用于机器人动力学学习与控制的李群上端口-Hamiltonian神经ODE网络
Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control
AI总结：
本文提出李群上的端口-Hamiltonian神经ODE网络，将能量守恒、李群约束与耗散效应嵌入机器人动力学学习，并结合能量整形和阻尼注入实现欠驱动系统的稳定与轨迹跟踪。
摘要：
准确的机器人动力学模型对于安全、稳定的控制以及向新运行条件的泛化至关重要。然而，即使经过仔细的参数整定，手工设计的模型仍可能不够准确。这促使人们使用机器学习技术，在状态-控制轨迹训练集上逼近机器人动力学。许多机器人的动力学是用其在矩阵李群上的广义坐标（例如地面、空中和水下航行器在$SE(3)$上的广义坐标）和广义速度来描述的，并满足能量守恒原理。本文提出一种李群上的端口-Hamiltonian表述，采用神经常微分方程（ODE）网络结构来逼近机器人动力学。与黑箱ODE网络相比，我们的表述将能量守恒原理和李群约束嵌入动力学模型，并在动力学模型中显式考虑摩擦和阻力等能量耗散效应。我们为学习到的、可能欠驱动的Hamiltonian动力学开发了能量整形和阻尼注入控制，从而实现一种适用于各种机器人平台的稳定化与轨迹跟踪统一方法。
英文摘要：
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 embeds energy conservation principle and Lie group's constraints in the dynamics model 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.
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