A Variational Approach to Mapping and Localization

A fundamental open problem in SLAM is the effective 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 we represent the map produces limitations which in many ways are unfavourable for application in real-world scenarios. In this paper, we explore a new approach to SLAM that redefines sensing and robot motion as acts of deformation of a differentiable surface. Distance fields and level set methods are utilized to define 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.