Dynamic modelling, simulation and control of a manipulator with flexible links and joints. Subudhi, B. and Morris, A. S. Robotics and Autonomous Systems, 41(4):257–270, December, 2002.
Dynamic modelling, simulation and control of a manipulator with flexible links and joints [link]Paper  doi  abstract   bibtex   
The paper presents a dynamic modelling technique for a manipulator with multiple flexible links and flexible joints, based on a combined Euler–Lagrange formulation and assumed modes method. The resulting generalised model is validated through computer simulations by considering a simplified case study of a two-link flexible manipulator with joint elasticity. Controlling such a manipulator is more complex than controlling one with rigid joints because only a single actuation signal can be applied at each joint and this has to control the flexure of both the joint itself and the link attached to it. To resolve the control complexities associated with such an under-actuated flexible link/flexible joint manipulator, a singularly perturbed model has been formulated and used to design a reduced-order controller. This is shown to stabilise the link and joint vibrations effectively while maintaining good tracking performance.
@article{subudhi_dynamic_2002,
	title = {Dynamic modelling, simulation and control of a manipulator with flexible links and joints},
	volume = {41},
	issn = {0921-8890},
	url = {http://www.sciencedirect.com/science/article/pii/S0921889002002956},
	doi = {10.1016/S0921-8890(02)00295-6},
	abstract = {The paper presents a dynamic modelling technique for a manipulator with multiple flexible links and flexible joints, based on a combined Euler–Lagrange formulation and assumed modes method. The resulting generalised model is validated through computer simulations by considering a simplified case study of a two-link flexible manipulator with joint elasticity. Controlling such a manipulator is more complex than controlling one with rigid joints because only a single actuation signal can be applied at each joint and this has to control the flexure of both the joint itself and the link attached to it. To resolve the control complexities associated with such an under-actuated flexible link/flexible joint manipulator, a singularly perturbed model has been formulated and used to design a reduced-order controller. This is shown to stabilise the link and joint vibrations effectively while maintaining good tracking performance.},
	number = {4},
	urldate = {2018-07-13TZ},
	journal = {Robotics and Autonomous Systems},
	author = {Subudhi, B. and Morris, A. S.},
	month = dec,
	year = {2002},
	keywords = {Flexible joint, Flexible link, Manipulator, Singular perturbation},
	pages = {257--270}
}
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