RI: Small: Ultra-Sparsifiers for Fast and Scalable Mapping and 3D Reconstruction on Mobile Robots

本课题开发并实现了移动机器人的高效、大比例尺测绘和三维重建。我们开发了一种新的优化范例，结合了直接方法和迭代方法的优点，通过(1)研究一类新的机器人映射问题的优化方法：子图预条件共轭梯度（SPCG），结合了直接法和迭代法的优点，同时最小化缺点，(2)研究子图预条件选择和质量分析，(3)将上述技术应用于大规模3D重建问题的移动机器人，以及(4)研究这些算法的在线版本。我们通过增量地构建图形稀疏器来调整SPCG，这给了我们一个很好的预处理条件。除了机器人学和视觉之外，我们还证明了近似分布的一般问题也可以推导出类似的边界。提出的工作的具体交付成果是一个软件包，该软件包嵌入了解决映射/重建非线性优化问题的新混合方法，并且易于部署到广泛的移动机器人平台：陆地，空中，水下或地下，单独或团队行动。机器人研究社区可以使用这项技术，它在问题的大小、速度和在线适用性方面都大大提高了当前绘图/重建软件的能力。最后，在更局部的层面上，这项研究影响了佐治亚理工学院研究生和本科生的教育。

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.