# Learned Risk Metric Maps for Kinodynamic Systems

arXiv: https://arxiv.org/abs/2302.14803 · HTML: https://mlsanity.com/paper/2302.14803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints](https://mlsanity.com/paper/1410.6445/) (2014)
- [Variational End-to-End Navigation and Localization](https://mlsanity.com/paper/1811.10119/) (2018)
- [Medical Dead-ends and Learning to Identify High-risk States and Treatments](https://mlsanity.com/paper/2110.04186/) (2021)
- [An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments](https://mlsanity.com/paper/1905.00532/) (2019)
- [Monte Carlo Motion Planning for Robot Trajectory Optimization Under Uncertainty](https://mlsanity.com/paper/1504.08053/) (2015)
- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling](https://mlsanity.com/paper/2008.10180/) (2020)
- [OptimizedDP: An Efficient, User-friendly Library For Optimal Control and Dynamic Programming](https://mlsanity.com/paper/2204.05520/) (2022)
- [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)
- [Tools and Practices for Responsible AI Engineering](https://mlsanity.com/paper/2201.05647/) (2022)
- [Distributionally robust risk map for learning-based motion planning and control: A semidefinite programming approach](https://mlsanity.com/paper/2105.00657/) (2021)

## Abstract (arXiv)

We present Learned Risk Metric Maps (LRMM) for real-time estimation of coherent risk metrics of high dimensional dynamical systems operating in unstructured, partially observed environments. LRMM models are simple to design and train -- requiring only procedural generation of obstacle sets, state and control sampling, and supervised training of a function approximator -- which makes them broadly applicable to arbitrary system dynamics and obstacle sets. In a parallel autonomy setting, we demonstrate the model's ability to rapidly infer collision probabilities of a fast-moving car-like robot driving recklessly in an obstructed environment; allowing the LRMM agent to intervene, take control of the vehicle, and avoid collisions. In this time-critical scenario, we show that LRMMs can evaluate risk metrics 20-100x times faster than alternative safety algorithms based on control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJ-reach), leading to 5-15% fewer obstacle collisions by the LRMM agent than CBFs and HJ-reach. This performance improvement comes in spite of the fact that the LRMM model only has access to local/partial observation of obstacles, whereas the CBF and HJ-reach agents are granted privileged/global information. We also show that our model can be equally well trained on a 12-dimensional quadrotor system operating in an obstructed indoor environment. The LRMM codebase is provided at https://github.com/mit-drl/pyrmm.