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A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators

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Dulęba I., Opałka M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
|
nr 2
373-382
EN
The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.
2
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Circular object detection using a modified Hough transform

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Smereka M., Dulęba I.
International Journal of Applied Mathematics and Computer Science
|
2008
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tom 18
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nr 1
85-91
EN
A practical modification of the Hough transform is proposed that improves the detection of low-contrast circular objects. The original circular Hough transform and its numerous modifications are discussed and compared in order to improve both the efficiency and computational complexity of the algorithm. Medical images are selected to verify the algorithm. In particular, the algorithm is applied to localize cell nuclei of cytological smears visualized using a phase contrast microscope.
3
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Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems

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Dulęba I., Jagodziński J.
International Journal of Applied Mathematics and Computer Science
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2011
|
tom 21
|
nr 3
525-534
EN
In this paper, an extension of the Lafferriere-Sussmann algorithm of motion planning for driftless nilpotent control systems is analyzed. It is aimed at making more numerous admissible representations of motion in the algorithm. The representations allow designing a shape of trajectories joining the initial and final configuration of the motion planning task. This feature is especially important in motion planning in a cluttered environment. Some natural functions are introduced to measure the shape of a trajectory in the configuration space and to evaluate trajectories corresponding to different representations of motion.
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