This project develops and realizes efficient and large scale mapping and 3D reconstruction on mobile robots. We develop a new optimization paradigm which combines the advantages of both direct and iterative methods by (1) investigating a novel class of optimization methods for robot mapping problems: subgraph-preconditioned conjugate gradients (SPCG) that combine the advantages of direct and iterative methods while minimizing the disadvantages, (2) investigating subgraph preconditioner selection and quality analysis, (3) applying the above techniques to large-scale 3D reconstruction problem mobile robots, and (4) investigating on-line versions of these algorithms. We adapt the SPCG for this setting by incrementally building the graph sparsifier that gives us a good preconditioner.
Beyond robotics and vision, we show that similar bounds can be derived for the general problem of approximating distributions. A concrete deliverable of the proposed work is a software package that embeds the new hybrid approach to solving the mapping/reconstruction non-linear optimization problem, and is easily deployable to a wide range of mobile robotic platforms: terrestrial, aerial, underwater, or underground, acting individually or in teams. The robotics research community has access to this technology, which provides great improvement over the capabilities of current mapping/reconstruction software, both in terms of the size of the problem, as well as in terms of speed and online applicability. Finally, at a more local level, this research impacts education of both graduate and undergraduate students at Georgia Tech.