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The International Journal of Robotics Research
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Inverse Kinematics Solution to Mobile Manipulators

Miroslaw Galicki

Institute of Organization and Management University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland and Institute of Medical Statistics Computer Science and Documentation Friedrich Schiller University Jena Jahnstrasse 3, D-07740 Jena, Germany, galicki{at}imsid.uni-jena.de

This paper presents the solution at the control feedback level to the inverse kinematics problem for mobile manipulators operating in both obstacle-free task spaces and task spaces including obstacles. Using the Frechet differential of a certain criterion function, the fully specified system of algebraic and differential equations of the minimal amount has been obtained to solve the inverse kinematics problem. Based on the Lyapunov stability theory, a full differential form generating the mobile manipulator trajectory, whose attractor attained in a finite time fulfills the above system of algebraic and differential equations, has been derived. The problem of both singularity and collision avoidance is solved here based on a concept of (local) velocity perturbation which results in continuous mobile manipulator velocities near singularities and obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both an obstacle-free task space and task space including obstacles, illustrate the trajectory performance of the proposed solution scheme.

Key Words: mobile manipulator • inverse kinematics • transversality conditions • stability

The International Journal of Robotics Research, Vol. 22, No. 12, 1041-1064 (2003)
DOI: 10.1177/0278364903022012004
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M. Fruchard, P. Morin, and C. Samson
A Framework for the Control of Nonholonomic Mobile Manipulators
The International Journal of Robotics Research, August 1, 2006; 25(8): 745 - 780.
[Abstract] [PDF]