Topological Information-Theoretic Belief Space Planning with Optimality Guarantees
This work addresses the computational bottleneck in belief space planning for robotics or AI systems, offering incremental improvements with provable guarantees.
The paper tackles the computational expense of globally optimal belief space planning in high-dimensional states by introducing a method to efficiently determine error bounds for topological belief space planning, providing global optimality guarantees or uncertainty margins, with empirical analysis showing tightness of these bounds and a relation to a more efficient metric for online performance.
Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. Our recently introduced topological belief space planning t-bsp instead performs decision making considering only topologies of factor graphs that correspond to posterior future beliefs. In this paper we contribute to this body of work a novel method for efficiently determining error bounds of t-bsp, thereby providing global optimality guarantees or uncertainty margin of its solution. The bounds are given with respect to an optimal solution of information theoretic BSP considering the previously introduced topological metric which is based on the number of spanning trees. In realistic and synthetic simulations, we analyze tightness of these bounds and show empirically how this metric is closely related to another computationally more efficient t-bsp metric, an approximation of the von Neumann entropy of a graph, which can achieve online performance.