UC San Diego

These days, robots are contributing to many aspects of our lives and this role is growing. One of the fundamental problems in robotics is shape representation and mapping, that is necessary for most robotic applications. In this regard, from a stream of lidar scans or RGB-D images we model an object shape or map an environment. One of the main challenges in this regard is an appropriate shape representation with appropriate ray-tracing speed and accuracy. There are many other challenges for mapping like being 3D, continuous, probabilistic, online, containing semantic information, and the possibility of the mapping algorithm to be distributed. In this thesis we propose a novel mapping algorithm based on existing shape representation signed distance function and Gaussian Processes which is able to reconstruct an online, continuous, probabilistic 3-D representations of the geometric surfaces and semantic classes in the environments. Then we extend it to a distributed mapping algorithm that is able to be perform in a network of robots. Additionally, we propose a novel shape representation signed directional distance function (SDDF) that measures signed distance from a query location to a set surface in a desired viewing direction. The main advantage of SDDF, compared to existing shape representations, is that ray tracing can be performed as a look-up operation through a single function call. Additionally, we propose a deep neural network model for SDDF shape learning. A key property of our DeepSDDF model is that it encodes by construction that distance to the surface decreases linearly along the viewing direction. This ensures that the model represents only valid SDDF functions and allows reduction in the input dimensionality and analytical confidence in the distance prediction accuracy even far away from the surface. We show that our DeepSDDF model can represent entire object categories and interpolate or complete shapes from partial views.