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Hybrid Method of Motion Planning for Driftless Systems

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Part of the book series: GeoPlanet: Earth and Planetary Sciences ((GEPS))

Abstract

In this paper a hybrid motion planning method is presented that couples a Lie-algebraic method with a Newton algorithm. The aim of the hybridization is to preserve advantages of both methods while avoiding their disadvantages. A few simulations performed on a model of the free-floating planar double pendulum placed atop of a base illustrate usefulness of the hybridization.

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References

  • Chow WL (1939) Uber systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math Ann 117(1):98–105

    Google Scholar 

  • Divelbiss AW, Wen J (1993) Nonholonomic path planning with inequality constraints. IEEE Conf Decis Control 3:2712–2717

    Google Scholar 

  • Dubowsky S, Papadopoulos E (1993) The kinematics, dynamics, and control of free-flying and free-floating space robotic system. IEEE Trans Rob and Autom 9(5):531–542

    Article  Google Scholar 

  • Duleba I (1998) Algorithms of motion planning for nonholonomic robots. Wroclaw University of Technology Publishing House, Wrocław

    Google Scholar 

  • Duleba I, Opalka M, (2013) Continuous controls for a sequence of motion plannings based on the endogenous configuration space method. In: International Workshop on Robot, Motion and control, Wasowo, Poland, Piscataway NJ, IEEE, pp 174–179

    Google Scholar 

  • Duleba I, Sasiadek J (2003) Nonholonomic motion planning based on Newton algorithm with energy optimization. IEEE Trans Control Syst Technol 11(3):355–363

    Article  Google Scholar 

  • Gantmacher FR (1988) Matrix theory. Nauka, Moscow

    Google Scholar 

  • Lafferriere, G., Sussmann, H. (1991) Motion planning for controllable systems without drift. IEEE Conf Rob Autom pp 1148–1153

    Google Scholar 

  • LaValle SM (2006) Planning algorithms. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Murray RM, Sastry SS (1993) Nonholonomic motion planning: steering using sinusoids. IEEE Trans Autom Control 38(5):700–716

    Article  Google Scholar 

  • Nakamura Y (1991) Advanced robotics: redundancy and optimization. Addison Wesley, New York

    Google Scholar 

  • Rouchon P, Fliess M, Levine J, Martin P (1993) Flatness, motion planning and trailer systems. IEEE Conf Decis Control 3:2700–2705

    Google Scholar 

  • Strichartz RS (1987) The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations. J Funct Anal 72(2):320–345

    Article  Google Scholar 

  • Tchon K, Jakubiak J (2003) Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms. Int J Control 26(14):1387–1419

    Article  Google Scholar 

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Correspondence to Ignacy Duleba .

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Duleba, I., Opalka, M. (2015). Hybrid Method of Motion Planning for Driftless Systems. In: Sąsiadek, J. (eds) Aerospace Robotics II. GeoPlanet: Earth and Planetary Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-13853-4_3

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