Open Access

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


Cite

Ben-Isreal, A. and Cohen, D. (1966). On iterative computation of generalized inverses and associated projections, SIAMJournal on Numerical Analysis 3(3): 410-419.10.1137/0703035Search in Google Scholar

Ben-Isreal, A. and Greville, T. (2003). Generalized Inverses:Theory and Applications, CMS Books in Mathematics, 2nd Edn., Springer, New York, NY.Search in Google Scholar

Chiacchio, P. and Siciliano, B. (1989). A closed-loop Jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists, Journal of RoboticSystems 6(5): 601-630.10.1002/rob.4620060507Search in Google Scholar

D’Souza, A., Vijaykumar, S. and Schaal, S. (2001). Learning inverse kinematics, International Conference on IntelligentRobots and Systems, Maui, HI, USA, pp. 298-303.Search in Google Scholar

Dulęba, I. and Jagodzi´nski, J. (2011). Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems, International Journal of Applied Mathematicsand Computer Science 21(3): 525-534, DOI: 10.2478/v10006-011-0041-y.10.2478/v10006-011-0041-ySearch in Google Scholar

Dulęba, I. and Sasiadek, J. (2002). Modified Jacobian method of transversal passing through the smallest deficiency singularities for robot manipulators, Robotica20(4): 405-415.10.1017/S0263574702004095Search in Google Scholar

Golub, G. and Van Loan, C. (1996). Matrix Computations, 3rd Edn., Johns Hopkins, Baltimore, MD.Search in Google Scholar

Horn, R. and Johnson, C. (1986). Matrix Analysis, Cambridge University Press, New York, NY.Search in Google Scholar

Hunek, W. and Latawiec, K.J. (2011). A study on new right/left inverses of nonsquare polynomial matrices, InternationalJournal of Applied Mathematics and Computer Science21(2): 331-348, DOI: 10.2478/v10006-011-0025-y.10.2478/v10006-011-0025-ySearch in Google Scholar

Lee, C. (1982). Robot arm kinematics, dynamics, and control, Computer 15(12): 62-80.10.1109/MC.1982.1653917Search in Google Scholar

Levenberg, K. (1944). A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics2: 164-168.10.1090/qam/10666Search in Google Scholar

Maciejewski, A. and Klein, C. (1989). The singular value decomposition: Computation and applications to robotics, International Journal of Robotics Research 8(6): 63-79.10.1177/027836498900800605Search in Google Scholar

Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics11(2): 431-441.10.1137/0111030Search in Google Scholar

Nakamura, Y. (1991). Advanced Robotics: Redundancy andOptimization, Addison Wesley, New York, NY.Search in Google Scholar

Nearchou, A. (1998). Solving the inverse kinematics problem of redundant robots operating in complex environments via a modified genetic algorithm, Mechanism and Machine Theory33(3): 273-292.10.1016/S0094-114X(97)00034-7Search in Google Scholar

Tchoń, K. and Dul˛eba, I. (1993). On inverting singular kinematics and geodesic trajectory generation for robot manipulators, Journal of Intelligent and Robotic Systems8(3): 325-359.10.1007/BF01257948Search in Google Scholar

Tchoń, K., Dul˛eba, I., Muszy´nski, R., Mazur, A. and Hossa, R. (2000). Manipulators and Mobile Robots: Models, MotionPlanning, Control, PLJ, Warsaw, (in Polish).Search in Google Scholar

Tchoń, K., Karpi´nska, J. and Janiak, M. (2009). Approximation of Jacobian inverse kinematics algorithms, InternationalJournal of Applied Mathematics and Computer Science19(4): 519-531, DOI: 10.2478/v10006-009-0041-3.10.2478/v10006-009-0041-3Search in Google Scholar

Tejomurtula, S. and Kak, S. (1999). Inverse kinematics in robotics using neural networks, Information Sciences116(2-4): 147-164.10.1016/S0020-0255(98)10098-1Search in Google Scholar

eISSN:
2083-8492
ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics