Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of physics or robotics. Especially for learning dynamics models, these black-box models are not desirable as the underlying principles are well understood and the standard deep networks can learn dynamics that violate these principles. To learn dynamics models with deep networks that guarantee physically plausible dynamics, we introduce physics-inspired deep networks that combine first principles from physics with deep learning. We incorporate Lagrangian mechanics within the model learning such that all approximated models adhere to the laws of physics and conserve energy. Deep Lagrangian Networks (DeLaN) parametrize the system energy using two networks. The parameters are obtained by minimizing the squared residual of the Euler-Lagrange differential equation. Therefore, the resulting model does not require specific knowledge of the individual system, is interpretable, and can be used as a forward, inverse, and energy model. Previously these properties were only obtained when using system identification techniques that require knowledge of the kinematic structure. We apply DeLaN to learning dynamics models and apply these models to control simulated and physical rigid body systems. The results show that the proposed approach obtains dynamics models that can be applied to physical systems for real-time control. Compared to standard deep networks, the physics-inspired models learn better models and capture the underlying structure of the dynamics.

@article{dadios_1998,
title = {Nonconventional control of the flexible pole-cart balancing problem: Experimental results},
author = {Dadios, E.P.; Williams, D.J.},
journal = {IEEE Transactions on Systems, Man, and Cybernetics},
year = {1998},
volume = {28},
number = {6},
institution = {De la Salle University, Manila, The Philippines},
abstract = {Emerging techniques of intelligent or learning control seem attractive for applications in manufacturing and robotics. It is however important to understand the capabilities of such control systems. In the past the inverted pendulum has been used as a test case, however, this problem is not sufficiently testing. This research therefore concentrates on the control of the inverted pendulum with additional degrees of freedom as a testing demonstrator problem for learning control system experimentation. A flexible pole is used in place of a rigid one. The transverse displacement of the flexible pole has distributed elasticity and therefore infinite degrees of freedom. The dynamics of this new system are more complex as the system needs additional parameters to be defined due to the pole's elastic deflection. This problem also has many of the significant features associated with flexible robots with lightweight links as applied in manufacturing. Novel neural network and fuzzy control systems are presented that control such a system in real time in one of its modes of vibration. A fuzzy-genetic approach is also demonstrated that allows the creation of fuzzy control systems without the use of extensive knowledge },
issn = {1083-4419},
keywords = {Flexible inverted pendulum, fuzzy logic system, genetic algorithms, learning controllers, neural networks},
language = {English},
publisher = {IEEE},
pages = {895 - 901}
}

Emerging techniques of intelligent or learning control seem attractive for applications in manufacturing and robotics. It is however important to understand the capabilities of such control systems. In the past the inverted pendulum has been used as a test case, however, this problem is not sufficiently testing. This research therefore concentrates on the control of the inverted pendulum with additional degrees of freedom as a testing demonstrator problem for learning control system experimentation. A flexible pole is used in place of a rigid one. The transverse displacement of the flexible pole has distributed elasticity and therefore infinite degrees of freedom. The dynamics of this new system are more complex as the system needs additional parameters to be defined due to the pole's elastic deflection. This problem also has many of the significant features associated with flexible robots with lightweight links as applied in manufacturing. Novel neural network and fuzzy control systems are presented that control such a system in real time in one of its modes of vibration. A fuzzy-genetic approach is also demonstrated that allows the creation of fuzzy control systems without the use of extensive knowledge

@conference{dadios_1995,
title = {Application of neural networks to the flexible pole-cart balancing problem},
author = {Dadios, E.P.; Williams, D.J.},
booktitle = {IEEE International Conference on Systems, Man and Cybernetics},
year = {1995},
volume = {3},
institution = {Loughborough University of Technology, UK},
abstract = {This paper investigates the use of neural networks in the control of highly nonlinear systems. Online and off line control of a cart balancing a flexible pole under its first mode of vibration using neural networks is presented. Backpropagation and Kohonen's self-organizing map have been used as neural network examples. The networks learned from a set of training data derived from a real system and were initially tested against a computer simulation of the derived dynamics of the flexible pole-cart balancing system and then applied to the real system },
keywords = {backpropagation, flexible structures, neurocontrollers, nonlinear control systems, self-organising feature maps},
language = {English},
publisher = {IEEE},
pages = {2506 - 2511}
}

This paper investigates the use of neural networks in the control of highly nonlinear systems. Online and off line control of a cart balancing a flexible pole under its first mode of vibration using neural networks is presented. Backpropagation and Kohonen's self-organizing map have been used as neural network examples. The networks learned from a set of training data derived from a real system and were initially tested against a computer simulation of the derived dynamics of the flexible pole-cart balancing system and then applied to the real system