# An Integrated Localisation, Motion Planning and Obstacle Avoidance Algorithm in Belief Space

arXiv: https://arxiv.org/abs/2101.11566 · HTML: https://mlsanity.com/paper/2101.11566/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 27 Jan 2021.

## Builds on (most cited first, 4 of 4)

- [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)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and actuation errors compound to the errors introduced while estimating features of the environment. We present a novel approach (1) to incorporate these uncertainties for robot state estimation and (2) to compute the probability of collision pertaining to the estimated robot configurations. The expression for collision probability is obtained as an infinite series and we prove its convergence. An upper bound for the truncation error is also derived and the number of terms required is demonstrated by analyzing the convergence for different robot and obstacle configurations. We evaluate our approach using two simulation domains which use a roadmap-based strategy to synthesize trajectories that satisfy collision probability bounds.