Recent advances in learning-based approaches have led to impressive dexterous manipulation capabilities. Yet, we haven't witnessed widespread adoption of these capabilities beyond the laboratory. This is likely due to practical limitations, such as significant computational burden, inscrutable policy architectures, sensitivity to parameter initializations, and the considerable technical expertise required for implementation. In this work, we investigate the utility of Koopman operator theory in alleviating these limitations. Koopman operators are simple yet powerful control-theoretic structures that help represent complex nonlinear dynamics as linear systems in higher-dimensional spaces. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop an imitation learning framework that leverages Koopman operators to simultaneously learn the desired behavior of both robot and object states. We demonstrate that a Koopman operator-based framework is surprisingly effective for dexterous manipulation and offers a number of unique benefits. First, the learning process is analytical, eliminating the sensitivity to parameter initializations and painstaking hyperparameter optimization. Second, the learned reference dynamics can be combined with a task-agnostic tracking controller such that task changes and variations can be handled with ease. Third, a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of task success rate and imitation error, while being an order of magnitude more computationally efficient. In addition, we discuss a number of avenues for future research made available by this work.

翻译：近年来，基于学习的方法取得了令人瞩目的灵巧操作能力。然而，我们尚未看到这些能力在实验室之外的广泛应用。这很可能源于实际限制，例如巨大的计算负担、难以理解的政策架构、对参数初始化的敏感性以及实现所需的大量专业技术知识。在本研究中，我们探讨了库普曼算子理论在缓解这些限制方面的效用。库普曼算子是一种简单而强大的控制理论结构，有助于将复杂的非线性动力学表示为高维空间中的线性系统。鉴于灵巧操作的基础是复杂的非线性动力学，我们开发了一种模仿学习框架，该框架利用库普曼算子同时学习机器人及其对象状态的期望行为。我们证明，基于库普曼算子的框架在灵巧操作中出奇地有效，并提供了若干独特优势。首先，学习过程是解析性的，消除了对参数初始化的敏感性和繁琐的超参数优化。其次，学习的参考动力学可与任务无关的跟踪控制器结合，从而轻松处理任务变化和变体。第三，基于库普曼算子的方法在任务成功率和模仿误差方面可与最先进的模仿学习算法相媲美，同时计算效率提高一个数量级。此外，我们还讨论了本工作为未来研究提供的若干方向。