Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these approaches output a multi-modal distribution of obstacle trajectories instead of a single deterministic prediction to account for the underlying uncertainty. However, existing planners cannot handle the multi-modality based on just sample-level information of the predictions. With this motivation, this paper proposes a trajectory optimizer that can leverage the distributional aspects of the prediction in a computationally tractable and sample-efficient manner. Our optimizer can work with arbitrarily complex distributions and thus can be used with output distribution represented as a deep neural network. The core of our approach is built on embedding distribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage in two ways. First, we propose an RKHS embedding approach to select probable samples from the obstacle trajectory distribution. Second, we rephrase chance-constrained optimization as distribution matching in RKHS and propose a novel sampling-based optimizer for its solution. We validate our approach with hand-crafted and neural network-based predictors trained on real-world datasets and show improvement over the existing stochastic optimization approaches in safety metrics.

翻译：安全自动驾驶的关键在于自车对周围车辆轨迹的预测能力。为此，现有文献提出了多种轨迹预测算法。许多方法输出障碍物轨迹的多模态分布而非单一确定性预测，以应对内在的不确定性。然而，现有规划器仅基于预测的样本级信息难以处理多模态特性。基于此动机，本文提出一种轨迹优化器，能以计算可行且样本高效的方式利用预测的分布特性。本优化器适用于任意复杂分布，可与深度神经网络输出的分布配合使用。方法核心建立在再生核希尔伯特空间（RKHS）的分布嵌入上，并在两方面加以利用：首先，提出一种RKHS嵌入方法来选择障碍轨迹分布中的高概率样本；其次，将机会约束优化重新表述为RKHS中的分布匹配问题，并设计新型基于采样的求解优化器。我们利用人工构造及基于真实数据训练的神经网络预测器验证方法有效性，结果表明在安全性指标上优于现有随机优化方法。