iX-BSP: Belief Space Planning through Incremental Expectation

Belief space planning (BSP) is a fundamental problem in robotics. Determining an optimal action quickly grows intractable as it involves calculating the expected accumulated cost (reward), where the expectation accounts for all future measurement realizations. State of the art approaches therefore resort to simplifying assumptions and approximations to reduce computational complexity. Importantly, while in robotics re-planning is essential, these approaches calculate each planning session from scratch. In this work we contribute a novel approach, iX-BSP, that is based on the key insight that calculations in consecutive planning sessions are similar in nature and can be thus re-used. Our approach performs incremental calculation of the expectation by appropriately re-using computations already performed in a precursory planing session while accounting for the information obtained in inference between the two planning sessions. The formulation of our approach considers general distributions and accounts for data association aspects. We evaluate iX-BSP in statistical simulation and show that incremental expectation calculations significantly reduce runtime without impacting performance.