利用位能場做三維物體之路徑規劃

Abstract

路徑規劃之目的在於使行進的物體在自由空間中由起點到達終點且不與障礙物發生任何的碰撞，本論文則是在探討如何利用位能場模型做三維物體的路徑規劃。我們是以廣義位能場模型來代表三維空間中的障礙物與移動物體。該模型假設任何三維物體的周界均勻的帶著正電荷，藉由障礙物對移動物體的推斥力來調整移動物體的位置與姿勢，以達到安全地避開障礙物並且不與之發生碰撞。在路徑規劃問題中，在空間中最容易發生碰撞的部份為瓶頸，而本論文的目的就是要利用位能場模型來協助物體通過瓶頸。本論文的路徑規劃演算法，除了能將三維物體順利通過障礙物的瓶頸，另外物體在移動的過程中的路徑亦是極為平順的。由實驗的結果看來，此一位能場模型的確是一個兼具理論與實用的模型。

The purpose of path planning is to move a robot from start position to destination with no collision with any obstacles. In this thesis, we consider the path planning of 3D objects based on a generalized potential model which assumes that the boundary of every 3D object is uniformly charged. According to the proposed approach, the repulsive force and torque between the moving object and the obstacles due to the above model is used to modify the position and orientation of the object so as to keep the moving object away from the obstacle. In the path planning, for the bottleneck region of the 3D space where collision between the moving object and the obstacles is most likely, the goal of the proposed approach is to help the 3D object to avoid the obstacles using potential field. According to the simulation results, a 3D object can indeed move through the bottleneck region safely and smoothly. Finally, the proposed potential field is analytically tractable which makes the path planning efficient and practical.