本文使用 Denavit-Hartenberg (D-H) 約定推導六自由度機械手臂的運動模型，包括運動學與動力學。為了克服運動模型的高度非線性問題，我們透過了 T-S 模糊系統來建立非線性系統之線性化模型。並利用此線性化模型，我們可以通過平行分佈式 PID 控制器來控制機械手臂。
根據連續軌跡的要求、各手臂的長度以及關節旋轉的角度限制，運動形式的設計需要擬合機器人手臂的運動模型。機械手臂系統中的 PID 控制器其參數係通過粒子群最佳化演算法（PSO）求得的。根據系統轉移函數，優化後的控制器參數可以在機械手臂運轉時抵抗系統的不確定性，使機械臂在運作時有能更高效且更平穩。
利用 Matlab 中的 Simulink 對系統進行模擬，分析範圍包括定點跟踪和軌跡跟踪。與傳統的 PID 控制器相比，結果顯示所提出的控制器參數具有更小的穩定性誤差且有較佳的調和性與較小的振動，並依此參數操作機械手臂觀察手臂之運動情形，其結果為手臂運作很均勻無抖動現象。

This paper uses the Denavit-Hartenberg (D-H) convention to derive the motion model, including the kinematics and dynamics, of the 6-DOF robotic arm. In order to overcome the highly nonlinear issue of the motion model, we linearize the nonlinear system by T-S fuzzy modeling.
Based on the linearized model, we can control the robotic arm through a parallel distributed PID controller. According to the requirements of the continuous trajectory, the length limits of each arm, and the angle limits of the joint rotation, the design of motion form needs to fit the motion model of the robot arm.
The parameters of the PID controller are found by the particle swarm optimization (PSO). According to the system transfer function, the controller with the optimized parameters can resist the uncertainty of the system, and make the robot arm move more efficiency and smoothly.
The system’s simulated in Matlab is used to simulate the system, and the analysis scope includes fixed-point tracking and trajectory tracking. Compared with the traditional PID controller, the results show that the proposed controller parameters have smaller stability errors, better harmonic and smaller vibration and operate the robotic arm according to these parameters to observe the movement of the arm,The result is that the arm operates evenly without shaking.

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