Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual physics during controller synthesis. This paper presents a self-supervised residual learning and trajectory optimization framework to address the aforementioned challenges. At first, unknown dynamic effects on the closed-loop model are learned and treated as residuals of the nominal dynamics, jointly forming a hybrid model. We show that learning with analytic gradients can be achieved using only trajectory-level data while enjoying accurate long-horizon prediction with an arbitrary integration step size. Subsequently, a trajectory optimizer is developed to compute the optimal reference trajectory with the residual physics along it minimized. It ends up with trajectories that are friendly to the following control level. The agile flight of quadrotors illustrates that by utilizing the hybrid dynamics, the proposed optimizer outputs aggressive motions that can be precisely tracked.

翻译：现实世界的物理规律对于现代复杂机器人系统而言，仅能以特定精度进行解析建模。因此，在控制器综合过程中，由于残余物理效应的存在，精确跟踪高动态轨迹可能面临挑战。本文提出一种自监督残差学习与轨迹优化框架以应对上述问题。首先，对闭环模型中未知的动态效应进行学习，并将其视为标称动力学的残差，共同构成混合模型。我们证明，仅利用轨迹级数据即可实现基于解析梯度的学习，并能以任意积分步长获得精确的长时程预测。随后，开发了一种轨迹优化器，用于计算使残余物理效应沿轨迹最小化的最优参考轨迹。最终生成的轨迹对后续控制层级具有良好适应性。通过四旋翼飞行器的敏捷飞行实验表明，利用该混合动力学模型，所提出的优化器能够生成可被精确跟踪的高动态运动。