iX-BSP: Incremental Belief Space Planning

TL;DR

This paper introduces iX-BSP, an incremental belief space planning method that re-uses calculations across planning sessions, significantly reducing computation time while maintaining accuracy, applicable to robotics and AI tasks like navigation and SLAM.

Contribution

The paper proposes a novel incremental approach to belief space planning that leverages re-using previous calculations, including a new wildfire approximation for efficiency-accuracy trade-offs.

Findings

iX-BSP reduces computation time substantially in simulations and real-world tests.

The wildfire approximation effectively balances accuracy and efficiency.

iX-BSP enhances existing planning methods by enabling incremental updates.

Abstract

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.