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.

翻译：我们提出了一个综合性框架，用于研究和利用机器人系统中的形态对称性。这些对称性源自运动学结构的复制和质量对称分布，是机器人形态的内在属性，在动物生物学和机器人学中频繁出现。我们阐明这些对称性如何扩展至机器人的状态空间以及本体感觉和外感受传感器测量，从而产生机器人运动方程和最优控制策略的等变性。因此，我们将形态对称性视为一种相关且此前未被探索的基于物理学的几何先验知识，对机器人建模、控制、估计与设计中使用的数据驱动和分析方法具有重要影响。对于数据驱动方法，我们证明形态对称性可通过数据增强或对模型架构施加等变/不变约束来提升机器学习模型的样本效率和泛化能力。在分析方法方面，我们采用抽象调和分析将机器人动力学分解为低维独立动力学的叠加。我们通过双足和四足机器人进行的合成实验和真实世界实验验证了上述主张。最后，我们引入MorphoSymm仓库以促进本工作中所述理论及实际应用。