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

arXiv: https://arxiv.org/abs/2109.09975 · HTML: https://mlsanity.com/paper/2109.09975/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 21 Sep 2021.

## Builds on (most cited first, 20 of 20)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Rules of the Road: Predicting Driving Behavior with a Convolutional Model of Semantic Interactions](https://mlsanity.com/paper/1906.08945/) (2019)
- [Multi-Modal Trajectory Prediction of Surrounding Vehicles with Maneuver based LSTMs](https://mlsanity.com/paper/1805.05499/) (2018)
- [DiversityGAN: Diversity-Aware Vehicle Motion Prediction via Latent Semantic Sampling](https://mlsanity.com/paper/1911.12736/) (2019)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Uncertainty-Aware Driver Trajectory Prediction at Urban Intersections](https://mlsanity.com/paper/1901.05105/) (2019)
- [Efficient Black-box Assessment of Autonomous Vehicle Safety](https://mlsanity.com/paper/1912.03618/) (2019)
- [Interaction-aware Multi-agent Tracking and Probabilistic Behavior Prediction via Adversarial Learning](https://mlsanity.com/paper/1904.02390/) (2019)
- [Evaluating Trajectory Collision Probability through Adaptive Importance Sampling for Safe Motion Planning](https://mlsanity.com/paper/1609.05399/) (2016)
- [Fast Risk Assessment for Autonomous Vehicles Using Learned Models of Agent Futures](https://mlsanity.com/paper/2005.13458/) (2020)
- [Deep Kinematic Models for Kinematically Feasible Vehicle Trajectory Predictions](https://mlsanity.com/paper/1908.00219/) (2019)
- [Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems](https://mlsanity.com/paper/2101.12490/) (2021)
- [Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments](https://mlsanity.com/paper/1810.01577/) (2018)
- [Sequential Chance Optimization For Flow-Tube Based Control Of Probabilistic Nonlinear Systems](https://mlsanity.com/paper/1912.03572/) (2019)
- [Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets](https://mlsanity.com/paper/1402.6382/) (2014)
- [Non-Gaussian Chance-Constrained Trajectory Planning for Autonomous Vehicles under Agent Uncertainty](https://mlsanity.com/paper/2002.10999/) (2020)

## Built on by (most cited first, 1 of 1)

- [Calibrating Perception Uncertainty for Autonomous Driving](https://mlsanity.com/paper/2211.04340/) (2022)

## Abstract (arXiv)

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.