# iX-BSP: Incremental Belief Space Planning

arXiv: https://arxiv.org/abs/2102.09539 · HTML: https://mlsanity.com/paper/2102.09539/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [General Purpose Incremental Covariance Update and Efficient Belief Space Planning via Factor-Graph Propagation Action Tree](https://mlsanity.com/paper/1906.02249/) (2019)
- [Bayesian Incremental Inference Update by Re-using Calculations from Belief Space Planning: A New Paradigm](https://mlsanity.com/paper/1908.02002/) (2019)

## Built on by (most cited first, 6 of 6)

- [Simplified Continuous High Dimensional Belief Space Planning with Adaptive Probabilistic Belief-dependent Constraints](https://mlsanity.com/paper/2302.06697/) (2023)
- [Probabilistic Loss and its Online Characterization for Simplified Decision Making Under Uncertainty](https://mlsanity.com/paper/2105.05789/) (2021)
- [Previous Knowledge Utilization In Online Anytime Belief Space Planning](https://mlsanity.com/paper/2412.13128/) (2024)
- [No Compromise in Solution Quality: Speeding Up Belief-dependent Continuous POMDPs via Adaptive Multilevel Simplification](https://mlsanity.com/paper/2310.10274/) (2023)
- [Achieving mouse-level strategic evasion performance using real-time computational planning](https://mlsanity.com/paper/2211.02700/) (2022)
- [Action-Gradient Monte Carlo Tree Search for Non-Parametric Continuous (PO)MDPs](https://mlsanity.com/paper/2503.12181/) (2025)

## Abstract (arXiv)

Deciding what's next? is a fundamental problem in robotics and Artificial Intelligence. Under belief space planning (BSP), in a partially observable setting, it involves calculating the expected accumulated belief-dependent reward, where the expectation is with respect to all future measurements. Since solving this general un-approximated problem quickly becomes intractable, state of the art approaches turn to approximations while still calculating planning sessions from scratch. In this work we propose a novel paradigm, Incremental BSP (iX-BSP), based on the key insight that calculations across planning sessions are similar in nature and can be appropriately re-used. We calculate the expectation incrementally by utilizing Multiple Importance Sampling techniques for selective re-sampling and re-use of measurement from previous planning sessions. The formulation of our approach considers general distributions and accounts for data association aspects. We demonstrate how iX-BSP could benefit existing approximations of the general problem, introducing iML-BSP, which re-uses calculations across planning sessions under the common Maximum Likelihood assumption. We evaluate both methods and demonstrate a substantial reduction in computation time while statistically preserving accuracy. The evaluation includes both simulation and real-world experiments considering autonomous vision-based navigation and SLAM. As a further contribution, we introduce to iX-BSP the non-integral wildfire approximation, allowing one to trade accuracy for computational performance by averting from updating re-used beliefs when they are "close enough". We evaluate iX-BSP under wildfire demonstrating a substantial reduction in computation time while controlling the accuracy sacrifice. We also provide analytical and empirical bounds of the effect wildfire holds over the objective value.