Variational map representation for robotics

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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.