3-PUU氣壓平行機構機械臂設計分析與軌跡追蹤伺服控制結合立體影像量測系統之研究

Abstract

本研究旨在提出新型三自由度氣壓平行機構機械臂，利用平行機構和氣壓系統的優勢-響應快、速度佳、成本低、自由度多、安全性高，發展兩套新型的平行機構機械臂，分別為鉛直型三自由度氣壓平行機構機械臂與金字塔型三自由度氣壓平行機構機械臂，以光學尺量測無桿式氣壓缸位置。 機構設計策略上，兩種型式之三自由度氣壓平行機構機械臂，皆選定無桿式氣壓缸作為致動器，採用閉合鏈的設計方式，以鉛直型與金字塔型之組合方式，進行機台設計，搭載連桿機構裝置與萬向接頭，進行整機設計與組裝，展現出結構簡單、易於量測、高速度、低成本、高安全性等優點。 機構分析上，首先進行機構自由度分析，接著，重點於運動學方程式理論的推導，採用D-H座標轉換，求得各桿件座標間的相對關係，得到順向與逆向運動學之解析解，並透過Matlab模擬軟體，驗證所推得的運動學方程式之正確性。由模擬結果顯示，所推得順向與逆向運動學解析解，確實符合鉛直型與金字塔型平行機構機械臂之架構。 控制器設計方面，為了能以伺服氣壓控制實現機械臂，採用以函數近似法為基礎之適應性滑動模式控制結合H∞追蹤補償之控制器，對三軸無桿式氣壓缸進行即時位置及軌跡控制，藉由代入所推得的機構運動學理論方程式，實現鉛直型與金字塔型三軸氣壓平行機構機械臂端點之運動控制。除此之外，利用立體影像量測系統，測量平台端點運動位置，量測機械臂平台端點實際運動情形，並與理論值與計算值比較，進而改善端點平台誤差值。 最後，分別建立鉛直型與金字塔型三軸氣壓平行機構機械臂實驗系統，整合鉛直型與金字塔型三軸氣壓平行機構機械臂系統、控制系統、立體影像量測系統，規畫不同之機械臂端點三維空間軌跡，實際實驗驗證其控制性能及可行性，實驗結果顯示，鉛直型與金字塔型三軸氣壓平行機構機械臂均可成功地實現。

This study aims to develop two novel three-degree-of-freedom (3-DOF) translational parallel manipulators driven by the nonlinear pneumatic servo system for path tracking servo control with a stereo vision measurement system. The 3-PUU vertical pneumatic parallel manipulator (VPPM) and the 3-PUU pyramid pneumatic parallel manipulator (PPPM) are the proposed parallel manipulators designed and implemented in this thesis. In detail, the mechanical system and the control system are the primary parts for developing the pneumatic 3-DOF translational parallel manipulators. In the mechanical system, each of the pneumatic 3-DOF translational parallel manipulators contains three serial chains, a fixed base, a movable platform and a pneumatic servo system. Based on the structure design theory of the mechanism, the end-effector of the parallel manipulators can achieve three-dimensional motions in the X-Y-Z coordinate system through the three pneumatic cylinders with ideal limb structures. Moreover, the mobility of the manipulator is analyzed by the Kutzbach-Gruebler’s equation. In addition, according to the characteristics of the mechanism, the inverse kinematics and the forward kinematics of the parallel manipulators are proposed by the coordinate transformation theory. The D-H notation method is used to resolve the problem of kinematics inclusive of inverse kinematics and forward kinematics in analytical forms for given the end-effector poses, which is used in the path planning of the end effetor. The pneumatic actuators for the three axes are modeled including the dynamics of the pneumatic servo valve and the cylinder. In the control system, the control scheme is performed to control the three pneumatic actuators for following the computed paths that are solved from the target path of the end effector in the path planning. In order to control the proposed pneumatic parallel manipulators and improve the path tracking accuracy for the pneumatic parallel manipulators, a Fourier series-based adaptive sliding mode controller with H∞ tracking performance (FSB-ASMC+ H∞ controller) is proposed for controlling the pneumatic actuators. The proposed controller first employs a Fourier series-based functional approximation technique to estimate the dynamic models and time-varying uncertainties of the system. Next, further efforts are made to improve the dynamic tracking performance by combining the H∞ tracking strategy with an adaptive sliding-mode control method to make the derived controller robust against approximation errors, un-modeled dynamics and disturbances. In addition, the stereo vision measurement system is used to measure the end-effector of the manipulator. Through a sensor collaboration strategy, the error between the calculated position and the stereo vision measuring position of the end-effector can be improved. The simulations and experiments illustrate the effectiveness and usefulness of the proposed manipulators.