A Unified Resource-Constrained Framework For Graph Slam

Graphical methods have proven an extremely useful tool employed by the mobile robotics community to frame estimation problems. Incremental solvers are able to process incoming sensor data and produce maximum a posteriori ( MAP) estimates in realtime by exploiting the natural sparsity within the graph for reasonable-sized problems. However, to enable truly longterm operation in prior unknown environments requires algorithms whose computation, memory, and bandwidth (in the case of distributed systems) requirements scale constantly with time and environment size. Some recent approaches have addressed this problem through a two-step process -first the variables selected for removal are marginalized which induces density, and then the result is sparsified to maintain computational efficiency. Previous literature generally addresses only one of these two components.In this work, we attempt to explicitly connect all of the aforementioned resource constraint requirements by considering the node removal and sparsification pipeline in its entirety. We formulate the node selection problem as a minimization problem over the penalty to be paid in the resulting sparsification. As a result, we produce node subset selection strategies that are optimal in terms of minimizing the impact, in terms of Kullback-Liebler divergence (KLD), of approximating the dense distribution by a sparse one. We then show that one instantiation of this problem yields a computationally tractable formulation. Finally, we evaluate the method on standard datasets and show that the KLD is minimized as compared to other commonly-used heuristic node selection techniques.