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Constrained rigid body stability and control
Author(s) -
Hemami Hooshang,
Utkin Vadim I.
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3162
Subject(s) - rigid body , control theory (sociology) , holonomic constraints , equilibrium point , stability (learning theory) , surface (topology) , lyapunov function , lyapunov stability , point (geometry) , computer science , exponential stability , holonomic , mathematics , control (management) , physics , classical mechanics , nonlinear system , mathematical analysis , geometry , quantum mechanics , artificial intelligence , machine learning , differential equation
Summary Stability and control of a single or three‐body constrained system are considered. Several different types of constrained motion are among them: the impact phase of a free body colliding with the ground, contact with a stationary or moving platform, movement on a frictionless surface or multiple rigid bodies connected by holonomic constraints, and moving as in the human arm. The single body constrained system is controlled by sliding mode control. The stability of the three‐link arm at arbitrary equilibrium points and Lyapunov stability in the vicinity of the equilibrium point are formulated. The formulation and derivations are by computational tools, that is, state space analysis and matrices. The approach can easily be extended to larger systems with many rigid bodies such as skeletal systems. The formulation minimizes human labor in formulations and simulations. The sliding mode behavior of the model on a frictionless surface and the three link arm stability are demonstrated via simulation. Challenges for application to natural systems are outlined. Copyright © 2014 John Wiley & Sons, Ltd.