Distributionally Robust Optimal Control (DROC) is a framework that enables robust control in a stochastic setting where the true disturbance distribution is unknown. Traditional DROC approaches require given ambiguity sets and KL divergence bounds to represent the distributional uncertainty; however, these quantities are often unavailable a priori or require manual specification. To overcome this limitation, we propose a data-driven approach that jointly estimates the uncertainty distribution and the corresponding KL divergence bound, which we refer to as $\mathrm{D}^3\mathrm{ROC}$. To evaluate the effectiveness of our approach, we consider a car-like robot navigation task with unknown noise distributions. The experimental results show that $\mathrm{D}^3\mathrm{ROC}$ yields robust and effective control policies, outperforming iterative Linear Quadratic Gaussian (iLQG) control and demonstrating strong adaptability to varying noise distributions.

翻译：分布鲁棒最优控制（DROC）是一种在真实扰动分布未知的随机环境下实现鲁棒控制的框架。传统的DROC方法需要给定模糊集和KL散度边界来表示分布不确定性；然而，这些量通常无法先验获得或需要人工指定。为克服这一限制，我们提出一种数据驱动方法，联合估计不确定性分布及相应的KL散度边界，我们称之为$\mathrm{D}^3\mathrm{ROC}$。为评估所提方法的有效性，我们考虑了一个具有未知噪声分布的类车机器人导航任务。实验结果表明，$\mathrm{D}^3\mathrm{ROC}$能够产生鲁棒且有效的控制策略，其性能优于迭代线性二次高斯（iLQG）控制，并展现出对不同噪声分布的强大适应能力。