  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.
