Learning schemes for planning and control are limited by the difficulty of collecting large amounts of experimental data or having to rely on high-fidelity simulations. This paper explores the potential of a proposed learning scheme that leverages dimensionless numbers based on Buckingham's $\pi$ theorem to improve data efficiency and facilitate knowledge sharing between similar systems. A case study using car-like robots compares traditional and dimensionless learning models on simulated and experimental data to validate the benefits of the new dimensionless learning approach. Preliminary results show that this new dimensionless approach could accelerate the learning rate and improve the accuracy of the model and should be investigated further.

翻译：规划与控制的学习方案受限于大量实验数据的收集困难或对高保真仿真的依赖。本文探索了一种利用基于白金汉$\pi$定理的无量纲数来提升数据效率并促进相似系统间知识共享的学习方案的潜力。通过一项采用类车机器人的案例研究，在仿真与实验数据上对比传统学习模型与无量纲学习模型，验证了这种新型无量纲学习方法的优势。初步结果表明，该无量纲方法能够加速学习速率、提升模型精度，值得进一步深入研究。