複雑な作業空間におけるロボットナビゲーションのための等角ナビゲーション変換
Conformal Navigation Transformations with Application to Robot Navigation in Complex Workspaces
任意形状の障害物がある作業空間で、等角ナビゲーション変換を用いて衝突のないロボットナビゲーションを実現する手法を提案し、フィードバック制御器を導出した。
著者: Li Fan, Jianchang Liu, Wenle Zhang, Peng Xu
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
Navigation functions provide both path and motion planning, which can be used to ensure obstacle avoidance and convergence in the sphere world. When dealing with complex and realistic scenarios, constructing a transformation to the sphere world is essential and, at the same time, challenging. This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with obstacles of arbitrary shapes. The properties of the conformal navigation transformation, including uniqueness, invariance of navigation properties, and no angular deformation, are investigated, which contribute to the solution of the robot navigation problem in complex environments. Based on navigation functions and the proposed transformation, feedback controllers are derived for the automatic guidance and motion control of kinematic and dynamic mobile robots. Moreover, an iterative method is proposed to construct the conformal navigation transformation in a multiply-connected workspace, which transforms the multiply-connected problem into multiple simply-connected problems to achieve fast convergence. In addition to the analytic guarantees, simulation studies verify the effectiveness of the proposed methodology in workspaces with non-trivial obstacles.
