Abstract
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.
Abstract (translated)
最近在基于学习的方法方面的进展已经带来了令人印象深刻的灵巧操纵能力。然而，我们在实验室以外并未观察到这些能力的普及。这可能是由于实际限制，例如巨大的计算负担、难以解释的政策架构、对参数初始化的敏感性以及实现所需的相当专业的技术知识。在本文中，我们研究了科恩代理理论在减轻这些限制方面的应用价值。科恩代理是简单但强大的控制理论结构，在更高维度的空间中帮助将复杂的非线性动态表现为线性系统。鉴于复杂的非线性动态是灵巧操纵的基础，我们开发了一个模仿学习框架，利用科恩代理来同时学习机器人和对象状态所需的期望行为。我们证明了科恩代理框架在灵巧操纵方面出乎意料有效，并提供了多项独特的好处。首先，学习过程是分析的，消除了对参数初始化的敏感性和繁琐的超参数优化。其次， learned reference dynamics可以与任务无关跟踪控制器一起使用，从而使任务变化和变异可以轻松处理。第三，基于科恩代理的方法可以在任务成功率和模仿误差方面与最先进的模仿学习算法相当，但计算效率更高。此外，我们讨论了本工作提供的一系列未来研究途径。
URL
https://arxiv.org/abs/2303.13446
