Modelling, Control and Validation of Flexible Robot Manipulators

The dynamics equations describing the motion of a flexible manipulator are developed. It is assumed that the manipulator supports the gravitational force, external punctual forces and torques applied at specific points along each link’s neutral axis, a punctual force and torque at the end effector, and loads resulting from the application of piezoelectric patches that are bonded at specific points along the elastic links. A discrete model of the Newton-Euler type capturing the fundamental dynamics required for flexible manipulator analysis is deduced for a generic link. A Eulerian formulation is used for the rigid body motion and a total Lagrangian formulation is used for the elastic deformation. To this end, Jourdain’s Principle or the Principle of Virtual Powers is adopted, assuming a Rayleigh-Ritz expansion of the elastic variables. The elastic variables, which are the links curvature and shear deformation, are assumed to be infinitesimal. However, nonlinear displacements are considered due to the large length/width aspect ratio of the links. The dynamics model of the manipulator is obtained from the assembling of the individual links. Both the Articulated Body (AB) method, and the Composite Inertia (CI) method are obtained. A validation and control exercise is performed on a single flexible link. Frequency domain and time domain validation is performed in regard to the order of the cross section rotation matrix. Linear and quadratic assumptions are compared against each other, and against the experimental apparatus. Curvature feedback control is compared against classical joint (collocated) feedback, and it’s improved performance is shown through the measurement of tip acceleration.

[1]  Z. Luo.  Direct strain feedback control of flexible robot arms: new theoretical and experimental results , 1993, IEEE Trans. Autom. Control..

[2]  Leonard Meirovitch,et al.  Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates , 1991 .

[3]  Kenneth Kreutz-Delgado,et al.  Multibody dynamical algorithms, numerical optimal control, with detailed studies in the control of jet engine compressors and biped walking , 1999 .

[4]  Victor Giurgiutiu,et al.  Active-Materials Induced-Strain Actuation for Aeroelastic Vibration Control , 2000 .

[5]  G. B. Sincarsin,et al.  Dynamics of an elastic multibody chain: Part D—Modelling of joints , 1993 .

[6]  G. D'Eleuterio,et al.  Dynamics of an elastic multibody chain: Part C - Recursive dynamics , 1992 .

[7]  Friedrich Pfeiffer,et al.  Experiments with flexible manipulators , 1994 .

[8]  I. Sharf.  GEOMETRICALLY NON‐LINEAR BEAM ELEMENT FOR DYNAMICS SIMULATION OF MULTIBODY SYSTEMS , 1996 .

[9]  Dinesh K. Pai,et al.  Forward Dynamics, Elimination Methods, and Formulation Stiffness in Robot Simulation , 1997, Int. J. Robotics Res..

[10]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[11]  Abhinandan Jain,et al.  RECURSIVE FLEXIBLE MULTIBODY SYSTEM DYNAMICS USING SPATIAL OPERATORS , 1992 .

[12]  Timothy J. Stemple,et al.  Dynamics and Control of Flexible Multibody Structures , 1998 .

[13]  Abhinandan Jain,et al.  Spatial Operator Algebra for multibody system dynamics , 1992 .

[14]  J.-C. Piedboef.  Recursive Modeling of Serial Flexible Manipulators , 1998 .

[15]  Miguel Ayala Botto,et al.  Vibration control of a very flexible manipulator system , 2005 .

[16]  Miguel Ayala Botto,et al.  Approaches for dynamic modelling of flexible manipulator systems , 2003 .

[17]  Dinesh K. Pai,et al.  Forward dynamics algorithms for multibody chains and contact , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[18]  Zheng-Hua Luo,et al.  Nonlinear torque control of a single‐link flexible robot , 1999 .

[19]  Hisham Abou-Kandil,et al.  Piezoelectric actuators and sensors location for active control of flexible structures , 2001, IEEE Trans. Instrum. Meas..

[20]  T. R. Kane,et al.  Dynamics of a cantilever beam attached to a moving base , 1987 .

[21]  Ch . Engstler,et al.  MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems , 1992 .

[22]  Reinhold von Schwerin.  MultiBody System SIMulation - Numerical Methods, Algorithms, and Software , 1999, Lecture Notes in Computational Science and Engineering.

[23]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[24]  André Preumont,et al.  Vibration Control of Active Structures: An Introduction , 2018 .

[25]  P. Coiffet,et al.  Generalization of Newton‐Euler model for flexible manipulators , 1996 .

[26]  Jorge Martins,et al.  Modeling of Flexible Beams for Robotic Manipulators , 2002 .