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 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 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.

当深度神经网络 (DNN) 生成其他智能体未来的概率预测时，本文提出了基于快速非采样的方法来评估自动驾驶汽车的轨迹风险。所提出的方法解决了不确定预测的广泛表示，包括高斯和非高斯混合模型，以预测以场景上下文为条件的代理位置和控制输入。我们表明，当学习代理位置的高斯混合模型时，风险评估问题可以通过现有的数值方法快速解决到任意精度水平。为了解决代理位置的非高斯混合模型的风险评估问题，我们建议使用非线性切比雪夫不等式和平方和规划来寻找风险的上限；它们都很有趣，因为前者要快得多，而后者可以任意紧。这些方法只需要代理位置的高阶统计矩来确定风险的上限。为了在为代理控制输入而不是位置学习模型时执行风险评估，我们通过非线性运动动力学传播不确定控制输入的时刻，以获得规划范围内不确定位置的确切时刻。为此，我们构建了确定性线性动力系统，该系统在存在不确定控制输入的情况下控制不确定位置时刻的精确时间演化。