Hogue, AndrewKhattak, Saad Rustam2012-10-112022-03-292012-10-112022-03-292012-07-01https://hdl.handle.net/10155/273Simultaneous Localization and Mapping (SLAM) algorithms are used by autonomous robots to build or update maps of an environment while maintaining their position simultaneously. A fundamental open problem in SLAM is the e ective representation of the map in unknown, ambiguous, complex, dynamic environments. Representing such environments in a suitable manner is a complex task. Existing approaches to SLAM use map representations that store individual features (range measurements, image patches, or higher level semantic features) and their locations in the environment. The choice of how the map is represented produces limitations which in many ways are unfavourable for application in real-world scenarios. In this thesis, a new approach to SLAM is explored that rede nes sensing and robot motion as acts of deformation of a di erentiable surface. Distance elds and level set methods are utilized to de ne a parallel to the components of the SLAM estimation process and an algorithm is developed and demonstrated. The variational framework developed is capable of representing complex dynamic scenes and spatially varying uncertainty for sensor and robot models.enSLAMLevel setDistance fieldsImplicit surfacesMappingThesis