# Provably Safe Robot Navigation with Obstacle Uncertainty

arXiv: https://arxiv.org/abs/1705.10907 · HTML: https://mlsanity.com/paper/1705.10907/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2017.

## Built on by (most cited first, 12 of 12)

- [Risk-Conditioned Distributional Soft Actor-Critic for Risk-Sensitive Navigation](https://mlsanity.com/paper/2104.03111/) (2021)
- [Exact and Bounded Collision Probability for Motion Planning under Gaussian Uncertainty](https://mlsanity.com/paper/2110.06348/) (2021)
- [Safe motion planning with environment uncertainty](https://mlsanity.com/paper/2305.06004/) (2023)
- [Generalizing Multi-Objective Search via Objective-Aggregation Functions](https://mlsanity.com/paper/2509.22085/) (2025)
- [An Integrated Localisation, Motion Planning and Obstacle Avoidance Algorithm in Belief Space](https://mlsanity.com/paper/2101.11566/) (2021)
- [Multi-Agent Chance-Constrained Stochastic Shortest Path with Application to Risk-Aware Intelligent Intersection](https://mlsanity.com/paper/2210.01766/) (2022)
- [MatterDoor: Sampling Zero-shot Spatio-semantic Priors using Generative Models](https://mlsanity.com/paper/2510.11014/) (2025)
- [Schr"odinger's Navigator: Imagining an Ensemble of Futures for Zero-Shot Object Navigation](https://mlsanity.com/paper/2512.21201/) (2025)
- [Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives](https://mlsanity.com/paper/2303.01631/) (2023)
- [Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments](https://mlsanity.com/paper/2305.17291/) (2023)
- [Multi-Objective Search: Algorithms, Applications, and Emerging Directions](https://mlsanity.com/paper/2510.25504/) (2025)
- [FlatLands: Generative Floormap Completion From a Single Egocentric View](https://mlsanity.com/paper/2603.16016/) (2026)

## Abstract (arXiv)

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.