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.

翻译：深度学习在机器人学习算法中得到了广泛应用。深度网络的一个缺点是这些网络是黑箱表示。因此，学习到的近似模型忽略了物理学或机器人学已有的知识。特别是对于学习动力学模型，这些黑箱模型并不理想，因为其底层原理已被充分理解，而标准深度网络可能学习到违反这些原理的动力学。为了利用深度网络学习保证物理上合理动力学特性的动力学模型，我们引入了受物理启发的深度网络，该网络将物理学的基本原理与深度学习相结合。我们在模型学习中融入了拉格朗日力学，使得所有近似模型都遵循物理定律并守恒能量。深度拉格朗日网络（DeLaN）利用两个网络对系统能量进行参数化。通过最小化欧拉-拉格朗日微分方程的平方残差来获得参数。因此，所得模型不需要特定系统的具体知识，具有可解释性，并且可以用作正向模型、逆向模型和能量模型。以往这些特性只能通过需要运动学结构知识的系统辨识技术获得。我们将DeLaN应用于学习动力学模型，并将这些模型用于控制仿真和物理刚体系统。结果表明，所提出的方法能够获得可应用于物理系统进行实时控制的动力学模型。与标准深度网络相比，受物理启发的模型学习到了更好的模型，并捕捉到了动力学的底层结构。