以位能場為基礎的物體模型及其應用

Abstract

在本論文中，我們提出以位能場為基礎的物體模型，並將其應用在一些二維及三維的問題上。在解決路徑規劃問題方面，利用位能場模型來表示工作空間中的物體是一種常見的方法，在[1]中即利用牛頓位能場模型來達到對障礙物的避碰，其中假設物體及障礙物表面都帶均勻的電荷；而在本論文中，我們考慮非均勻分佈的位能場模型，並把它應用到路徑規劃問題上面。同時也將該路徑規劃演算法推廣到三維空間中，所利用的是[2]中所提出的廣義位能場模型．根據演算法，我們可以利用物體與障礙物之間的推斥力與轉矩來調整移動物體的位置及角度，讓物體在行經障礙物之間的瓶頸區域時，能保持最安全的距離以避免與障礙物發生碰撞。 除此之外，我們把在[3]中所提出以位能場為基礎的二維骨架抽取演算法推廣到三維空間中，該方法是利用找尋物體內部由廣義位能場所產生的位能谷點來求得一個物體的骨架，與一般定義的三維物體骨架(面)不同的地方是，我們的方法找出的骨架完全是一維的曲線，這種一維的骨架較骨架面顯得直接且實際。另外本演算法的特點是它不會受物體表面雜訊的影響，可以直接找到部分的骨架，而在計算複雜度上又相當地低。最後，我們更進一步利用上述骨架抽取的演算法來求得一個三維物體的廣義圓柱體表示法。實驗的結果顯示，我們所求得的表示法較某些特殊型態的廣義圓柱體更近似原來的物體，因為我們不會限制圓柱體的主軸方向與截面的形狀；反過來，也可以由我們的廣義圓柱體表示法，經由限制主軸與截面形狀的方式來得到一些簡化的表示法。

Potential-based object models and their applications in several 2D and 3D problems are considered in this dissertation. One of existing approaches to path planning problems uses a potential function to represent the topological structure of the free space. Newtonian potential was used in [1] to represent object and obstacles in the 2D workspace wherein their boundaries are assumed to be uniformly charged. In this dissertation, more general, non-uniform distributions are considered. A 3D extension of the above potential-based path planning approach is also proposed. The algorithm is based on a generalized potential model of workspace [2] 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 potential model are used to adjust the position and orientation of the object so as to keep it away from the obstacles while passing through a bottleneck in the free space. In addition, the potential-based skeletonization approach for 2D MAT (media axis transform) [3], which identifies object skeleton as potential valleys using a Newtonian potential model in place of distance function, is generalized to three dimension in this dissertation. While the medial axis (surface) is 2D in general for a 3D object, the potential valleys, being one dimensional, form a more realistic skeleton. Other desirable attributes of the algorithm include the stability against perturbations of the object boundary, the flexibility to obtain partial skeleton directly, and low time complexity. Finally, the potential-based skeletonization algorithm is further extended to obtain a shape description of 3D objects based on generalized cylinder (GC) representation. Simulation results demonstrate that the derived GC representation will yield better approximation of object shape than that based on simpler subclasses of GC since there is, in principle, no restriction on the topology of the GC axis and the shape of the cross-sections. On the other hand, any subclass of the GC which has a simpler GC topology may also be obtained from the potential-based representation through appropriate adjustments of its cross-sections as well as axis direction.