Skip to main content

A STOCHASTIC OFF LINE PLANNER OF OPTIMAL DYNAMIC MOTIONS FOR ROBOTIC MANIPULATORS

  • Conference paper

Abstract

We propose a general and simple method that handles free (or point-to-point) motion planning problem for redundant and non-redundant serial robots. The problem consists of linking two points in the operational space, under constraints on joint torques, jerks, accelerations, velocities and positions while minimizing a cost function involving significant physical parameters such as transfer time and joint torque quadratic average. The basic idea is to dissociate the search of optimal transfer time T from that of optimal motion parameters. Inherent constraints are then easily translated to bounds on the value of T. Furthermore, a stochastic optimization method is used which not only may find a better approximation of the global optimal motion than is usually obtained via traditional techniques but that also handles more complicated problems such as those involving discontinuous friction efforts and obstacle avoidance.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  • Angeles J., 1997, Fundamentals of robotic mechanical systems. Theory, methods, and algorithms,” Springer Edition.

    Google Scholar 

  • Barraquand J., Langlois B., Latomb J. C., 1992, Numerical Potential Field Techniques for robot path planning, IEEE Tr. On Sys., Man, and Cyb., 22(2):224–241.

    Article  Google Scholar 

  • Barraquand J., Kavraki L., Latombe J. C., Li T. Y., Motwani R., Raghavan P., 1996, A random Sampling Scheme for path planning, 7th Int. conf. on Rob. Research ISRR.

    Google Scholar 

  • Bobrow J.E., Dubowsky S., Gibson J.S., 1985, Time- Optimal Control of robotic manipulators along specified paths, The Int. Jour. of Rob. Res., 4 (3), pp. 3–16.

    Google Scholar 

  • Bessonnet G., 1992, Optimisation dynamique des mouvements point à point de robots manipulateurs, Thèse d’état, Université de Poitiers, France.

    Google Scholar 

  • Betts J. T., 1998, Survey of numerical methods for trajectory optimization, J. Of Guidance, Cont. & Dyn., 21(2), 193–207.

    Google Scholar 

  • Chen Y., Desrochers A., 1990, A proof of the structure of the minimum time control of robotic manipulators using Hamiltonian formulation, IEEE Trans. On Rob. & Aut. 6(3), pp. 388–393.

    Google Scholar 

  • Chettibi T., 2000, Contribution à l’exploitation optimale des bras manipulateurs, Magister thesis, EMP, Algiers, Algeria.

    Google Scholar 

  • Chettibi T., 2001a, Optimal motion planning of robotic manipulators, Maghrebine Conference of Electric Engineering, Constantine, Algeria.

    Google Scholar 

  • Chettibi T., Yousnadj A., 2001b, Optimal motion planning of robotic manipulators along specified geometric path, International Conference on productic, Algiers.

    Google Scholar 

  • Chettibi T., Lehtihet H. E., 2002a, A new approach for point to point optimal motion planning problems of robotic manipulators, 6th Biennial Conf. on Engineering Syst. Design and Analysis (ASME), Turkey, APM10.

    Google Scholar 

  • Chettibi T., 2002b, Research of optimal free motions of manipulator robots by non-linear optimization, Séminaire international sur le génie Mécanique, Oran, Algeria.

    Google Scholar 

  • Danes F., 1998, Critères et contraintes pour la synthèse optimale des mouvements de robots manipulateurs. Application à l’évitement d’obstacles, Thèse d’état, Université de Poitiers.

    Google Scholar 

  • Dombre E. & Khalil W., 1988, Modélisation et commande des robots, First Edition, Hermes.

    Google Scholar 

  • Fletcher R., 1987, Practical methods of optimization, Second Edition, Wiley Interscience Publication.

    Google Scholar 

  • Garber M., Lin. M.C., 2002, Constrained based motion planning for virtual prototyping, SM’02, Germany.

    Google Scholar 

  • Glass K., Colbaugh R., Lim D., Seradji H., 1995, Real time collision avoidance for redundant manipulators, IEEE. on Rob. & Aut., 11(3), pp. 448–457.

    Google Scholar 

  • Hull D. G., 1997, Conversion of optimal control problems into parameter optimization problems, J. Of Guidance, Cont. & Dyn., 20(1), 57–62.

    Article  MATH  Google Scholar 

  • Jaques J., Soltine E., Yang H. S., 1989, Improving the efficiency of time-optimal path following algorithms, IEEE Trans. on Rob. & Aut., 5 (1).

    Google Scholar 

  • Kang G. S., McKay D. N., 1986, Selection of near minimum time geometric paths for robotic manipulators, IEEE Trans. on Aut. & Contr., AC31(6), pp. 501–512.

    Article  Google Scholar 

  • Kavraki L., Latombe J. C., 1994, Randomized Preprocessing of Configuration Space for Fast Path Planning, Proc. Of IEEE Int. Conf. on Rob. & Aut., pp. 2138–2139, San Diego.

    Google Scholar 

  • Kavraki L., Svesta P., Latombe J. C., Overmars M., 1996, Probabilistic Roadmaps for Path Planning in High Dimensional Configuration space, IEEE trans. Robot. Aut., 12:566–580.

