Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This motivates the use of machine learning techniques to approximate the robot dynamics over a training set of state-control trajectories. The dynamics of many robots are described in terms of their generalized coordinates on a matrix Lie group, e.g. on SE(3) for ground, aerial, and underwater vehicles, and generalized velocity, and satisfy conservation of energy principles. This paper proposes a (port-)Hamiltonian formulation over a Lie group of the structure of a neural ordinary differential equation (ODE) network to approximate the robot dynamics. In contrast to a black-box ODE network, our formulation guarantees energy conservation principle and Lie group's constraints by construction and explicitly accounts for energy-dissipation effect such as friction and drag forces in the dynamics model. We develop energy shaping and damping injection control for the learned, potentially under-actuated Hamiltonian dynamics to enable a unified approach for stabilization and trajectory tracking with various robot platforms.

翻译：准确的机器人动力学模型对于安全稳定的控制以及泛化到新型操作条件至关重要。然而，即便经过精细的参数调优，手工设计的模型仍可能精度不足。这促使人们利用机器学习技术，基于状态-控制轨迹训练集来逼近机器人动力学。许多机器人的动力学可借助矩阵李群（例如地面、空中及水下航行器的SE(3)群）上的广义坐标与广义速度进行描述，并满足能量守恒原理。本文提出一种基于李群结构的（端口-）汉密尔顿神经常微分方程（ODE）网络公式，用于逼近机器人动力学。与黑箱ODE网络相比，我们的公式通过构造保证能量守恒原理和李群约束，并明确在动力学模型中考虑摩擦、阻力等能量耗散效应。针对学习得到且可能欠驱动的汉密尔顿动力学，我们开发了能量整形与阻尼注入控制方法，从而为各类机器人平台提供统一的镇定与轨迹跟踪方案。