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arXiv · 1505.06842

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

Ranjan Jha·Damien Chablat·Fabrice Rouillier·Guillaume Moroz
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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 Gr{ö}bner 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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Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. 2015-05-26. An algebraic method to check the singularity-free paths for parallel robots. https://arxiv.org/abs/1505.06842

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