2017年 詹景裕教授基於最小生成樹方法和三角剖分的概念，在O(nlog n)的時間複雜度下，提出多面體表面上完全區域覆蓋路徑規劃演算法，其中n為三角剖分後的三角形數目。這項研究應用一個展開化過程，將多面體表面展開化為二維平面可供工業噴漆機器人進行路徑規劃。與先前技術文獻相比，該方法將二維平面完全覆蓋的觀念應用到多面體表面噴漆問題，並且透過嶄新的演算法來降低時間複雜度。本文透過生成樹方法以及將子三角形組合成大三角形的概念，在O(n)時間複雜度下完成多面體表面噴漆問題。此方法可使機器人噴漆問題達到時間複雜度之最佳化與有效降低轉彎次數。該工業噴漆機器人會根據已規劃好的區域進行走訪且以路徑不重疊方式返回至起始點。根據效能分析，我們的方法對於多面體表面之噴漆已證明為最快的演算法，且可使完整區域覆蓋規劃之路徑長度為最短並具有合理的轉彎次數。

This thesis presents the complete area coverage planning for industrial painting robots on polygonal surfaces with O(n) time, where n is the number of triangles. We unfold a three-dimensional object into a two-dimensional polygonal model with triangle mesh for the industrial painting robot to perform path planning. The painting robot implements the concepts of spanning tree, decomposing triangles, and combining the decomposed sub triangles into large triangles for path planning. The industrial painting robot will start and return to the original starting point without any energy and time constraints. It will travel through all the arrangement of areas planned by the method without any overlap. Through the performance analysis, the proposed method is proven to be the fastest algorithm with minimal path length and a reasonable number of turns for solving the complete area coverage planning for industrial painting robots on polygonal surfaces.

摘要 I
Abstract II
誌謝辭 III
Table of Contents IV
List of Figures VI
List of Tables VII
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation and Objective 3
1.3 Research Framework 3
Chapter 2 Literature Review 5
2.1 Complete Area Coverage on Polygonal Surfaces 5
2.2 Continuous Unfolding Using Motion Planning 6
Chapter 3 Methodology and Algorithm 7
3.1 Methodology 7
3.1.1 Unfold 7
3.1.2 Centroids 10
3.1.3 Connected Graph and Spanning Tree 11
3.1.4 Decomposition of a Triangle 12
3.1.5 Combining Small Triangles into a Large Triangle 13
3.1.6 Degree for Circumnavigation 14
3.1.7 Painting Direction 16
3.2 Algorithm 17
Chapter 4 Performance Analysis 19
Chapter 5 Experimental Result 21
Chapter 6 Conclusion 30
References 31

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