The application of spline functions to trajectory generation for computer-controlled manipulators

  • C. C. Cook
  • C. Y. Ho


This paper describes how cubic spline functions may represent both the trajectory of the tool tip of the manipulator hand in three space and the trajectories of the manipulator joints in time. Mathematically, the curve is continuous through the second derivative providing continuous velocity and acceleration functions for the tool tip moving along its trajectory. The boundary conditions for liftoff and setdown of tool tip are also accommodated. This approach offers flexibility, computational efficiency, and a compact representation


Spline Function Seam Welding Joint Position Manipulator Joint Trajectory Generation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    User’s Guide to VAL—A Robot Programming and Control System, Unimation Inc., June 1980.Google Scholar
  2. 2.
    Rogers, P. F. and Adams, J. A., Mathematical Elements for Computer Graphics, McGraw-Hill, 1976.Google Scholar
  3. 3.
    Churchhill, R. V., Brown, J. W., and Verhhey, R. F., Complex Variables and Applications, McGraw-Hill, 1976.Google Scholar
  4. 4.
    Ahlberg, J. H., Nelson, E. N., and Walsh, J. L., The Theory of Splines and Their Application, Academic Press, 1967.Google Scholar
  5. 5.
    Paul, R. C., Modeling Trajectory Calculation and Servoing of a Computer Controlled Arm, Ph.D. Dissertation, Stanford University, 1972.Google Scholar

Copyright information

© Crane Russak & Company Inc 1984

Authors and Affiliations

  • C. C. Cook
    • 1
  • C. Y. Ho
    • 2
  1. 1.Autographix, Inc.WalthamUSA
  2. 2.Computer Science DepartmentUniversity of Missouri-RollaRollaUSA

Personalised recommendations