# Provably Safe Robot Navigation with Obstacle Uncertainty

## TL;DR

This paper develops mathematically rigorous methods to ensure safe robot navigation under uncertain, noisy environmental observations, enabling reliable planning for autonomous systems like drones and cars.

## Contribution

It introduces new algorithms for safety verification that are computationally efficient and effective even in complex environments, improving upon prior approaches.

## Key findings

- Algorithms provide tighter safety bounds than previous methods.
- Safety evaluation complexity is independent of environment complexity.
- A safe variant of the RRT planning algorithm is proposed.

## Abstract

As drones and autonomous cars become more widespread it is becoming increasingly important that robots can operate safely under realistic conditions. The noisy information fed into real systems means that robots must use estimates of the environment to plan navigation. Efficiently guaranteeing that the resulting motion plans are safe under these circumstances has proved difficult. We examine how to guarantee that a trajectory or policy is safe with only imperfect observations of the environment. We examine the implications of various mathematical formalisms of safety and arrive at a mathematical notion of safety of a long-term execution, even when conditioned on observational information. We present efficient algorithms that can prove that trajectories or policies are safe with much tighter bounds than in previous work. Notably, the complexity of the environment does not affect our methods ability to evaluate if a trajectory or policy is safe. We then use these safety checking methods to design a safe variant of the RRT planning algorithm.