3D列印之路徑規劃演算法於三軸氣壓式並聯機構機械臂之研究

Abstract

本研究旨在發展3D列印的軌跡規劃演算法並應用於三軸氣壓式並聯機構機械臂，置重點於3D列印的軌跡規劃於三軸氣壓式並聯機構機械臂，結合實驗室已發展之三軸氣壓式並聯機構機械臂之運動學分析與控制器設計，以模擬及實際實驗驗證。 在3D列印的軌跡規劃方面，將欲列印的物體，採用圖論(Graph Theory)的向量形式建立。透過深度優先搜尋(Depth-First Search, DFS)定義一個平面的所有分歧路徑，並由基因演算法(Genetic Algorithm, GA)計算如何以最低代價連接所有分歧路徑。最後將每個平面的路徑串接，即可得軌跡規劃。 在三軸氣壓式並聯機構機械臂的運動學分析方面，採用幾何向量的理論與空間中向量迴圈的封閉性質，透過逆向與順向運動學的定義分別推導出致動器與運動平台的關係。 在三軸氣壓式並聯機構機械臂的控制器設計方面，單軸氣壓伺服系統採用雙迴圈回授控制策略，其中包含內圈的壓力控制與外圈的位置控制。根據上述方法，並額外採用逆向動力學控制策略，以實現三軸氣壓式並聯機構機械臂的控制與解決三軸的非線性耦合。 在本論文最後，透過數值模擬，檢測三軸氣壓式並聯機構機械臂之推導模型與3D列印之軌跡規劃的正確性。為證明實用性，藉由實驗室已建立之三軸氣壓式並聯機構機械臂實驗系統的實驗，輸入與數值模擬相同的軌跡，驗證控制器的效能與3D列印整合三軸氣壓式並聯機構機械臂的可行性。

This study aims to develop 3D-printing path planning algorithms and applies to a three-axial pneumatic parallel manipulator. The emphasis is on the research of 3D-printing path planning algorithms, integrating the three-axial pneumatic parallel manipulator which has developed on its kinematic analysis and controller design in lab before, and verifying the performance through the whole system simulations and experiments. In path planning algorithms for 3D printing, the desired-printing object was established from graph theory as vector form. From the view of a layer, all sub-paths are defined through the depth-first search, and the genetic algorithm is used to find the minimum costs linking sub-paths. After cascading all layers, the overall path is accomplished. In analysis of kinematics, the geometric method is introduced to solve the relation of manipulator between actuated joints and moving platform through vector-loop closure equations, including inverse and forward kinematics. In controller design, control strategy of single-axial pneumatic servo system is applied with dual-loop feedback control scheme, i.e. inner pressure control and outer position control. Based on that, controller of three-axial pneumatic parallel manipulator is established with extra inverse dynamics control strategy to decouple the nonlinear terms. Finally, numerical simulations are carried out to verify the correctness of the derived models and the path-planning trajectories. To show the practicality, real-time experiments are implemented in the test rig of three-axial pneumatic parallel mechanism robot with the same trajectories in simulations for testifying the control performance and the possibility of 3D printing integrating with three-axial pneumatic parallel manipulator.