3次元空間における閉運動学的鎖の配置構成について
On the Configurations of Closed Kinematic Chains in three-dimensional Space
球面関節で連結されたリンクからなる閉運動学的鎖の配置空間を調べ、対角長パラメータで単純な立方体領域として記述できる場合を見出し、運動計画や特異点解析への応用可能性を数値例で示した。
著者: Gerhard Zangerl, Alexander Steinicke
分類: cs.RO, cs.CG
原文アブストラクト
A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n-3$. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples.