Abstract
The paper is devoted to the singularity robust Jacobian inverse kinematics algorithm for mobile manipulators. The endogenous configuration space approach is assumed as a guideline. The main contribution of the paper consists in establishing completeness of this algorithm, and in stating its convergence condition in terms of the mobile manipulator’s dexterity matrix. Computer simulations illustrate the performance and the convergence of the algorithm.
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References
Davidenko, D.F. (1953), On a new method of numerically integrating a system of nonlinear equations, Dokl. Akad. Nauk SSSR 88, 601-603.
Chelouah, A. and Chitour, Y. (2003), On the motion planning of rolling surfaces, Forum Math. 15,727-758.
Chitour, Y. and Sussmann, H.J. (1998), Motion planning using the continuation method, in Es-says on Mathematical Robotics, J. Baillieul et al. (Eds.), Springer-Verlag, New York, pp. 91-125.
Chitour, Y. (2006), A homotopy continuation method for trajectories generation of nonholo-nomic systems, ESAIM: Control, Optim. Calc. Var. 12, pp. 139-168.
Nakamura, Y. (1991), Advanced Robotics: Redundancy and Optimization, Addison-Wesley, Reading.
Richter, S.L. and DeCarlo, R.A. (1983), Continuation methods: Theory and applications, IEEE Trans. Circuits Syst. 30, 347-352.
Tcho n , K. and Jakubiak, J. (2003), Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms, Int. J. Control 76, 1387-1419.
Tchon, K. and Jakubiak, J. (2005), A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators, IEEE Trans. Syst., Man, Cybern. B, Cybern. 35 (5),1051-1057.
Tcho n , K. (2006), Repeatable, extended Jacobian inverse kinematics algorithm for mobile manipulators, Syst. Control Lett. 55, 87-93.
Wa Żewski, T. (1947), Sur l’évaluation du domaine d’existence des fonctions implicites réelles ou complexes, Ann. Soc. Pol. Math. 20, 81-120.
WaŻewski, T. (1948), Sur la limitation des intégrales des systemes d’équations différentielles linéaires ordinaires, Studia Math. 10, 48-59.
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Tchoń, K., Małek, Ł. (2008). Singularity Robust Jacobian Inverse Kinematics for Mobile Manipulators. In: Lenarčič, J., Wenger, P. (eds) Advances in Robot Kinematics: Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8600-7_17
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DOI: https://doi.org/10.1007/978-1-4020-8600-7_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8599-4
Online ISBN: 978-1-4020-8600-7
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