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Open AccessArticle

Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms

by Ivan Giorgio 1,2,*,† and Dionisio Del Vescovo 1,2,†
1
Department of Mechanical and Aerospace Engineering, SAPIENZA Università di Roma, via Eudossiana 18, 00184 Rome, Italy
2
Research center on Mathematics and Mechanics of Complex Systems, Università degli studi dell’Aquila, 67100 L’Aquila, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Robotics 2018, 7(4), 60; https://doi.org/10.3390/robotics7040060
Received: 28 June 2018 / Revised: 9 September 2018 / Accepted: 21 September 2018 / Published: 25 September 2018
(This article belongs to the Special Issue Kinematics and Robot Design I, KaRD2018)
The problem of the trajectory-tracking and vibration control of highly flexible planar multi-links robot arms is investigated. We discretize the links according to the Hencky bar-chain model, which is an application of the lumped parameters techniques. In this approach, each link is considered as a kinematic chain of rigid bodies, and suitable springs are added in order to model bending resistance. The control strategy employed is based on an optimal input pre-shaping and a feedback of the joint angles to treat the effects of undesired disturbances. Some numerical examples are given to show the potentialities of the proposed control, and a comparison with a standard collocated Proportional-Derivative (PD) control strategy is performed. In particular, we study the cases of a linear and a parabolic trajectory with a polynomial time law chosen to minimize the onset of possible vibrations. View Full-Text
Keywords: nonlinear flexible beams; discrete modeling; underactuated robots; optimal preshaping input nonlinear flexible beams; discrete modeling; underactuated robots; optimal preshaping input
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Giorgio, I.; Del Vescovo, D. Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms. Robotics 2018, 7, 60.

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