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A new approach to the incorporation of servo constraints in multibody dynamics
Author(s) -
Yang Yinping,
Betsch Peter,
Altmann Robert
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610022
Subject(s) - underactuation , control theory (sociology) , holonomic constraints , constraint (computer aided design) , realization (probability) , reduction (mathematics) , computer science , mathematics , control (management) , physics , artificial intelligence , statistics , geometry , classical mechanics
A new index reduction approach is developed to solve the servo constraint problems [2] in the inverse dynamics simulation of underactuated mechanical systems. The servo constraint problem of underactuated systems is governed by differential algebraic equations (DAEs) with high index. The underlying equations of motion contain both holonomic constraints and servo constraints in which desired outputs (specified in time) are described in terms of state variables. The realization of servo constraints with the use of control forces can range from orthogonal to tangential [3]. Since the (differentiation) index of the DAEs is often higher than three for underactuated systems, in which the number of degrees of freedom is greater than the control outputs/inputs, we propose a new index reduction method [1] which makes possible the stable numerical integration of the DAEs. We apply the proposed method to differentially flat systems, such as cranes [1,4,5], and non‐flat underactuated systems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)