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, including ground, aerial, and underwater vehicles, are described in terms of their SE(3) pose and generalized velocity, and satisfy conservation of energy principles. This paper proposes a Hamiltonian formulation over the SE(3) manifold of the structure of a neural ordinary differential equation (ODE) network to approximate the dynamics of a rigid body. In contrast to a black-box ODE network, our formulation guarantees total energy conservation by construction. We develop energy shaping and damping injection control for the learned, potentially under-actuated SE(3) Hamiltonian dynamics to enable a unified approach for stabilization and trajectory tracking with various platforms, including pendulum, rigid-body, and quadrotor systems.
翻译:精确的机器人动态模型对于安全稳定的控制和对新操作条件的概括至关重要。 手工设计的模型可能不够准确, 即使在仔细的参数调整之后也是如此。 这促使使用机器学习技术来将机器人动态近似于一套国家控制的轨迹训练, 许多机器人的动态, 包括地面、 空中和水下飞行器的动态, 以其SE(3) 构成和通用速度来描述, 并满足能源保护原则的要求。 本文建议对神经普通差异方程式( ODE) 结构的 SE(3) 组合进行汉密尔顿式配方, 以近似硬体体的动态。 与黑箱 ODE 网络相反, 我们的配方保证了建筑的完全节能。 我们开发了能源成型, 并对所学的、 可能作用不足的 SE(3) 汉密尔密尔顿 动力进行注射控制, 以便能够对各种平台, 包括支架、 硬体 和 孔体 系统进行统一的稳定性和轨迹追踪。