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

Ranjan Jha (1) , Damien Chablat (1) , Fabrice Rouillier (2, 3) , Guillaume Moroz (4)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility

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.

Domaines: Robotique [cs.RO]

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⟩