SE(3)-等变机器人学习与控制：教程综述
SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey
AI总结：
本教程综述系统梳理SE(3)-等变神经网络在机器人学习与控制中的应用，通过显式利用旋转平移对称性提升样本效率与泛化，并展望了未来挑战。
摘要：
近年来，深度学习与Transformer的进展，通过采用模仿学习、强化学习以及基于大语言模型的多模态感知与决策等技术，推动了机器人领域的重大突破。然而，传统深度学习与Transformer模型在处理具有内在对称性和不变性的数据时往往面临困难，通常依赖大规模数据集或广泛的数据增强。等变神经网络通过将对称性和不变性显式地集成到其架构中，克服了这些限制，从而提高了效率和泛化能力。本教程综述回顾了从经典到最先进的广泛等变深度学习与机器人控制方法，重点关注利用视觉机器人操作与控制设计中自然的三维旋转和平移对称性的SE(3)-等变模型。使用统一的数学符号，我们首先回顾群论中的关键概念，以及矩阵李群和李代数。然后，我们介绍基础的群等变神经网络设计，并展示如何通过其结构获得群等变性。接下来，我们讨论SE(3)-等变神经网络在机器人模仿学习和强化学习中的应用。从几何控制的角度，也综述了SE(3)-等变控制设计。最后，我们强调了等变方法在开发更鲁棒、样本高效和多模态的真实世界机器人系统中的挑战和未来方向。
英文摘要：
Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However, conventional deep learning and Transformer models often struggle to process data with inherent symmetries and invariances, typically relying on large datasets or extensive data augmentation. Equivariant neural networks overcome these limitations by explicitly integrating symmetry and invariance into their architectures, leading to improved efficiency and generalization. This tutorial survey reviews a wide range of equivariant deep learning and control methods for robotics, from classic to state-of-the-art, with a focus on SE(3)-equivariant models that leverage the natural 3D rotational and translational symmetries in visual robotic manipulation and control design. Using unified mathematical notation, we begin by reviewing key concepts from group theory, along with matrix Lie groups and Lie algebras. We then introduce foundational group-equivariant neural network design and show how the group-equivariance can be obtained through their structure. Next, we discuss the applications of SE(3)-equivariant neural networks in robotics in terms of imitation learning and reinforcement learning. The SE(3)-equivariant control design is also reviewed from the perspective of geometric control. Finally, we highlight the challenges and future directions of equivariant methods in developing more robust, sample-efficient, and multi-modal real-world robotic systems.
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