多載具擬剛體隊形之設計

Abstract

本論文主要為發展一可改變隊形之多載具運動模式，將擬剛體形變的理論應用在最佳化的隊形設計上，整個系統的隊形變化由一齊性形變張量所規範，稱之為擬剛體隊形，每一個載具的位置可透過隊形幾何中心的位置及齊性形變張量求得。從幾何的觀點來看，擬剛體運動之系統可用 來描述，係一維度為12的空間，設計一個隊形在空間中移動的問題可以簡化為求解12個系統變數。避開障礙物及到達目標的最佳化設計成本函數可以由系統變量及隊形的初始狀態來表示，所獲得的最佳化隊形可以容許發生旋轉、拉伸及剪應變等變形。根據實例設計結果驗證我們的研究是可行且有效的。

The main purpose of this thesis is to design the motion of a multi-agent system which can change its formation. We apply the pseudo-rigid body theory to design the optimal formation, which can be controlled by a homogenous deformation gradient tensor. Such concept is called a Pseudo-Rigid Formation. The position of each agent can be determined by the position of geometric center and a homogenous deformation gradient tensor. In geometry, the configuration space is the product of the three dimensional real vector space and the general linear group , a twelve dimensional manifold. The design of the formation for a system with many agents moving in space can be then transformed into that of the twelve system variables. The objective function in the optimal design for collision avoidance and destination approaching can be represented by the system variables and the initial configuration of the system.The optimal formation of our system are allowed to translate, rotate, stretch, and shear. By the design examples, the proposed scheme is feasible and effective.