双対四元数とリー微分を用いたパラレルロボットの解析
Using Lie derivatives with dual quaternions for parallel robots
双対四元数にリー微分を導入し、パラレルロボットのアクチュエータがエンドエフェクタに与える影響の解析や順運動学の解法、運動方程式の導出を行った論文。
著者: Stephen Montgomery-Smith, Cecil Shy
分類: cs.RO
原文アブストラクト
We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.
