An algebraic method to check the singularity-free paths for parallel robots
This addresses the critical issue of avoiding singular configurations during robot programming, which is incremental as it builds on existing algebraic techniques for specific robotic applications.
The paper tackles the problem of trajectory planning for parallel robots by presenting an algebraic method to check for singularity-free paths, enabling the use of larger and more complex workspaces beyond simple shapes like cubes or spheres.
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.