1) The document discusses inverse and forward kinematics problems for the motion of manipulators in PUMA robotics systems. It focuses on modeling the kinematics using homogeneous transformation matrices and the Denavit-Hartenberg parameterization. 2) Neural network control methods are explored for the PUMA robot, including using an Elman recurrent neural network with feedback to solve the inverse kinematics problem. Simulation results are shown to evaluate the network's performance. 3) The conclusion states that an accurate kinematic model of the PUMA manipulator has been developed and some modifications have been made to the inverse kinematics solutions to avoid contradictory joint configurations.

1. ‫كريم‬ ‫هديل‬
‫ياسين‬ ‫مريم‬
Supervisor
Dr. Lafta

2. INTRODUCTION
4
 The task of manipulator has been put up with motion of
manipulator’s industrial robotics and it is significant in systems with
real time for puma robotics system.
 The motion of manipulator occurs in a space with Cartesian axel,
and the generality of robots’ manufacturing, mostly industrial with
the expressed ones and their joint spaces can be controlled.
 In order to execute a motion of puma robotics, a transformation of
kinematics is done between space of joint and the calculation of the
space with Cartesian axis is necessary.

3.  The problem of kinematics in puma robotics system can be
classified into two parts: kinematics tasks of inverse and
forward.
 The problem of inverse kinematics comprises the space of
Cartesian axis data in a not closed form in order to determine
the joint variable.
 The structure of transformation of inverse kinematics is
nonlinear.
 The task of robotic manipulator in inverse kinematics gets the
wanted values for the joint of manipulator required for
orientation and position.

4. PROBLEM OF INVERSE
KINEMATICS
 The problem of inverse kinematics is not easy for
manipulators in puma robotic.
 The problem of Forward kinematics is that the variable of
joint manipulator in the end effector in orientation and
position is determined in the axes of Cartesian space with
closed form.
 Research have provided a controller for robotic in
therapeutic in order to help the patients with neurologic
disorders. 7

5.  The joint of manipulator of puma robotics can be modeled and calculated
in an articulated chain of open loop with numerous rigid links coupled in
series by either prismatic or revolute links, which are impelled by
actuators.
 The analytical study of robot kinematics deals with the reference
coordinates system related to moments or time that do not require the
forces for movement with respect to geometry for the motion of a puma
robot.
 Fig. 1 shows the robotics manipulator’s structure in this paper. The
analysis of kinematics for puma robotics is done in two ways: inverse
kinematics and forward kinematics task, which is mostly explained in
Research Method

6. Fig. 1. The structured of the 6-dof of
PUMA robotics

7.  Forward kinematics method bargains with motion of the end
effector for the puma relating to a system with coordinate
axes.
 A system with axes (Wx,Wy,Wz) is colonized with the
immoral of the link as seen in Fig. 1.
Forward kinematics method

8.  The manipulator of puma robotics link is structured and this
modeling gives a rundown of the ‘A’ homogenous
transformation matrix that uses four parameters for link.
 This transformation in modeling of robotics is known as the
Denvit-Hartenberge notation:
Manipulator Of Puma Robotics

9.  The angles of the link have been scaled in counter clockwise and
the joint longitudes are supposed to be positive giving from one
joint axis to the promptly distal joint axis.
 Equation (3) shows the savings of three equations that depict the
relationship between joint coordinates and effectors coordinates
end.
 It should be noticed that there are evident equations of the end-
effectors for coordinates axes in terms of link coordinates axes.
 In order to find the link coordinates axes for a given group of end-
effectors for coordinates axes (φ,x,y), The manipulator of planner
R-P for kinematics of is simple to subedit.
 The equations for manipulators are:
MODELING OF KINEMATICS OF
MANIPULATOR

10. Neural Network And Control Of Puma Robotics
• The recurrent neural network model can apply the dynamic
systems by state space representation.
• this method is used as an equalizer for recurrent neural and
linked by a network if it is a feed forward and this method
with elman network is offered shown down with the learning
algorithm as seen in fig. 2.
• the structure of the elman network with feedback in
kinematics inverse can be utilized if the input has three layers
of this network with hidden and output.
• the layer of output nodes, the layer of hidden and the
activation function with sigmoid function, that is a nonlinear
function, have been utilized as in fig. 3.

12. 0 2 4 6 8 1
0
1
2
1
4
1
6
1
8
2
0
0
0
.05
0
.1
0
.15
0
.2
0
.25
0
.3
0
.35
0
.4
Number of samples
MRN output
Plant output
Fig. 4. The output from NN (learning stage) (y) and (y,) reference position for y2
Fig. 5. The output from NN (learning stage) (y) and (y,) reference position for y3

13. CONCLUSION
 A modeling of kinematic for PUMA robotics, which accurately
identifies the actual manipulator, has been developed.
 Some of the link parameters have not been properly considered, and
tool particulars have been neglected.
 In this coincidence, the coordinate frames of the link have been
redefined and a new transformation for the value of end-effector offset
has been introduced.
 In addition, some modifications have been made on the solutions of the
kinematics, if it is inverse, so that no contradiction has happened when
the configuration of the joint of manipulator has been done in right/left
or above/below.

14. REFERENCES
• [1] JUAN MANUEL FLOREZ, MANAN SHAH, EDUARDO MARTIN MORAUDY, SOPHIE
WURTHY, LAETITIA BAUD, JOACHIM VON ZITZEWITZZ, RUBIA VAN DEN BRANDZ, SILVESTRO
MICERAY?, GREGOIRE COURTINEZ AND JAMIE PAIK, REHABILITATIVE SOFT EXOSKELETON FOR
RODENTS, IEEE TRANSACTIONS ON NEURAL SYSTEM AND REHABILITATION ENGINEERING,
VOL. 25, NO. 2, 2017,
• [2] DEEPAK GOPINATH, SIDDARTH JAIN, AND BRENNA D. ARGALL. HUMANIN-THE-LOOP
OPTIMIZATION OF SHARED AUTONOMY IN ASSISTIVE ROBOTICS. IEEE ROBOTICS AND
AUTOMATION LETTERS, VOL. 2, NO. 1, JANUARY 2017.
• [3] RAN XU, YURKEWICH, AND RAJNI V. PATEL, CURVATURE, TORSION, AND FORCE
SENSING IN CONTINUUM ROBOTS USING HELICALLY WRAPPED FBG SENSORS, IEEE ROBOTICS
AND AUTOMATION LETTERS, VOL. 1, NO. 2, JULY 2016.
• [4] D. PARDO, L. MÖLLER, M. NEUNERT, A. W. WINKLER AND J. BUCHLI, EVALUATING
DIRECT TRANSCRIPTION AND NONLINEAR OPTIMIZATION METHODS FOR ROBOT MOTION
PLANNING, IN IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 1, NO. 2, PP. 946-953, JULY
2016. 10.1109/LRA.2016.2527062
• [5] SIVANAGARAJA TATINATI, WEI TECH ANG, AND KALYANA C. VELUVOLU, MULTI-
DIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN
HAND-HELD SURGICAL ROBOTICS,
• [6] REEM K. AL-HALIMI, MEDHAT MOUSSA PERFORMING COMPLEX TASKS BY USERS
WITH UPPER-EXTREMITY DISABILITIES USING A 6-DOF ROBOTIC ARM: A STUDY, IEEE
TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION ENGINEERING, VOL.25, ISSUE 6,