A Unified Approach to Input-output Linearization and Concurrent Control of Underactuated Open-chain Multi-body Systems with Holonomic and Nonholonomic Constraints

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• 作者：Robin Chhabra ; M. Reza Emami
• 关键词：Open ; chain multi ; body system ; Dynamical reduction ; Nonholonomic constraints ; Input ; output linearization ; Nonlinear control
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：22
• 期：1
• 页码：129-168
• 全文大小：932 KB
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• 作者单位：Robin Chhabra (1)
  M. Reza Emami (2) (3)
  
  1. MacDonald, Dettwiler and Associates Ltd., Brampton, Canada
  2. Institute for Aerospace Studies, University of Toronto, Toronto, Canada
  3. Space Technology Division, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology, Kiruna, Sweden
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

This paper presents a unified geometric framework to input-output linearization of open-chain multi-body systems with symmetry in their reduced phase space. This leads us to an output tracking controller for a class of underactuated open-chain multi-body systems with holonomic and nonholonomic constraints. We consider the systems with multi-degree-of-freedom joints and possibly with non-zero constant total momentum (in the holonomic case). The examples of these systems are free-base space manipulators and mobile manipulators. We first formalize the control problem, and rigorously state an output tracking problem for such systems. Then, we introduce a geometrical definition of the end-effector pose and velocity error. The main contribution of this paper is reported in Section 5, where we solve for the input-output linearization of the highly nonlinear problem of coupled manipulator and base dynamics subject to holonomic and nonholonomic constraints. This enables us to design a coordinate-independent controller, similar to a proportional-derivative with feed-forward, for concurrently controlling a free-base, multi-body system. Finally, by defining a Lyapunov function, we prove in Theorem 3 that the closed-loop system is exponentially stable. A detailed case study concludes this paper.