    Article  Google Scholar 

  • Khatib O., 1986, Real-time Obstacle Avoidance for Manipulators and Mobile Robots, Int. Jour. of Rob. Research, vol. 5(1).

    Google Scholar 

  • Latombe J. C., 1991, Robot Motion Planning, Kluwer Academic Publishers.

    Google Scholar 

  • Latombe J. C., 1999, Motion planning: A journey of, molecules, digital actors and other artifacts, Int. Jour. Of Rob. Research, 18(11), pp. 1119–1128.

    Article  Google Scholar 

  • LaValle S. M., 1998, Rapidly exploring random trees: A new tool for path planning, TR98-11, Computer Science Dept., Iowa State University. http://janowiec.cs.iastate.edu/papers/rrt.ps.

    Google Scholar 

  • LaValle S. M., Kuffner J. J., 1999, Randomized kinodynamic planning, Proc. IEEE Int. Conf. On Rob. & Aut., pp. 473–479.

    Google Scholar 

  • Lazrak M., 1996, Nouvelle approche de commande optimale en temps final libre et construction d’algorithmes de commande de systèmes articulés, Thèse d’état, Université de Poitiers.

    Google Scholar 

  • Macfarlane S., Croft E. A., 2001, Design of jerk bounded trajectories for on-line industrial robot applications, Proceeding of IEEE Int. Conf. Rob. & Aut. pp. 979–984.

    Google Scholar 

  • Martin B. J., Bobrow J. E., 1997, Minimum effort motions for open chain manipulators with task dependent endeffector Proc. of IEEE Int. Conf. on rob. & Aut. Albuquerque, New Mexico, pp. 2044–2049.

    Google Scholar 

  • Martin B. J., Bobrow J. E., 1999, Minimum effort motions for open chain manipulators with task dependent endeffector constraints, Int. Jour. Rob. of Research, 18(2), pp.213–224.

    Google Scholar 

  • Mao Z., Hsia T. C., 1997, Obstacle avoidance inverse kinematics solution of redundant robots by neural networks, Robotica, 15, 3–10.

    Article  Google Scholar 

  • Mayorga R. V., 1995, A framework for the path planning of robot manipulators, IASTED third Int. Conf. on Rob. and Manufacturing, pp. 61–66.

    Google Scholar 

  • Mitsi S., Bouzakis K. D., Mansour G., 1995, Optimization of robot links motion in inverse kinematics solution considering collision avoidance and joints limits, Mach. & Mec. Theory,30 (5), pp. 653–663.

    Article  Google Scholar 

  • Ola D., 1994, Path-Constrained robot control with limited torques. Experimental evaluation, IEEE Trans. On Rob. & Aut., 10(5), pp. 658–668.

    Article  Google Scholar 

  • Overmars M. H., 1992, A random Approach to motion planning, Technical report RUU-CS-92–32, Utrecht University.

    Google Scholar 

  • Piazzi A., Visioli A., 1998, Global minimum time trajectory planning of mechanical manipulators using internal analysis, Int. J. Cont., 71(4), 631–652.

    Article  MathSciNet  MATH  Google Scholar 

  • Pfeiffer F., Rainer J., 1987, A concept for manipulator trajectory planning, IEEE J. of Rob. & Aut., Ra-3 (3): 115–123.

    Article  Google Scholar 

  • Powell M. J., 1984, Algorithm for non-linear constraints that use Lagrangian functions, Mathematical programming, 14, 224–248.

    Article  MathSciNet  Google Scholar 

  • Pontryagin L., Boltianski V., Gamkrelidze R., Michtchenko E., 1965, Théorie mathématique des processus optimaux, Edition Mir.

    Google Scholar 

  • Rana A.S., Zalazala A. M. S., 1996, Near time optimal collision free motion planning of robotic manipulators using an evolutionary algorithm, Robotica, 14, pp. 621–632.

    Article  Google Scholar 

  • Richard M. J., Dufourn F., Tarasiewicz S., 1993, Commande des robots manipulateurs par la programmation dynamique, Mech. Mach. Theory, 28(3), 301–316.

    Article  Google Scholar 

  • Rebai S., Bouabdallah A., Chettibi T., 2002, Recherche stochastique des mouvements libres optimaux des bras manipulateurs, Premier congrès international de génie mécanique, Constantine, Algérie.

    Google Scholar 

  • Tan H. H., Potts R. B., 1988, Minimum time trajectory planner for the discrete dynamic robot model with dynamic constraints, IEEE Jour. Of Rob. & Aut.4(2), 174–185.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this paper

Cite this paper

Chettibi, T., Haddad, M., Rebai, S., Hentout, A.E. (2006). A STOCHASTIC OFF LINE PLANNER OF OPTIMAL DYNAMIC MOTIONS FOR ROBOTIC MANIPULATORS. In: BRAZ, J., ARAÚJO, H., VIEIRA, A., ENCARNAÇÃO, B. (eds) INFORMATICS IN CONTROL, AUTOMATION AND ROBOTICS I. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4543-3_8

Download citation

  • DOI: https://doi.org/10.1007/1-4020-4543-3_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4136-5

  • Online ISBN: 978-1-4020-4543-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics