Archives of Control Sciences
Volume 25(LXI), 2015
No. 4, pages 513–527
Reference trajectory tracking for a multi-DOF
RÓBERT KRASŇANSKÝ, PETER VALACH, DÁVID SOÓS, JAVAD ZARBAKHSH
This paper presents the problem of tracking the generated reference trajectory by the
simulation model of a multi-DOF robot arm. The kinematic transformation between task
space and joint configuration coordinates is nonlinear and configuration dependent. To
obtain the solution of the forward kinematics problem, the homogeneous transformation
matrix is used. A solution to the inverse kinematics is a vector of joint configuration coordi-
nates calculated using of pseudoinverse Jacobian technique. These coordinates correspond
to a set of task space coordinates. The algorithm is presented which uses iterative solution
and is simplified by considering stepper motors in robot arm joints. The reference trajec-
tory in Cartesian coordinate system is generated on-line by the signal generator previously
developed in MS Excel. Dynamic Data Exchange communication protocol allows sharing
data with Matlab-Simulink. These data represent the reference tracking trajectory of the end
effector. Matlab-Simulink software is used to calculate the representative joint rotations.
The proposed algorithm is demonstrated experimentally on the model of 7-DOF robot arm
Key words: inverse kinematics, real-time reference tracking, signal generator, multi-DOF,
dynamic data exchange.
Robotics represents one of the main disciplines in the industry. The synergy of ro-
botics with other applications like car assembly operations, vision systems or artificial
intelligence allows not only for innovations but also reduces the manufacture costs. In
the kinematic analysis of a robot arm position, two separate problems have to be solved:
forward kinematics and inverse kinematics. Forward kinematics includes solving the
forward transformation equation to find the location of the hand in terms of the angles
and displacements between the links of the robot arm.
R. Krasňanský, P. Valach and D. Soós are with Faculty of Electrical Engineering and IT, Slovak Uni-
versity of Technology in Bratislava, Ilkovicova 3, 81219 Bratislava, Slovak Republic. E-mails:(robert.kras-
nansky, peter.valach, david.soos)@stuba.sk. J. Zarbakhsh is with Carinthia University of Applied Science,
Europastrasse 4, 9524 Villach, Austria. E-mail: email@example.com.
This work has been supported by Grant N. 1/1241/12 of the Slovak Scientific Grant Agency.
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514 R. KRASŇANSKÝ, P. VALACH, D. SOÓS, J. ZARBAKHSH
In order to find the corresponding sets of joint angle given the desired position and
orientation of the end effector it is necessary to solve the inverse kinematics problem.
Inverse kinematics, on the other hand, includes solving the inverse transformation equa-
tions in order to find the relationships between the links of the robot arm from its...