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An algebraic method to check the singularity-free paths for parallel robots

Abstract : Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gröbner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.
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Contributor : Damien Chablat <>
Submitted on : Thursday, April 16, 2015 - 2:38:12 PM
Last modification on : Friday, April 10, 2020 - 5:23:02 PM
Long-term archiving on: : Tuesday, April 18, 2017 - 9:36:35 PM


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  • HAL Id : hal-01142989, version 1
  • ARXIV : 1505.06842


Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. An algebraic method to check the singularity-free paths for parallel robots. International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, ASME, Aug 2015, Boston, United States. ⟨hal-01142989⟩



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