本許多機械系統中經常出現非完整約束的問題，即約束方程式具有不可積分的性質。如冰橇問題、輪型機器人、騎腳踏車等均為非完整約束之經典範例。本文針對三輪式移動機器人的運動方程式提出一套完整的控制策略，以達到全域軌跡追蹤之目標。為了方便控制器的設計，運動方程式可以轉換成近似線性系統的反對稱鏈狀模型，以李雅普諾夫合成之方法巧妙地設計控制器。然而，在系統轉換成鏈狀模型的過程中，部份路徑會有奇異點的問題發生。亦即存在某些方位角的參考路徑，鏈狀系統的參考狀態與輸入是無法定義的，更無法進行所謂控制器的設計，進而限制軌跡追蹤的範圍。為了解決這個問題，本文採用兩組互補的反對稱鏈狀模型交互使用，避開奇異點的問題，使得參考路徑上的每個軌跡得以被追蹤。文中設計一套連續性的切換機制，根據目前的行進軌跡適當地切換兩組互補的鏈狀模型。不僅避開因座標轉換所引發的奇異點問題，同時保証切換瞬間控制信號的連續與平滑。透過李雅普諾夫穩定法則與連續性的切換機制所設計出來的控制信號，使得所有狀態均可滿足追蹤性能的要求。模擬結果證實本文所提出來的控制策略，在三輪式移動機器人之全域軌跡追蹤上，可獲得令人滿意之效果。

With the nonholonomic constraints naturally arising from the non-sliding wheels, a global tracking controller for a tri-wheeled mobile robot is investigated in this paper. To facilitate controller design, the kinematic equation can be converted into the skew chained form so that the Lyapunov synthesis method can be adopted artfully. However, in the transformation from the kinematic equation to a skew chained system, a singularity problem may occur in the desired path which restricts the region of application. To solve this problem, two sets of complementary skew chained systems are used interchangeably so that the tracking is global and every desired trajectory can be followed. A switching mechanism and a continuation method are proposed to generate smooth signals for the kinematic equation, which subsequently drives all system variables to the desired values. In this paper, we restrict our attention to kinematic level of nonholonomic systems. Simulation results demonstrate such a trajectory tracking strategy for the kinematics indeed gives rise to an effective methodology to follow the desired trajectory asymptotically.