非完整約束系統反對稱模型之滑動模式控制

A Sliding Mode Control of Nonholonomic Mechanical Systems in Skew Symmetric Form

蔡樸生(Pu-Sheng Tsai) ； 陳珍源(Jen-Yang Chen) ； 吳德豐(Ter-Feng Wu)

《中華技術學院學報》 25期 (2002/09) Pp. 148-164

https://doi.org/10.7095/JCIT.200209.0148

摘要

許多機械系統中經常出現非完整約束的特性，即約束方程式具有不可積分的性質。如冰橇問題、滾球問題、騎腳踏車等均為不完整約束之經典範例。本文針對不確定參數之非完整約束機械系統，提供一套強健適應追蹤控制器。首先將非完整約束方程式應用輸入／狀態線性化的技巧轉換成一組反對稱之鏈狀模型，並提供轉換程序之充要條件。其次，整合反對稱鏈狀模型與系統之動力方程式，採用階層式之觀念，結合適應控制與滑動模式之架構分別對付系統參數未知以及外部干擾的問題。模擬結果證實本文所提之階層式控制架構，對於3輪式移動機械人在姿態穩定控制上，可獲得很好之效果。

關鍵字

非完整約束系統 ； 適應控制器 ； 反對稱鏈狀模型 ； 運動模型 ； 動力模型 ； 移動式機械人 ； 李雅普諾夫穩定準則

並列摘要

Nonholonomic properties most commonly arise in mechanical systems where constraints are imposed on the motions that are not integrable, i.e. the constraints cannot be written as time derivatives of some function of the generalized coordinates. Classical examples of nonholonomic control systems include sledges or knife-edge systems that slide on the plane, simple wheels rolling without slipping on a plane and spheres rolling without slipping on a plane. A point stabilization adaptive control methodology via time-varying state feedback based on the skew-symmetry form is proposed for nonholonomic mechanical systems with parametric uncertainty. Based on the diffeomorphic input-state transformations, we introduce a set of sufficient condition for determining if a nonlinear kinematic model can be converted to a skew symmetry chained form. Next, a hybrid controller is developed to incorporate the kinematic controller into the dynamic controller for deal with uncertain dynamic parameters with robust feature under Lyapunov stability criterion. Finally, the efficacy of the proposed point stabilization strategies is illustrated with 3-wheels mobile robots. Simulation results are utilized to illustrate the effectiveness of the proposed control algorithm.

並列關鍵字

Nonholonomic System ； Adaptive Control ； Skew Symmetry Chained Form ； Kinematic Model ； Dynamic Model ； Mobile Robot ； Lyapunov Stability Criterion