Abstract
In this paper a singularities avoidance method suitable for the optimal local path generation of robot manipulators is presented. This method is based on establishing proper bounds for the rate of change of the Jacobian matrix of the transformation between the joints speeds and end effector Cartesian speed. These bounds are computationally inexpensive and easy to deal with by their conversion into additional constraints for an optimization problem (local or global) which may be formulated to obtain the optimal path of the considered robot manipulator. Here, this approach is used while studying the optimal path plannning of (redundant) robot manipulators under a simple local nonlinear programming formulation. This problem is considered as a minimum energy problem with given robot kinematics (and dynamics) and subject to the robot requirements and singularities avoidance constraints.
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References
Baillieul J. “A Constraint Oriented Approach To Inverse Problems For Kinematically Redundant Manipulators”, IEEE Intl. Conf. on Robotics And Automation, Raleigh N.C., March 31-April 3, 1987.
Baillieul J., “Avoiding Obstacles And Resolving Kinematic Redundancy” IEEE Intl. Conf. on Robotics And Automation, San Francisco, Cal., April 1986.
Baillieul J., “Kinematic Programming Alternatives For Redundant Manipulators”, IEEE Intl. Conf. on Robotics And Automation, St. Louis Missouri, March 1985.
Baker D. R., Wampler II C. W., “Some Facts Concerning The Inverse Kinematics of Redundant Manipulators”, IEEE Intl. Conf. on Robotics And Automation, Raleigh N.C., March 31-April 3, 1987.
Chang P. H., “A Closed-Form Solution For The Control of Manipulators With kinematic Redundancy”, IEEE Intl. Conf. on Robotics And Automation, San Francisco CA, Vol. 1, 1986.
Fenton R.G., Benhabib B., Goldenberg A. A., “Optimal Point-to- Point Motion Control of Robots With Redundant Degrees of Freedom”, Trans. A.ME, J. of Eng. for Ind., Vol. 108, May 1986.
Gilbert E. G., Johnson D. W., “Distance Functions And Their Application To Path Planning In The Presence of Obstacles”, IEEE Journal of Robotics And Automation, Vol. RA-1, No. 1, March 1985.
Gotlieb D. H. “Robots And Topology”, IEEE Intl. Conf. on Robotics And Automation, San Francisco CA, April 1986.
Hollerbach J., M., Suh K. C. “Redundancy Resolution of Manipulators Through Torque Optimization”, IEEE Intl. Conf. on Robotics And Automation, St. Louis Missouri, March 1985.
Klein C. A., “Use of Redundancy in the Design of Robotic Systems”, The Robotics Research, 2nd. Intl. Symposium, Eds. H. Hanafusa, H. Inoue, MIT, 1985.
Konstantinov M. S., Markov M. D., Nenchev D. N., “Kinematic Control of Redundant Manipulators”, Proc. 11th. Intl. ‘Symp. on Industrial Robots, Tokyo, Japan, October 1981.
Kosuge K., Furuta K., “Kinematic And Dynamic Analysis of Robot Arm”, IEEE Intl. Conf. on Robotics and Automation, St. Louis Missouri, March 1985.
Luenberger D. G., “Linear And Nonlinear Programming”, Addison - Wesley Publ. Co., Second Edition, 1984.
Mayorga R. V., Wong A. K. C., “On the Singularities Avoidance and the Optimal Path Planning For Robot Manipulators”, 10th IASTED Intl. Symposium on Robotics And Automation, Lugano, Switzerland, June 29-July 2, 1987.
Mayorga R. V., Wong A. K. C., “A Singularities Avoidance Method for the Trajectory Planning of Redundant and Nonredundant Robot Manipulators”, IEEE Intl. C.nf. on Robotics and Automation, Raleigh N. C., March 31-April 3, 1987.
Nakamura Y., Hanafusa H., “Task Priority Based Redundancy Control of Robot Manipulators”, The Robotics Research, 2nd Intl. Symposium, Eds. H. Hanafusa, H. Inoue, MIT, 1985.
Stewart G. W., “Introduction To Matrix Computations”, Academic Press, 1973.
Suh K. C., Hollerbach J. M., “Local Versus Global Torque Optimization of Redundant Manipulators”, IEEE Intl. Conf. on Robotics and Automation, Raleigh N.C., March 31-April 3, 1987.
Uchiyama M., Schimizu K., Hakomori K., “Performance Evaluation of Manipulators Using The Jacobian And Its Application To Trajectory Planning”, The Robotics Research, 2nd Intl. Symposium, Eds. H. Hanafusa, H. Inoue, MIT, 1985.
Yoshikawa T. “Manipulability And,Redundancy Control of Robotic Mechanisms”, IEEE Intl. Conf. 00n Robotics And Automation, St. Louis Missouri, March 1985.
Yoshikawa T. “Analysis And Control of Robot Manipulators with Redundancy”, The Robotics Research, 1st Intl. Symposium, Eds. M. Brady, R. Paul, MIT 1984.
Wampler II C. W., “Inverse Kinematic Functions For Redundant Manipulators”, IEEE Intl. Conf. on Robotics and Automation, Raleigh N.C., March 31-April 3, 1987.
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Mayorga, R.V., Wong, A.K.C. (1990). On the Optimal Path Planning for Robot Manipulators. In: Taylor, G.E. (eds) Kinematic and Dynamic Issues in Sensor Based Control. NATO ASI Series, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84012-8_10
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DOI: https://doi.org/10.1007/978-3-642-84012-8_10
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