Variational map representation for robotics

想象一下，在一个不知名的城市散步，却没有地图。当你走路时，你会记住路径：街道名称、建筑、你所做的转弯以及它们之间的距离，从而创建一幅你的路线的心理地图。同时，你使用这种动态表示法来估计你的位置，例如，通过识别远处的教堂尖顶，或者通过记住你走了多远。第二天，你可以用这张“地图”进一步探索这座城市。这种方法在移动机器人中被称为同步定位和映射(SLAM)，用于创建未知环境的表示。这些地图同时(和后来)用于估计机器人的位置，而不依赖于全球定位系统等外部系统。SLAM的基本数学基础现在已为人所知：从传感器数据中提取和识别特征，处理不确定的测量，融合来自多个传感器的噪声数据，以及减少识别先前访问过的站点时的累积误差。许多成功的SLAM演示都是在平面世界的假设下进行的(3自由度估计)。但与SLAM相关的许多悬而未决的问题仍然存在，包括在大规模、动态的3D环境中估计不受约束的传感器运动和地图。拟议的研究计划调查针对SLAM问题的复杂环境表示策略的开发--因此通常更有效的算法。特别是，我计划科学地评估现有地图表示的效率和有效性，并开发一种新的方法，将变分技术结合到概率SLAM估计框架内对环境(即基于能量的隐式曲面)进行建模。

Imagine going for a walk in an unknown city without a map. As you walk, you memorize the path: street names, buildings, turns that you made and distances between them, creating a mental map of your route. At the same time you use this dynamic representation to estimate your location by recognizing, for example, church steeples from a distance or by remembering how far you have walked. You can use this "map" to explore the city even further on the next day. This approach is known in mobile robotics as Simultaneous Localization and Mapping (SLAM) and is used to create representations of unknown environments. These maps are concurrently (and later) used to estimate the robot's location without relying on external systems such as the Global Positioning System. Basic mathematical foundations of SLAM are now known: extraction and recognition of features from sensor data, dealing with uncertain measurements, fusion of noisy data from multiple sensors, and the reduction of accumulated errors upon recognition of previously visited sites. Numerous successful SLAM demonstrations have been carried out under assumptions of planar worlds (3 degree of freedom estimation). But many open issues related to SLAM remain, including the estimation of unconstrained sensor motion and maps within large-scale, dynamic, 3D environments. The proposed research program investigates the development of sophisticated environment representation strategies--and thus more effective algorithms in general--for the SLAM problem. In particular, I plan to scientifically evaluate the efficiency and effectiveness of existing map representations and to develop a novel method to incorporate variational techniques to model the environment (i.e. energy-based implicit surfaces) within a probabilistic SLAM estimation framework.