球型機器人控制

Control of a Ballbot

黃柏凱(Po-Kai Huang)

指導教授 ： 蕭俊祥

國立臺北科技大學/機電學院/機電整合研究所/碩士(2008年)

https://doi.org/10.6841/NTUT.2008.00587

摘要

本文以滑動模式的理論，使用分層滑動模式控制(hierarchical sliding-mode control)的方法控制二階欠致動性系統(under-actuated system)的球型機器人(ballbot)。第一步先將系統分成兩個子系統，對於每個子系統個別定義出滑動面(sliding surface)，第二步將一個子系統的滑動面視為第一層滑動面。然後將第一層滑動面與另一個子系統建構出第二層的滑動面。利用Lyapunov穩定法則以及Barbalat’s輔助定理確保每一層的滑動面和子系統的滑動面都能夠達到漸進穩定。我們利用電腦模擬方式來驗證此分層滑動模式控制對球型機器人平衡控制與軌跡追蹤的有效性。此外球型機器人的機構及電路設計已完成，初步平衡控制亦得到驗證。

關鍵字

球型機器人 ； 分層滑動模式控制 ； 欠致動性系統

並列摘要

Based on sliding mode theory, this paper presents a hierarchical sliding-mode control for under-actuated system of a ballbot. Firstly, the nominal system is divided into two subsystems and sliding mode surface of every subsystem is defined. Secondly, one of the subsystems is selected as the first layer sliding surface. The first layer sliding surface is then used to construct the second layer sliding mode surface with the sliding mode surface of another subsystem. The asymptotic stability of every layer sliding surface and sliding surface of each subsystem is proven theoretically by Barbalat’s lemma and Lyapunov theorem. Computer simulation results show the effectiveness and validity of the developed hierarchical sliding-mode controller for balancing and tracking control of the ballbot. In addition, mechanism and control circuits design have been finished and preliminary result of balancing control of the ballbot has been obtained.

並列關鍵字

Ballbot ； Hierarchical sliding-mode control ； Under-actuated system

參考文獻

[2] 黃正豪，兩輪自走車之設計與實現-以NIOS為核心之行動控制，碩士論文，國立中央大學電機工程研究所，桃園，2006。

[3] T. B. Lauwers, G. A. Kantor, R. L. Hollis, "A dynamical stable single-wheeled mobile robot with inverse mouse-ball drive", Proceedings of the IEEE International Conference on Robotics and Automation, 2006, pp. 2884-2889.

[5] J. Y. Hung, W. Gao, and J. C. Hung, "Variable structure control:Ａ survey", IEEE Trans. Ind. Electron, Vol. 40, No. 1, Feb 1993, pp. 2-22.

[6] V. I. Utkin, "Variable Structure System with Sliding Mode", IEEE Trans. Automatic Control, Vol.AC-22, No.2, April 1977 pp.212-222.

[9] W. Wang, J. Yi, D. Zhao, and D. Liu, "Design of a stable sliding-mode controller for a class of second-order underactuated systems", IEE Proceeding of Control Theory and Applications, Vol. 151, Nov 2004. pp. 683-690.