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Minimum-Jerk Trajectory Planning of a 3-DOF Translational Parallel Manipulator

[+] Author Affiliations
Song Lu

University of Macau, Taipa, Macao, China

Yangmin Li

University of Macau, Taipa, Macao, ChinaTianjin University of Technology, Tianjin, China

Paper No. DETC2015-46866, pp. V05CT08A009; 7 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5C: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5714-4
  • Copyright © 2015 by ASME


Since jerk-limiting is universally recognized to possess the advantages of reducing residual vibration and improving accuracy, this paper utilizes a minimum-jerk trajectory planning algorithm in trajectory planning of a three degree-of-freedom 3-Prismatic-Universal-Universal (3PUU) translational parallel manipulator. The trajectory execution time is set to fixed time duration. The sequence of joint positions are derived by a series of predefined via-points in Cartesian space through kinematic inversion. In order to generate a trajectory featuring great continuity and fine smoothness, a piecewise fifth-order polynomial is used to interpolate the joint position series and generate a smooth trajectory characterized by continuous velocity, acceleration, and jerk. The minimum jerk trajectory planning algorithm, which minimizes the maximum of the absolute value of joints’ jerk, is actually a constrained minimax optimization problem. Subjecting to the specified limitations of kinematic constraints, this multi-variables constrained optimization problem is solved by the sequential quadratic programming (SQP) strategy. The simulated results demonstrate that this trajectory planning algorithm for the designed parallel manipulator is effective and feasible.

Copyright © 2015 by ASME



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