# Safe motion planning with environment uncertainty

arXiv: https://arxiv.org/abs/2305.06004 · HTML: https://mlsanity.com/paper/2305.06004/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 6 of 6)

- [Online Replanning in Belief Space for Partially Observable Task and Motion Problems](https://mlsanity.com/paper/1911.04577/) (2019)
- [Monte Carlo Motion Planning for Robot Trajectory Optimization Under Uncertainty](https://mlsanity.com/paper/1504.08053/) (2015)
- [Provably Safe Robot Navigation with Obstacle Uncertainty](https://mlsanity.com/paper/1705.10907/) (2017)
- [Towards Multi-Robot Task-Motion Planning for Navigation in Belief Space](https://mlsanity.com/paper/2010.00780/) (2020)
- [Efficient motion planning for problems lacking optimal substructure](https://mlsanity.com/paper/1703.02582/) (2017)
- [An Integrated Localisation, Motion Planning and Obstacle Avoidance Algorithm in Belief Space](https://mlsanity.com/paper/2101.11566/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Framework for Task and Motion Planning based on Expanding AND/OR Graphs](https://mlsanity.com/paper/2509.00317/) (2025)
- [Reinforcement learning with timed constraints for robotics motion planning](https://mlsanity.com/paper/2601.00087/) (2025)
- [A Horizon-slicing Approach to Minimum Obstacle Displacement Planning for Robot Navigation](https://mlsanity.com/paper/2609.22974/) (2026)

## Abstract (arXiv)

We present an approach for safe motion planning under robot state and environment (obstacle and landmark location) uncertainties. To this end, we first develop an approach that accounts for the landmark uncertainties during robot localization. Existing planning approaches assume that the landmark locations are well known or are known with little uncertainty. However, this might not be true in practice. Noisy sensors and imperfect motions compound to the errors originating from the estimate of environment features. Moreover, possible occlusions and dynamic objects in the environment render imperfect landmark estimation. Consequently, not considering this uncertainty can wrongly localize the robot, leading to inefficient plans. Our approach thus incorporates the landmark uncertainty within the Bayes filter estimation framework. We also analyze the effect of considering this uncertainty and delineate the conditions under which it can be ignored. Second, we extend the state-of-the-art by computing an exact expression for the collision probability under Gaussian distributed robot motion, perception and obstacle location uncertainties. We formulate the collision probability process as a quadratic form in random variables. Under Gaussian distribution assumptions, an exact expression for collision probability is thus obtained which is computable in real-time. In contrast, existing approaches approximate the collision probability using upper-bounds that can lead to overly conservative estimate and thereby suboptimal plans. We demonstrate and evaluate our approach using a theoretical example and simulations. We also present a comparison of our approach to different state-of-the-art methods.