分段式NURBS曲線與修正型Dijkstra演算法實現路徑規劃與應用

Abstract

本文目的是以飛機作為載具模型，在環境模型的基礎下，建構一條連接起始點(起飛)到終點(降落)的非均勻有理B-spline (NURBS)平滑曲線，除了滿足飛行載具飛行姿態、轉彎時最小曲率半徑等限制，以及其起始點(起飛)到終點(降落)的運動約束之外，並可成功地避開障礙區域(類如禁航區或山丘等)。首先在飛行平面上，因環境而造成的障礙區域的邊界，我們加入一個凸邊形的安全防護網，防止飛行載具與障礙區域發生碰撞。其次，本文提出修正型Dijkstra演算法，以凸邊形障礙區域的頂點為網路節點，最短路徑為代價評估函數，尋找一條連接起始點(起飛)與終點(降落)的最佳避障路徑。我們採用分段NURBS曲線來取代傳統的遞迴表示式，基於B-spline基底函數作為平滑路徑的設計，將曲率限制以及運動約束引入最小路徑的代價函數中，將軌跡規劃的問題轉換成求解約束最佳化的問題。由模擬結果顯示，本文所提出路徑規劃的方法不僅成效良好並且具有可行性。上述作法亦可運用在飛航管制方面，以實現相關規劃與應用。

This paper proposed a solution for the problem of path planning for a flying vehicle (airplane) moving in complex areas. The purpose is to generate a smooth segmental NURBS trajectory connecting the initial point (for taking off) and the final point (for landing) so that no collisions with obstacle areas (such as forbidden regions, or mountain, etc.) under various constraints conditions. The modified Dijkstra’s algorithm will be used to search for the shortest path. Obstacle areas are modeled by polygonal sets with the appropriate safety margins. To find a smooth trajectory which meets the capability of the flying vehicle, the method of segmental NURBS curves is adopted. The curvature restrictions and kinematic constraints are introduced into the constrained optimization problems. The control points are generated to characterize the curve forms. The syntheses of the above concepts lead to successful approaches for path planning, which are demonstrated by simulation results based on a software package using MATLAB GUI toolbox. It’s also good for related flying trajectory planning and application on Air Traffic Control by using the above methods.