# Belief Space Planning: A Covariance Steering Approach

arXiv: https://arxiv.org/abs/2105.11092 · HTML: https://mlsanity.com/paper/2105.11092/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2021.

## Built on by (most cited first, 5 of 5)

- [Filter-Aware Model-Predictive Control](https://mlsanity.com/paper/2304.10246/) (2023)
- [IBBT: Informed Batch Belief Trees for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2304.10984/) (2023)
- [Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance](https://mlsanity.com/paper/2508.06052/) (2025)
- [Digital Twins: McKean-Pontryagin Control for Partially Observed Physical Twins](https://mlsanity.com/paper/2510.00937/) (2025)
- [Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control](https://mlsanity.com/paper/2604.24663/) (2026)

## Abstract (arXiv)

A new belief space planning algorithm, called covariance steering Belief RoadMap (CS-BRM), is introduced, which is a multi-query algorithm for motion planning of dynamical systems under simultaneous motion and observation uncertainties. CS-BRM extends the probabilistic roadmap (PRM) approach to belief spaces and is based on the recently developed theory of covariance steering (CS) that enables guaranteed satisfaction of terminal belief constraints in finite-time. The nodes in the CS-BRM are sampled in belief space and represent distributions of the system states. A covariance steering controller steers the system from one BRM node to another, thus acting as an edge controller of the corresponding belief graph that ensures belief constraint satisfaction. After the edge controller is computed, a specific edge cost is assigned to that edge. The CS-BRM algorithm allows the sampling of non-stationary belief nodes, and thus is able to explore the velocity space and find efficient motion plans. The performance of CS-BRM is evaluated and compared to a previous belief space planning method, demonstrating the benefits of the proposed approach.