We present a comprehensive framework for studying and leveraging
morphological symmetries in robotic systems. These are intrinsic properties of
the robot's morphology, frequently observed in animal biology and robotics,
which stem from the replication of kinematic structures and the symmetrical
distribution of mass. We illustrate how these symmetries extend to the robot's
state space and both proprioceptive and exteroceptive sensor measurements,
resulting in the equivariance of the robot's equations of motion and optimal
control policies. Thus, we recognize morphological symmetries as a relevant and
previously unexplored physics-informed geometric prior, with significant
implications for both data-driven and analytical methods used in modeling,
control, estimation and design in robotics. For data-driven methods, we
demonstrate that morphological symmetries can enhance the sample efficiency and
generalization of machine learning models through data augmentation, or by
applying equivariant/invariant constraints on the model's architecture. In the
context of analytical methods, we employ abstract harmonic analysis to
decompose the robot's dynamics into a superposition of lower-dimensional,
independent dynamics. We substantiate our claims with both synthetic and
real-world experiments conducted on bipedal and quadrupedal robots. Lastly, we
introduce the repository MorphoSymm to facilitate the practical use of the
theory and applications outlined in this work.

研究和利用机器人系统中的形态对称性，证明其对机器学习模型的样本效率和泛化能力有显著影响，并将机器人动力学分解为低维度、独立动力学，为机器人学中的建模、控制、估计和设计提供了新的物理信息几何先验。

机器人中的形态对称性

Morphological Symmetries in Robotics

Human life is populated with articulated objects. Current Category-level
Articulation Pose Estimation (CAPE) methods are studied under the
single-instance setting with a fixed kinematic structure for each category.
Considering these limitations, we reform this problem setting for real-world
environments and suggest a CAPE-Real (CAPER) task setting. This setting allows
varied kinematic structures within a semantic category, and multiple instances
to co-exist in an observation of real world. To support this task, we build an
articulated model repository ReArt-48 and present an efficient dataset
generation pipeline, which contains Fast Articulated Object Modeling (FAOM) and
Semi-Authentic MixEd Reality Technique (SAMERT). Accompanying the pipeline, we
build a large-scale mixed reality dataset ReArtMix and a real world dataset
ReArtVal. We also propose an effective framework ReArtNOCS that exploits RGB-D
input to estimate part-level pose for multiple instances in a single forward
pass. Extensive experiments demonstrate that the proposed ReArtNOCS can achieve
good performance on both CAPER and CAPE settings. We believe it could serve as
a strong baseline for future research on the CAPER task.

该研究提出了一种 CAPE-Real 任务设置，旨在解决真实环境下多实例、变化运动结构的各类关节对象建模问题。提出了 ReArtNOCS 框架，利用 RGB-D 输入单次向前推断多个实例的分层姿态估计，并在大规模混合现实数据集 ReArtMix 和真实世界数据集 ReArtVal 上进行了广泛实验证明其性能良好，将成为以后 CAPER 任务相关研究的强有力基准。