We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving inference problems formulated in terms of either discrete or continuous graphical models, at present, no similarly general tools exist enabling the same functionality for hybrid discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for inference problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous inference problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a "discrete part" and a "continuous part" that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to approximate the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to distinct robot perception applications, including robust pose graph optimization, and object-based mapping and localization.
翻译:我们描述在机器人应用中常见的一组离散、连续因素图中,一个最大误判(MAP)的一般方法。虽然有公开可用的工具,提供灵活和容易使用的界面,以说明和解决以离散或连续图形模型或连续图形模型拟订的推论问题,但目前没有类似的通用工具,能够对混合离散、连续问题产生相同的功能。我们的目标是解决这一问题。我们特别提供一个图书馆(DC-SAM),将因子图中界定的误判问题的现有工具扩大到离散、连续模型的设置。我们工作的一个关键贡献是,为高效恢复离散、连续和连续的推论问题所形成的近似解决办法,我们的方法的主要洞察力是,虽然对连续和离散的离散状态空间的共同误判往往很难,许多常见的离散、连续的问题可以自然地分为一个“离散”部分和“连续部分”,可以单独轻易地解决。我们的工作的主要贡献是一个新的解决办法,即高效地恢复离散和连续的解算的精确度模型,我们通过直径的精确的推算方法,我们提出的离和连续的演算方法,我们提出的离和连续地推算了离的精确的推算。