雙軸機械手臂之平順控制

Abstract

本論文研究主旨為將各種平順控制方法應用於雙軸機械手臂之定位。雙軸機械手臂為耦合的非線性系統，在此我們使用計算力矩控制(Computed Torque Control)方法將其解耦為線性系統之後，再設計各種時間最佳化平順控制器。 研究動機是因為機械系統中若急動度(即，加速度對時間的微分量)太大常常會對系統造成不好的影響。基於此點，本論文限制雙軸機械手臂的最大急動度，設計急動度限制下時間最佳化控制(Jerk-Constrained Time-Optimal Control, JCTOC)；此外，更進一步限制痙攣度，其為急動度的再一次微分量，設計痙攣度限制下時間最佳化控制(Snap-Constrained Time-Optimal Control, SCTOC)。 在實作上，本研究將平順控制法則實現於雙軸機械手臂，使用的實驗平台核心控制器為DSP搭配具可程式陣列閘(FPGA)之實驗室自製擴充子板，FPGA方面使用VHDL規劃週邊界面，而DSP方面使用C語言實現各種控制法則。實驗結果顯示，藉由限制住受控體輸出之高階微分量，雙軸機械手臂在定位時能擁有平順的響應，且相較於傳統的線性控制器能達到更短的安定時間。

This paper presents two smooth control methods for the positioning of a two-link robot manipulator. The two-link robot manipulator is a coupled nonlinear system, and the so-called computed torque control method is employed to obtain a linear model. Then, the linear model is used to develop the smooth control methods. In mechanical systems, if jerk (i.e., the time derivative of acceleration) is too high, it may have adverse effects on the systems and even cause system instability. To avoid the problems with high jerk, jerk-constrained time-optimal control (JCTOC) method is proposed, which constrains the maximum admissible jerk and uses the time-optimal control (TOC) method to produce smooth but fast responses. Furthermore, snap-constrained time-optimal control (SCTOC) method is proposed to constrain the snap, which is the time derivative of jerk, for even smoother responses. In the experimental system, the control kernel is a DSP/FPGA system, and the C language and the VHDL are utilized as development tools for the control system. Experiments of the smooth control methods have been conducted and results show that the proposed smooth control methods are able to yield smoother and also faster responses than the conventional linear approach.