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.

In this paper an idea of the elas c band method was exploited to design a repeatable inverse kinema cs algorithm for robot manipulators. The method incorporates an op miza on process at many stages of its performance and admits some extensions. Performance of the algorithm was illustrated on models of the three DOF planar pendulum and the PUMA robot. A comparison with a standard pseudo-inverse Jacobian algorithm, which does not preserve repeatability of inverse kinema cs, is also provided.

SUMMARYIn this paper a motion planner for nonholonomic stratified systems was proposed. Those systems may arise easily when reliable systems are designed to be robust against failures in difficult servicing environments. For a special class of the systems, a strong controllability condition was introduced, and a criterion to satisfy the condition was formulated and used to plan the motion of free-floating space manipulators. Modules of the planner were enumerated and their roles were emphasized. Some features of the planner were examined and discussed based on simulation results performed on two models of space manipulators.

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