應用於滿致動器系統與欠致動器系統之滑模控制器設計

Abstract

機器手臂的核心技術包括智慧感測及運動控制技術，目前大多數機械手臂為手臂自由度與致動器數量相等，稱為滿致動器(fully-actuated)系統，如一般工業用機械手臂。若致動器數量少於運動自由度，則稱之為欠致動器(underactuated)系統；本研究為了解決在欠致動器系統下之被動軸有干擾或系統不準確性(uncertainty)，因此選擇設計滑模控制器能夠對付匹配與非匹配干擾之非線性系統。 本研究之滑模控制器演算法主要先將狀態部份以標準型式(regular form)表示，利用滑模控制理論，定義滑動變數與我們所控制的誤差訊號，並且證明這些變數最終將漸進穩定即在滑動面上滑動，其中我們假設許多可調變之參數與描述系統不準確性之參數上限值，最後，在依據不同的系統下，選取適當的系統狀態將其轉為標準型式，套入此演算法並將參數微調，即可實現此滑模控制器。本研究將HIWIN RA605六軸工業用機械手臂作為滿致動器系統實驗平台，且將此六軸機械手臂末端點外掛一維軌道，並在軌道上端放置一顆藍色塑膠球，能於軌道自由活動不受驅動器控制，因此整體系統視為七軸欠致動系統，且我們使用實驗室所發展之高速相機陣列將球體位置資訊回傳於控制器中作回授控制。在實驗結果中，我們能夠看到若在滿致動器系統下做測試，軌跡追蹤誤差能夠有良好的效果，而若在欠致動器系統中做測試，可得到未受驅動器直接控制之球體位置，也能夠透過我們控制演算法得到良好的軌跡追蹤效果。

Most robot manipulators have the same degrees of freedom as the number of actuators. Such a system is called a fully-actuated system. If the number of actuators is less than the degrees of freedom, then the system is underactuated. This thesis aims at developing a universal sliding mode control law for state trajectory tracking and dealing with matched and mismatched disturbances in both kinds of systems. We design the sliding mode algorithm for systems represented in regular form. Define the sliding variables and error signals properly and derive the control law such that asymptotical stability is guaranteed based on Lyapunov theorem. For either fully-actuated or underactuated system, we just choose appropriate state variables and convert the system model to the regular form. Then the proposed control algorithm can be applied directly. To experimentally verify the proposed control algorithm, we use the HIWIN RA605 six-axis robot manipulator as a fully-actuated system. For under-actuated systems, we mount a track at the end of RA605 with a ball sliding freely on the track. The motion of the ball is regarded as the 7th axis of the system which is unactuated. The ball’s position is fed back to the controller by a high-speed camera array. Experimental results show that satisfactory state trajectory tracking is achieved for both fully-actuated and underactuated systems.