並列ロボットの特異点回避経路を検証する代数的手法
An algebraic method to check the singularity-free paths for parallel robots
グレブナー基底を用いた消去法で軌道の多項式方程式を関節空間に射影し、ヤコビ行列式が2姿勢間で零になるかを時間の関数として解析的に判定する手法を提案。Orthoglideで検証。
著者: Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz
分類: cs.RO
原文アブストラクト
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{\"o}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.
