact with these worlds. Behavior-based

simulation allows for actions that are more

biological in nature when compared to

simulators that are more binary, or

computational. In addition, behavior-based

simulators may "learn" from mistakes and are

capable of demonstrating the

anthropomorphic quality of tenacity. [17]

Sensor-based robot actions are much more

difficult to simulate and/or to program off-

line, since the robot motion depends on the

instantaneous sensor readings in the real

world. [17]

Modern simulators tend to provide the

following features:

Fast robot prototyping Using the own

simulator as creation tool (Virtual Robot

Experimentation Platform, Webots, R-

Station, Marilou).Using external tools.

Physics engines for realistic movements.

Most simulators use ODE (Gazebo, LPZ

Robots, Marilou, Webots) or PhysX

(Microsoft Robotics Studio).

Realistic 3d rendering. Standard 3d

modeling tools or third party tools can be

used to build the environments.

Dynamic Robot bodies with scripting. C,

C++, Perl, Python, Java, URBI, MATLAB

languages used by Webots, Python used by

Gazebo.




………………………………………………………………………………………………

WORKSPACE SIMULATION

The general use of robots is to give a complex

operation in a 3 D environment. The design of

the links as well as the actuation mechanism

[25] must be so perfect so that they are capable

of doing the exact work what we need within

their work envelope.

Figure 4:- Robotic Workspace Simulation

Workspace simulation (Fig. 4) also gives

some virtual experiences of problems that can

occur in real time while working with the

industrial robots. There are so many advance

simulator softwares like Roboanalyzer in the

market that are capable of recording the link

properties as well as simulating them along

with.

ACTUAL WORKING STEPS AND

THEIR CALCULATIONS

The complete operation of robot is basically

combination of 2 major operations: - 1-

Loading Raw Material in the XLMILL

Machine 2- Unloading Finished work piece

from the vice of XLMILL Machine.

In both these steps there are several other sub

steps which needs to be performed and which

are the heart of both the steps :-

A. Load Raw Material in the XLMILL

Machine

Movement of robot’s end effector along

with other links to reach till pallet (Fig. 5)

position from its home position.

Figure 5:- Loading Step 1

Grasping the raw material billet from the

pallet [21] (Gripper Close) and picking it up

(Fig. 6).

Figure 6:- Gripping the raw workpiece smoothly in

pallete

Carrying out this billet till the vice of the

XLMILL Machine (Fig. 7).

Figure 7:- Loading Step 2

Placing the piece in the Vice smoothly.




………………………………………………………………………………………………

Again reaching till pallet position (Not to

interrupt the XLMILL Machine)

Operations.

B. Unloading Finished work piece form

the XLMILL Machine

Reaching end-effector of robot till

machine vice.

Grasping of the finished work piece

(Gripper Close) and picking it up.

Again reaching end-effector till the pallet

position.

Gripper Open and placing of the finished

work piece in the Palette smoothly.

Reaching back to its home position from

pallet position.

Calculation is made to find out the end-

effector DH matrix of the robot after both

these two steps and for this work

Roboanalyzer proved so helpful software.

These are the DH Tables (Table 1 and Table

2) of both the Loading steps:-

Table 1:- Home Position to Pallet Position

Table 2:- Pallet Position to Vice

POSITION

When we are taking about the unload cycle

then these value of Initial Value and Final

Value will be Interchanged when it need to go

in a reverse direction of movement. If we are

talking about the grasping and relieving

action, picking up and placing object in the

pallet and vice smoothly of robot gripper[18]

then it will take at least 5 seconds of overall

operation. When an Industrial robot is under

the operation of very important industrial

work then even a second of time lag matters.

So this 5 second time lag must be associated

and managed along with the operation in a

manner so that it can’t affect the whole work

time.

There is an error in the software that the joint

offset is taken as 0.322m in it, but it is exactly

the 0.375m of Joint 1. This will affect the end-

effector DH parameter Matrix slightly if we

find out the DH table as per the exact

dimensions of the robot.




