Evaluation of Parameterizations in Local Lie-Algebraic Motion Planning

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


In this paper some parameterizations of controls are examined in a Lie algebraic method of motion planning for driftless nonholonomic systems. The purpose of the examination is to establish how numerous the parameterization should be and which items of a harmonic basis are to be included into the parameterization. An algorithm is presented to evaluate parameterizations without (or reduced) impact of a local, desired direction of motion.


Nonholonomic systems Motion planning Control parameterization Evaluation 


  1. 1.
    LaValle, S.: Planning Algorithms. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  2. 2.
    Jakubiak, J., Tchon, K.: Motion planning in velocity affine mechanical systems. Int. J. Control 83(9), 1965–1974 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ratajczak, A., Tchon, K.: Parametric and non-parametric jacobian motion planning for non-holonomic robotic systems. J. Intell. Rob. Syst. 77(3), 445–456 (2015). Scholar
  4. 4.
    Duleba, I.: Algorithms of Motion Planning for Nonholonomic Robots. WUST Publ. House, Wroclaw (1998)zbMATHGoogle Scholar
  5. 5.
    Duleba, I.: Kinematic models of doubly generalized n-trailer systems. J. Intell. Rob. Syst. 94(1), 135–142 (2019)CrossRefGoogle Scholar
  6. 6.
    Strichartz, R.: The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations. J. Funct. Anal. 72, 320–345 (1987)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Spivak, M.: A Comprehensive Introduction to Differential Geometry, 3rd edn. Publ or Perish Inc., Houstron (1999)zbMATHGoogle Scholar
  8. 8.
    Duleba, I., Khefifi, W.: Pre-control form of the gCBHD formula for affine nonholonomic systems. Syst. Control Lett. 55(2), 146–157 (2006)CrossRefGoogle Scholar
  9. 9.
    Chow, W.: Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann. 117(1), 98–105 (1939)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Nakamura, Y.: Advanced Robotics: Redundancy and Optimization. Addison-Wesley Publ., Boston (1991)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Cybernetics and RoboticsWroclaw University of Science and TechnologyWroclawPoland

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