Accurate models of mechanical system dynamics are often critical for
model-based control and reinforcement learning. Fully data-driven dynamics
models promise to ease the process of modeling and analysis, but require
considerable amounts of data for training and often do not generalize well to
unseen parts of the state space. Combining data-driven modelling with prior
analytical knowledge is an attractive alternative as the inclusion of
structural knowledge into a regression model improves the model's data
efficiency and physical integrity. In this article, we survey supervised
regression models that combine rigid-body mechanics with data-driven modelling
techniques. We analyze the different latent functions (such as kinetic energy
or dissipative forces) and operators (such as differential operators and
projection matrices) underlying common descriptions of rigid-body mechanics.
Based on this analysis, we provide a unified view on the combination of
data-driven regression models, such as neural networks and Gaussian processes,
with analytical model priors. Further, we review and discuss key techniques for
designing structured models such as automatic differentiation.

本文综述了一些通过将数据驱动建模与先前的解析知识相结合的监督回归模型，以在具有刚体力学描述的系统动力学建模中提高数据的效率和物理完整性，并分析了刚体力学的各种潜在函数和算子。

刚体动力学的结构化学习：从机器人学角度的调查和统一视角

Structured learning of rigid-body dynamics: A survey and unified view  from a robotics perspective

Planning for robotic manipulation requires reasoning about the changes a
robot can affect on objects. When such interactions can be modelled
analytically, as in domains with rigid objects, efficient planning algorithms
exist. However, in both domestic and industrial domains, the objects of
interest can be soft, or deformable, and hard to model analytically. For such
cases, we posit that a data-driven modelling approach is more suitable. In
recent years, progress in deep generative models has produced methods that
learn to `imagine' plausible images from data. Building on the recent Causal
InfoGAN generative model, in this work we learn to imagine goal-directed object
manipulation directly from raw image data of self-supervised interaction of the
robot with the object. After learning, given a goal observation of the system,
our model can generate an imagined plan -- a sequence of images that transition
the object into the desired goal. To execute the plan, we use it as a reference
trajectory to track with a visual servoing controller, which we also learn from
the data as an inverse dynamics model. In a simulated manipulation task, we
show that separating the problem into visual planning and visual tracking
control is more sample efficient and more interpretable than alternative
data-driven approaches. We further demonstrate our approach on learning to
imagine and execute in 3 environments, the final of which is deformable rope
manipulation on a PR2 robot.

本文提出了一种基于数据驱动的建模方法，利用深度生成模型学习目标定向的物体操作，采用视觉规划和视觉跟踪控制解决目标检测问题。