………………………………………………………………………………………………

FINAL DH MATRIX FOR END-

EFFECTOR

When the end-effector will reach till the pallet

position in the loading step then there will be

some variation in the DH values of joint

placed at end-effector with the base frame of

the robot. The DH values (DH Matrix) (Fig.8)

that is obtained after this step (reaching the

robot end effector from its home position to

the pallet position) will be as:-

Figure 8:- DH Matrix of End-Effector after loading

Step 1

And after reaching the end-effector till the

machine vice to place the work piece [23] , the

DH matrix (Fig.9) of end-effector will be

Figure 9:- DH Matrix of End-Effector after loading

Step 2

When the end effector will be in home

position then its end-effector’s DH matrix

(Fig. 10) will be,

Figure 10:- DH Matrix of End-Effector in Home

Position

Parameters of DH value will be considered

only with respect to the base frame only; it

doesn’t matter wherever the robot end-

effector is.

JOINT VALUE, VELOCITY AND

ACCELARATION CHARACTERISTICS

Each joint angles and position at the end of

both these two steps will depend upon the

final position of end-effector after each step,

their velocity and acceleration [22] property

will depend upon the time taken to complete

the operation and number of steps taken.

1000

400242.0051813.00998657.0

602411.0997129.0055299.0051734.0

033364.0055224.099847.0002865.0

1000

628509.0065229.0099787.0

248266.0450446.0892318.0029445.0

49076.0890418.0451407.0058205.0

1000

559.0100

0010

375.0001




………………………………………………………………………………………………

There are several properties of the

manipulators that can be seen easily by

analyzing these graphs,

Graph 1:- Loading Step 1




………………………………………………………………………………………………

Graph 2:- Unloading Step 2

Graph 3:- Loading Step 2




………………………………………………………………………………………………

Graph 4:- Unloading Step 1

RESULTS AND DISCUSSION

The objective was to check whether the work

dimension in which we are working is under

the work envelope of the manipulator and if so

then it is taking how much of the work space to

easily complete the operation. The DH matrix

of maximum work envelope dimension

(Fig.11) will be

Figure 11:- Maximum Work Dimension DH Matrix

By calculating the percent of use of work

envelope (Table 3) space according to the

displacement ( when the robot is operating

under the operation) per the maximum reach of

robot arm we find :-

JOINT # METHOD TO

CALCULATE

PERCENT

AGE

Joint1 (86.83/340)*100 25.00%

Joint 2 (40.58/45)*100 90.17%

Joint 3 (17.61/25)*100 70.44%

Joint4 (0/340)*100 0%

Joint5 (110/180)*100 61.11%

Joint 6 (0/340)*100 0%

Table 3 :- Percentage of use of Work Space

Accuracy of the trajectory planning depends

upon the smooth operation of the robot and this

smooth operation [24] depends upon the number

1000

346674.0939693.0034202.0

185707.0116978.0939693.0321394.0

510224.0321394.034202.0883022.0




………………………………………………………………………………………………

of steps taken in a certain time to reach till the

end-effector position. This will also help in

controlling the overall motion of the robotic

manipulator by varying these parameters.

By reading the given joint characteristics we

got the following details:-

LOADING SUB STEP 1 VS UNLOADING

SUB STEP 2

All the characteristics of the Joint 1 and

Joint 3 in loading sub step 1 will be

identically opposite to the unloading sub

step 2 because in loading step Joint 1 will

move in forward direction but in the

unloading step it will move in reverse

direction.

There is no movement in the Joint 4, Joint 6

so no fluctuation will be seen in the plots of

both these steps.

Same analysis is being taken into

consideration for the loading Sub step 2 vs

Unloading sub step 1.

CONCLUSION

We Conclude that during the whole cycle

operation we got that approx. 41.11% of the

overall work space is utilizing. There is also a

wide space availability in the work envelope so

that there can be some more operation added

with the loading and unloading. When the work

is under the repetitive manufacturing then the

configuration that is explained under this paper

is best for operation but some change in the

operational procedure will take place.

This is the best method to mathematically

verify and check how much of the work space

a manipulator is utilizing and if there exist any

problem in the overall operation, rectify that

and use the best of it. Method of finding the DH

matrix for orientation of the end-effectors is

novel for the industrial robotics.

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A Kinematic Notation for Lower-Pair

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Conference on Robotic and Automation,

pp. 1998-2004,. Nakamura, Y., (1991)

Advanced Robotics: Redundancy and

Optimization, Addison-Wesley,

Yoshikawa, T., Zheng, X., (1993)




………………………………………………………………………………………………

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Roborealm,.Khurshid, A Ghafoor, M. A.

Malik, (2010)

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………………………………………………………………………………………………

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