Closed-form control oriented model of highly flexible manipulators

Abstract This paper first presents a highly flexible 3D manipulator with links of arbitrary shape, then develops a closed-form dynamic model that best describes it. The model is based on a Newton–Euler formulation and the substructuring method is used to account for large deformations. The formulation of the motion equations starts from a data set which can be either analytically or numerically computed by finite elements(FE) codes. Simulation has been used to validate the model and compare the results with those of two different multibody software and one experimental, which was obtained from the Multi-Elastic-Link Robot Identification Dataset (MERIt), developed by the TU Dortmund. Then, thanks to the approach here adopted, an integral manifold model is derived, suitable for advanced control system design.

[1]  Ahmed A. Shabana,et al.  Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems , 1999 .

[2]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[3]  Gianni Ferretti,et al.  Multibody Model of a Motorbike with a Flexible Swingarm , 2014 .

[4]  Peter Eberhard,et al.  Model Order Reduction in Elastic Multibody Systems using the Floating Frame of Reference Formulation , 2012 .

[5]  Gerasimos Rigatos,et al.  Model-based and model-free control of flexible-link robots: A comparison between representative methods , 2009 .

[6]  V. Sobolev.  Integral manifolds and decomposition of singularly perturbed systems , 1984 .

[7]  Jörn Malzahn,et al.  Dynamics identification of a damped multi elastic link robot arm under gravity , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[8]  Gianni Ferretti,et al.  Closed form Newton–Euler dynamic model of flexible manipulators , 2015, Robotica.

[9]  Alessandro De Luca,et al.  Closed-form dynamic model of planar multilink lightweight robots , 1991, IEEE Trans. Syst. Man Cybern..

[10]  W. Book.  Recursive Lagrangian Dynamics of Flexible Manipulator Arms , 1984 .

[11]  Gianni Ferretti,et al.  Object-Oriented Modelling of Flexible Beams , 2006 .

[12]  Henk A. van der Vorst,et al.  Approximate solutions and eigenvalue bounds from Krylov subspaces , 1995, Numer. Linear Algebra Appl..

[13]  Paolo Rocco,et al.  Two-time scale visual servoing of eye-in-hand flexible manipulators , 2006, IEEE Transactions on Robotics.

[14]  Ahmed A. Shabana,et al.  APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS , 1997 .

[15]  Amir Fijany,et al.  A new factorization of the mass matrix for optimal serial and parallel calculation of multibody dynamics , 2013 .

[16]  Bruno Siciliano,et al.  An integral manifold approach to control of a one link flexible arm , 1986, 1986 25th IEEE Conference on Decision and Control.

[17]  W. Hurty.  Dynamic Analysis of Structural Systems Using Component Modes , 1965 .

[18]  Eric H. K. Fung,et al.  Dynamic modelling of a rigid-flexible manipulator for constrained motion task control , 1999 .

[19]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[20]  A. Shabana.  Substructure synthesis methods for dynamic analysis of multi-body systems , 1985 .

[21]  E.T. Baumgartner,et al.  The Mars Exploration Rover instrument positioning system , 2005, 2005 IEEE Aerospace Conference.

[22]  Alin Albu-Schäffer,et al.  The DLR lightweight robot: design and control concepts for robots in human environments , 2007, Ind. Robot.

[23]  Eric Courteille,et al.  A Systematic Procedure for the Elastodynamic Modeling and Identification of Robot Manipulators , 2010, IEEE Transactions on Robotics.

[24]  Mete Kalyoncu.  Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint , 2008 .

[25]  H. Tran,et al.  Modeling and control of physical processes using proper orthogonal decomposition , 2001 .

[26]  Petar V. Kokotovic,et al.  An integral manifold approach to the feedback control of flexible joint robots , 1987, IEEE J. Robotics Autom..