Inverse Kinematics Analysis Trajectory Planning for a Robot Arm

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INVERSE KINEMATICS
ANALYSIS TRAJECTORY
PLANNING FOR
A ROBOT ARM
Proceedings of 2011 8th Asian Control Conference
Kaohsiung, Taiwan, May 15-18, 2011
Guo-Shing Huang, Chiou-Kou Tung, Hsiung-Cheng Lin, and Shun-Hui Hsiao
Department of Electronic Engineering, National Chin-Yi University of Technology
Taichung 41101, Taiwan, ROC
1
Adviser
: Ming-Yuan Shieh
Student ID : M9920105
Student
: Chun-Ming Su
OUTLINE
Abstract
 Introduction
 Structure of the 6-DOF humanoid robot arm

A.
B.

Hardware description
Structure of the 6-DOF humanoid robot arm
Kinematics of the humanoid robot arm
A.
B.
Forward kinematics
Inverse kinematics
Simulation results
 Conclusion

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ABSTRACT



This paper presents a 6-DOF robot arm system.
Using the robot arm assembled by seven AI
servos (RX-64), set up robot‘s coordinate system
with the D-H notation method.
To adjust and drive the robot arm to the
coordinates of folder and place between ones and
the target object, make the angle of the shaft
position can accurately locate the direction for all
axes of the robot arm and obtain the optimal
motion path.
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

Under the experimental test, we position the
object using the camera which was installed on
robot arm, according to the attitude of the object,
control the robot arm through the analysis result
of inverse kinematics equation in order to make
the robot arm achieve the action of exact
grasping object.
Finally, the robot arm system will be used on the
meal service robot to serve for guests.
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INTRODUCTION



The robot arm system is widely used in
production, processing, product transportation,
domestic services and other fields.
But the robot arm which is fixed on the platform,
its work space is very limited.
In addition, the motion path of a pairs of moving
robot arm makes the analysis more complex
using inverse kinematics, all these questions are
concerned by a lot of experts of the robot field.
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

This paper proposes a method to solve the
inverse kinematics for the robot arm which
makes up with six-degree-of-freedom joints in
order to analyze the inverse kinematics of the
robot arm, can find the end-effector position and
posture of the robot arm that can meet the
qualification in the workspace, and then realize
the operation to reach the target.
The experimental results verify that the proposed
inverse kinematics analysis approach in this
paper has the higher accuracy.
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STRUCTURE OF THE 6-DOF
HUMANOID ROBOT ARM

This section describes in more detail the main
hardware structure and system structure that
were adopted in this work.
A.
Hardware description
B.
Structure of the 6-DOF humanoid robot arm
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A. HARDWARE DESCRIPTION

In this paper, the embedded computer is as the
main controller, adopt Dynamixel RX-64 servo
motor which is produced by ROBOTIS Company
as the main motive force of the robot arm, as
shown in Fig. 1.
(a)
(b)
Figure 1. (a) Dynamixel RX-64 servo motor. (b) Robot arm.
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
The system structure is shown in Fig. 2.
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B. STRUCTURE OF THE 6-DOF
HUMANOID ROBOT ARM

The robot arm comprises shoulder joint, upper
arm, elbow joint, lower arm, wrist and the endeffecter. The robot arm has six degrees of
freedom, three degrees of freedom are located at
the shoulder, the elbow has two degrees of
freedom, and one degree of freedom is assigned
on the wrist.
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
Fig. 3 shows the structure diagram of the right
robot arm.
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KINEMATICS OF THE HUMANOID
ROBOT ARM

A D-H coordinate system of the humanoid robot
arm is found in Fig 4. The parameters of link are
shown in Table I.
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13

According to D-H coordinate system, the
homogeneous trans-formation matrix i T (i =
1,2,...,6) expresses
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A. FORWARD KINEMATICS

Institute the link parameters from Table I into
(1), the pose of end-effector can be obtained
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B. INVERSE KINEMATICS

In finding out solution of the inverse kinematics,
using the obtained homogeneous transform
matrix of robot arm, to the formula of
homogeneous transform matrix of the fix target
coordinate in (2), multiples inverse matrix
in
(3), the inverse kinematics is derived by using to
compare with every element of two matrices.
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

Let elements (1, 4), (2, 4), (3, 4) of both sides in (3)
be equal respectively, add the above three
equations after them to be squared.
where
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
Since
∈ (−180°~ −70°) , we have
where Atan 2(⋅) is the four quadrant arctangent
function.
 According to the orthogonality of rotation matrix,
elements of homogenous matrix described in (2)
satisfy following equations:

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

In (2), we get
Let elements (1, 4), (2, 4), (3, 4) of both sides in (8)
be equal respectively, we have
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

Add the above three equations after them to be
squared, and follow up (7), we obtain the solution
of
where
20


In (9), let
Since
of ,
∈ (−180°~ −70°) , we obtain the solution
21

Then the solution of
is

Where sign(⋅) is the sign function, it is defined as

We rearrange (2) and get
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
Let element of both sides in (14) be equal, we get
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
Let
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

Since ∈( −180°~ −70°) , we can obtain the
solutions of and
.
It is obvious that there are two groups of results
to guarantee a small variable, we should choose
one group according to “the shortest route”.
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SIMULATION RESULTS
Figure 5. Initialized position of end-effector.
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Figure 6. Moved position of end-effector.
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In experiments, we used the cine camera that
fixed on robot to confirm the goal position of
object as the vision orientation method.
 Then, robot picked up the goal object through the
robot arm.

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CONCLUSION


In this paper, the kinematics of the six-degree-offreedom robot arm of humanoid robot was
analyzed.
The proposed method can obtain the kinematics
equation at the same time with the geometric
structure and the homogeneous transformation
matrix to control the robot arm.
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Finally, the paper presents the robot arm
successfully pick-ups the goal (a bottle) utilizing
Matlab Software to imitate the kinematics data
and actual experiments.
 The experimental result verifies the validity of
the kinematics equation.
 Next work, the robot arm system will apply to the
order meal service robot, can be used for guest to
receive, wait, order, check out, see a visitor out,…
and so on in every restaurants or hotels in the
early future.

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