三軸角錐形氣壓式並聯機構機械臂分析及控制之研究

Abstract

本研究旨在針對三軸角錐形氣壓式並聯機構機械臂進行分析及控制，結合並聯機構和氣壓伺服系統之優點，包括高響應、高速度、多自由度及低成本等，本研究發展出一套具有三自由度的氣壓式並聯機構機械臂系統。此機械臂系統在機構設計上，選用無桿式氣壓缸作為致動器，採用封閉鏈設計方式，搭配平行連桿組件與球狀關節，進行機台設計與組裝，並且在空間規劃上將三軸氣壓缸致動器排列成一角錐形式之幾何結構以換取較大的工作空間。 系統分析上分為兩部分。第一部份為並聯機構機械臂之運動學分析，此部分採用幾何向量方法，利用空間中向量迴圈的封閉性質建立出致動器與運動平台端點間之逆向及順向運動關係，推導逆向與順向運動學之解析解，並藉此進一步推導出機械臂的Jacobian矩陣，得到致動器與運動平台間的速度關係，再透過Matlab數值分析軟體，進行逆向與順向運動學模擬，驗證所推得的運動學模型之正確性。第二部分為系統的動態分析，此部分包括了氣壓伺服系統的數學模型推導以及並聯機構機械臂之動態模型建立，其中在機械臂動態模型建立上採用動力學的虛功原理進行動態推導，並利用Simulink軟體進行機械臂系統模型的動態模擬。 控制器設計方面，本研究針對單軸氣壓伺服系統採用雙迴圈回授控制策略，將氣壓缸位置及內部壓差做為回授信號進行氣壓缸致動器的位置追蹤控制。針對三軸並聯機構機械臂，本研究將所推得的機械臂動態納入控制器設計，採用逆向動力學控制方法進行三軸非線性動態解耦合，再結合單軸控制系統中使用的內迴圈壓力控制，實現三軸氣壓並聯機構機械臂的運動控制，並使用Simulink軟體進行控制系統模擬。 最後，本文建立即時控制實驗，整合並聯機構機械臂系統、量測與資料擷取系統以及控制演算法進行單軸氣壓伺服系統軌跡追蹤控制實驗，接著藉由運動學模型規劃機械臂端點平台三維空間軌跡，進行端點平台軌跡追蹤控制實驗，驗證其控制性能，效果及可行性。實驗結果顯示此控制策略可成功應用於三軸氣壓並聯機構機械臂之運動控制，並且實現端點平台的軌跡定位。

This study aims to investigate the analysis and control of a novel three-axial parallel manipulator driven by the pneumatic servo system. The proposed parallel manipulator is composed of a fixed base frame, a moving platform and three sets of parallel kinematic chains. In addition, three identical pneumatic rodless cylinders are employed to be the linear actuators of the manipulator. The assembly configuration of the cylinder actuators makes the manipulator in a pyramidal structure, which can offer more working space to the manipulator. Moreover, from the mobility analysis of the parallel mechanism, the manipulator is verified to possess three translational degrees of freedom. In this study, the analysis of the system contains two major parts: kinematic analysis and dynamic analysis. In the kinematic analysis, the geometric method is introduced to solve the kinematic relation between the actuated joints and the moving platform. A vector-loop closure equation is first established for each limb of the manipulator, and then the solutions for both the inverse and forward kinematics are obtained by solving the vector-loop equations. Furthermore, the velocity relation between the actuators and the moving platform are also considered and obtained by deriving the manipulator Jacobian matrix. In the dynamic analysis, the actuator dynamics is first derived by introducing the mathematical model of the pneumatic cylinder system. Then, the dynamic model of the parallel manipulator is derived using principle of virtual work. In this study, the controller design of the single-axial pneumatic cylinder system is first introduced. The proposed control design applies a dual-loop feedback control scheme with an inner pressure control loop and an outer position control loop using the pressure difference feedback and the position feedback. For the control of three-axial manipulator, the proposed scheme takes the manipulator dynamics into consideration and uses the inverse dynamics control approach to decouple the nonlinear manipulator system. The inverse dynamics control are then combined with the inner pressure control loop for each pneumatic cylinder and implemented in the overall control system to realize the motion control for the overall manipulator system. Numerical simulations are carried out to verify the correctness and effectiveness of the derived kinematic and dynamic models as well as the proposed control schemes using Matlab/Simulink software. Finally, the real-time experiments for the path tracking control of the single-axial pneumatic cylinder system and of the three-axial manipulator end-effector are setup and conducted to exhibit the control performance and accuracy of the proposed control design in the actual system.