| 摘要: | 近年來，所謂的回步法在眾多相關控制設計中，已躍升為可移式機器人控制之主流。在所謂之運動設計階段，多數設計不可避免的含有一參考速度之高次方多項式函數，將導致在高速應用中輸入力矩過高而造成馬達之燒毀；而在所謂動力設計階段，多數設計皆假設輸入矩陣為完全已知，因而限制了其實用性，本計畫主要目的在提出一可克服上述兩缺點之控制設計。首先針對地一項缺失，初步構想師是以一修正之飽和函數取代上述多項式函數，此函數經過適當之修正後，其有限輸出的特性將可有效克制現有設計快速發散之缺點，同時，其奇函數特性亦可使得原先漸進穩定的特性不被破壞。 其次，本計畫將以過去我們在可線性化系統的平滑切換控制設計成果為基礎，推廣至可移式機器人系統，以有效克服上述第二項問題。之所以採用此方法的原因有二：1. 此切換機制的平滑特性，對於回步控制在設計過程中，對虛擬輸入微分的必要性，提供了良好解決知道；2. 最重要的，此種切換設計已成功克服了可線性化系統適應性控制之奇異點問題，相信對於可移式機器人系統之相關設計亦能獲得相當之成功。 延續上述之工作，由於假設輸入矩陣參數未知之情況下所可能導致系統運動模型之參數不確定性，亦將一併考慮解決。
Among others, the backstepping tool has played a major role in the tracking control designs of a wheeled mobile robot system in recent years. At the so-called kinematic level, most of the existing designs inevitably contain a high-order polynomial of the desired velocity which may result in extremely high control torques in fast motion applications. While at the dynamic level, mostly they deal with the restricted case with the input matrix being exactly known a priori. It motivates us to develop control schemes which avoid the drawbacks mentioned above in this project. For conquering the former drawback, our idea is to replace the high-order polynomial with some modified saturation function, whose limited output is believed to be able to keep the control from growing unbounded while preserve the asymptotic tracking stability simultaneously. Next, based on our earlier smooth switching control designs for the fully linearisable systems, we intend to develop a hybrid control scheme for conquering the second restriction mentioned above in this project. The reasons for adopting such a method are twofold, firstly, the smooth switching feature of this scheme is beneficial to the backstepping scheme which inevitably involves the differentiation of the virtual control input, secondly, such a switching mechanism has demonstrated its ability in preventing the occurrence of the so-called singularity phenomenon, which may result in a extremely high control torques and even the destroy of the actuators. Continuing to these works, the case with the parametric uncertainty in the kinematic model, resulting from the unknown input matrix, will also be considered in the latter stage of this project. |
