KSME Journal

, 10:443 | Cite as

A global collision-free path planning using parametric parabola through Geometry Mapping of obstacles in robot work space

  • Ihn Namgung


In this paper, a new algorithm for palnning collision-free path connecting from start to target point is developed using Bézier curve of order two. The control point, i. e. the mid-point of quadratic Bézier curve, determines the shape of parabola and constitutes the Control Point Space, and this process is difined a Geometry Mapping. After Geometry Mapping of all obstacles, the clear area of CPS, an area not occupied by obstacle images, identifies collision-free path. The path planning algorithm, heance, transform path planning problem in Euclidian Space to point selection problem in CPS. The calculations involved in the algorithm do not require iterative procedures and all the formulas of the solution are derived in closed form. A CPS completely filled with obstacle images indicates that path planning based on parabola is not possible and requires higher order curve with more than one control point.

Key Words

Robot Path Planning Geometry Mapping Robot Task Planning Collision Avoidance 


  1. Bézier, P., 1972,Numerical Control-Mathematics and Application, Translated by Forrest A. R. and Pankhurst, A. F., Wiley John & Sons, New York.Google Scholar
  2. Brooks, R. A., 1983, “Solving the Find-Path Problem by Good Representation of Free Space,”IEEE Trans. on Systems, Man and Cybernetics, Vol. SMC-13, No. 3, pp. 190–197.MathSciNetGoogle Scholar
  3. Faux, I. D. and Paratt, M. J., 1979,Computational Geometry for Design and Manufacture, John Wiley & Sons, New York.MATHGoogle Scholar
  4. Khosla, P. and Volpe, R., 1988, “Superquadric Artificial Potential for Obstacle Avoidance and Approach,”IEEE Proc. Int. Conf. on Robotics and Automation, Philadelphia, pp. 1778–1784.Google Scholar
  5. Lozano-Pérez, T., 1987, “A Simple Motion-Planning Algorithm for General Robot Manipulators,”IEEE J. of Robotics and Automation, Vol. RA-3, No. 3, pp. 224–238.CrossRefGoogle Scholar
  6. Namgung, Ihn, 1989, “Planning Collision-Free Paths with Applications to Robot Manipulators,” Ph. D. Dissertation, University of Florida.Google Scholar
  7. Shin, D. H. and Ollero, A., 1995, “Mobile Robot Path Planning for Fine-Grained and Smooth Path Specifications,”Journal of Robotic Systems, Vol. 12(7), pp. 491–503.MATHCrossRefGoogle Scholar
  8. Volpe, R. and Khosla, P., 1987, “Artificial Potentials with Elliptical Isopotential Contours for Obstacle Avoidance,”IEEE Proc. 26th Conf. Decision and Control, Los Angeles, pp. 180–185Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1996

Authors and Affiliations

  • Ihn Namgung
    • 1
  1. 1.Mechanical Systems EngineeringKorea Atomic Energy Research InstituteYusong Taejon

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