機器臂在奇異點附近的運動控制

Abstract

緩阻最小平方法常被用來解決分解加速度控制法的奇異問題，但是當機 器臂在某些情況下，將發生振盪或自我運動的現象，不論機器臂是多餘自 由度或是非多餘自由度皆會發生此現象。這些問題的原因是因為當機器臂 在奇異點上時，存在不需要的軸速度。在本論文中將提出緩阻速度控制法 、混合緩阻控制法與修正後的混合緩阻控制法來去除掉這些不需要的軸速 度。這三種控制法則各有它的優缺點，但是都可以克服原來控制法則的缺 點。在本論文中，我們也證明這三種控制法則是漸進穩定，它們的收斂特 性也將被討論。另外，本論文也提出一個類似高斯函數的函數作為阻尼參 數，此函數比以前由其他學者提出的函數使緩阻最小平方解有較小的誤差 。最後由模擬與實驗的結果驗證這些方法確實可以解決原先控制法則的缺 點。 The damped least-squares method has frequently been used to solve thesingularity problem of resolved-acceleration control schemes. However, whenthe manipulator is in some configurations near singularity, fluctuation orself-motion may occur no matter when the manipulator is redundant ornonredundant. The reason of these problems is that the unnecessary jointvelocities exist when the manipulator is at a singular configuration.In this thesis, we propose the damped-rate control scheme, the hybrid- dampedcontrol scheme, and the modified hybrid-damped control scheme to remove theseunnecessary joint velocities. Each proposed control scheme has its own advantageand drawback, but they all overcome the problems of the original controlscheme. The thesis also shows that three proposed control schemes areasymptotically stable, and discusses the convergent properties. On the otherhand, the thesis proposes a normal-like function as the damping factor, theerror of the this function in the damped least-squares solution is smallerthan that of other functions proposed by the researchers. Simulations andexperiments have been undertaken to verify the proposed control schemes.