任意の3R直列マニピュレータがカスピダルとなるための必要十分条件
Necessary and sufficient condition for a generic 3R serial manipulator to be cuspidal
3R直列ロボットの逆運動学を幾何学的に再解釈し、特異点を経ずに姿勢を切り替えられる「カスピダル」性の必要十分条件が、直交型に限らず任意の一般的3Rロボットでも作業空間のカスプ点の存在であることを証明した。
著者: Durgesh Haribhau Salunkhe, Christoforos Spartalis, Jose Capco, Damien Chablat, Philippe Wenger
分類: cs.RO
原文アブストラクト
Cuspidal robots can travel from one inverse kinematic solution to another without meeting a singularity. The name cuspidal was coined based on the existence of a cusp point in the workspace of 3R serial robots. The existence of a cusp point was proved to be a necessary and sufficient condition for orthogonal robots to be cuspidal, but it was not possible to extend this condition to non-orthogonal robots. The goal of this paper is to prove that this condition stands for any generic 3R robot. This result would give the designer more flexibility. In the presented work, the geometrical interpretation of the inverse kinematics of 3R robots is revisited and important observations on the nonsingular change of posture are noted. The paper presents a theorem regarding the existence of reduced aspects in any generic 3R serial robot. Based on these observations and on this theorem, we prove that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal.
