Fast adaptive control is a critical component for reliable robot autonomy in rapidly changing operational conditions. While a robot dynamics model may be obtained from first principles or learned from data, updating its parameters is often too slow for online adaptation to environment changes. This motivates the use of machine learning techniques to learn disturbance descriptors from trajectory data offline as well as the design of adaptive control to estimate and compensate the disturbances online. This paper develops adaptive geometric control for rigid-body systems, such as ground, aerial, and underwater vehicles, that satisfy Hamilton's equations of motion over the SE(3) manifold. Our design consists of an offline system identification stage, followed by an online adaptive control stage. In the first stage, we learn a Hamiltonian model of the system dynamics using a neural ordinary differential equation (ODE) network trained from state-control trajectory data with different disturbance realizations. The disturbances are modeled as a linear combination of nonlinear descriptors. In the second stage, we design a trajectory tracking controller with disturbance compensation from an energy-based perspective. An adaptive control law is employed to adjust the disturbance model online proportional to the geometric tracking errors on the SE(3) manifold. We verify our adaptive geometric controller for trajectory tracking on a fully-actuated pendulum and an under-actuated quadrotor.

中文翻译：

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SE(3) 哈密顿动力学的学习自适应控制

快速自适应控制是在快速变化的操作条件下实现可靠​​机器人自主的关键组成部分。虽然机器人动力学模型可以从第一原理获得或从数据中学习，但更新其参数对于在线适应环境变化来说通常太慢。这促使使用机器学习技术从离线轨迹数据中学习干扰描述符，以及设计自适应控制来在线估计和补偿干扰。本文为刚体系统（如地面、空中和水下航行器）开发了自适应几何控制，该系统满足 SE(3) 流形上的 Hamilton 运动方程。我们的设计包括一个离线系统识别阶段，然后是一个在线自适应控制阶段。在第一阶段，我们使用从具有不同干扰实现的状态控制轨迹数据训练的神经常微分方程 (ODE) 网络学习系统动力学的哈密顿模型。扰动被建模为非线性描述符的线性组合。在第二阶段，我们从基于能量的角度设计具有干扰补偿的轨迹跟踪控制器。采用自适应控制律来在线调整与 SE(3) 流形上的几何跟踪误差成正比的扰动模型。我们验证了我们的自适应几何控制器，用于在全驱动摆锤和欠驱动四旋翼飞行器上进行轨迹跟踪。扰动被建模为非线性描述符的线性组合。在第二阶段，我们从基于能量的角度设计具有干扰补偿的轨迹跟踪控制器。采用自适应控制律来在线调整与 SE(3) 流形上的几何跟踪误差成正比的扰动模型。我们验证了我们的自适应几何控制器，用于在全驱动摆锤和欠驱动四旋翼飞行器上进行轨迹跟踪。扰动被建模为非线性描述符的线性组合。在第二阶段，我们从基于能量的角度设计具有干扰补偿的轨迹跟踪控制器。采用自适应控制律来在线调整与 SE(3) 流形上的几何跟踪误差成正比的扰动模型。我们验证了我们的自适应几何控制器，用于在全驱动摆锤和欠驱动四旋翼飞行器上进行轨迹跟踪。