Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures

TL;DR

This paper introduces fast, non-sampling methods for risk assessment in autonomous vehicles using deep neural network predictions of other agents' futures, applicable to Gaussian and non-Gaussian models, with demonstrated efficiency on real datasets.

Contribution

It develops rapid, non-sampling risk assessment techniques for complex probabilistic models of agent behavior, including bounds for non-Gaussian distributions and moment propagation for control inputs.

Findings

Methods are computationally efficient and accurate.

Effective on real-world datasets like Argoverse and CARLA.

Able to rapidly assess low probability risk events.

Abstract

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.