This paper presents fast non-sampling based methods to assess the risk for trajectories of autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models to predict both agent positions and control inputs conditioned on the scene contexts. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using nonlinear Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require higher order statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent control inputs as opposed to positions, we propagate the moments of uncertain control inputs through the nonlinear motion dynamics to obtain the exact moments of uncertain position over the planning horizon. To this end, we construct deterministic linear dynamical systems that govern the exact time evolution of the moments of uncertain position in the presence of uncertain control inputs. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.
翻译:本文介绍了在深神经网络(DNNs)对其他物剂未来前景进行概率预测时,评估自主车辆轨迹风险的快速非抽样方法,评估自主车辆轨迹风险的快速非抽样方法; 介绍的方法涉及对不确定预测的广泛表述,包括高塞夫的不平等和非高塞夫混合模型,以预测代理人位置和控制根据现场环境条件提供的投入; 我们表明,当Gausian混合模型(GMMM)了解代理人职位时,风险评估问题可以迅速得到解决,以现有数字方法任意确定准确度; 为了解决非加西安混合剂职位模型的风险评估问题,我们提议使用非线性Chebyshev的不平等和非加西安混合模型(SOS)编程来发现风险的上限; 这两种模型都有兴趣,因为前者更快,而后者可能任意收紧。 这些方法只需要更稳定的物剂位置的统计时,才能确定风险的上限。 在了解代理人控制投入的概率模型时,而不是位置,我们提议使用非线性风险评估风险范围,我们通过对动态的动态进行不固定的状态评估,从而确定准确度控制。