In this paper we introduce a novel concept, topological belief space planning (BSP), that uses topological properties of the underlying factor graph representation of future posterior beliefs to direct the search for an optimal solution. This concept deviates from state-of-the-art BSP approaches and is motivated by recent results which indicated, in the context of graph pruning, that topological properties of factor graphs dominantly determine the estimation accuracy. Topological space is also often less dimensional than the embedded state space. In particular, we show how this novel concept can be used in multi-robot decentralized belief space planning in high-dimensional state spaces to overcome drawbacks of state-of-the-art approaches: computational intractability of an exhaustive objective evaluation for all candidate path combinations from different robots and dependence on the initial guess in the announced path approach, which can lead to a local minimum of the objective function. We demonstrate our approach in a synthetic simulation.
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