# Learned Risk Metric Maps for Kinodynamic Systems

## TL;DR

This paper introduces Learned Risk Metric Maps (LRMM), a fast and adaptable method for estimating collision risks in high-dimensional dynamical systems, enabling real-time safety decisions in complex environments.

## Contribution

LRMM provides a simple, trainable approach for real-time risk estimation applicable to various systems and environments, outperforming traditional safety algorithms in speed and collision reduction.

## Key findings

- LRMM evaluates risk 20-100x faster than control barrier functions and Hamilton-Jacobi reachability.
- LRMM reduces obstacle collisions by 5-15% compared to traditional methods.
- LRMM effectively models risk in high-dimensional, partially observed systems like quadrotors.

## Abstract

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.