- 學位論文
擬剛體編隊設計之最佳虛擬位能函數研究
Optimal Virtual Potential Functions in Pseudo-Rigid Formation Design
摘要
本論文主旨為發展一套多載具團隊運動編隊設計法，使得多載具系統能藉由改變隊形來迴避障礙物並到達目的地。我們將擬剛體的形變理論應用在多載具編隊設計上，使多載具隊伍的形狀可由一組空間齊性形變張量來規範，容許隊形旋轉、拉伸以及剪變。相較於剛體隊形，擬剛體隊形能夠適應複雜度較高的環境。整個規劃方案分成兩個部分，第一個部分為路徑規劃，利用快速探索隨機樹(RRT)並配合軌跡平滑技巧建構一條適合的隊伍中心路徑；另一個部分為擬剛體編隊，編隊方法是利用計算虛擬位能函數極小值得到擬剛體形變張量，並依需求調整虛擬位能函數參數找到最佳函數，再由最佳函數解得最佳形變張量。最後在整合路徑規劃和擬剛體編隊時，使用篩選孤立障礙物法使兩個部分的規劃優勢互補。一般在使用位能函數設計路徑時，多採用固定位能函數，找到最佳路徑。我們則是將位能函數本身的設計最佳化納入，使得路徑或隊形的設計更為理想。根據設計結果，我們所提出的規劃方案可適應於多種不同的環境，同時保有隊伍的整體性，換而言之，此方案是可行且有效的。
並列摘要
The main purpose of this thesis is to develop a formation design method of a multi-vehicle system, which can produce collision-free paths and reach the destination by changing the formation of the system. We apply the pseudo-rigid body theory to the formation design. The formation can be determined by a homogenous deformation tensor, which permits rotation, stretch and shear. Comparing to rigid body formation, pseudo-rigid formation can adapt to environments of higher complexity. The total scheme is divided into two parts. The first part is path planning, in which are used Rapidly-exploring Random Tree (RRT) method along with some path-smoothing algorithms design to find a proper path for the system center. The second part is pseudo-rigid formation, in which the minimum of a virtual potential function is found to obtain the deformation tensor. Here, the function parameters of the virtual potential are adjusted according to the needs, and the optimal deformation tensor is computed. Finally, the path planning and the pseudo-rigid formation design are integrated to yield an overall scheme. In most design method of using potential functions, the function is fixed. Instead, here the optimal design of the potential function is taken into consideration. Such that the overall design become more desirable. According to the design examples, our approach can be used in a variety of environments, which shows that, the proposed scheme is feasible and effective.