occupancy mapping for mobile robotics
The ability of a robot to map its own surroundings is one of the major requirements for it to be considered truly autonomous. Mapping is an infinite dimensional problem, since there are infinitely many ways an environment can be populated. This high dimensional space is what makes mapping challenging, grid maps solve this by approximating the occupancy field with a large but finite number of discrete cells. We are seeking to solve the occupancy mapping problem in its original infinite dimensional space.
This research deals intimately with stochastic processes. By definition a stochastic process is any set of random variables, indexed on the same set, that have a joint probability distribution. Nicholas is interested in researching various stochastic processes and applying them to perform exact inference on an infinite dimensional occupancy field.
Sparse approximations for online applications
Although exact inference is desired, it is not always feasible for online applications. Sparse approximations are often sort after to reduce computational and storage requirements, allowing otherwise infeasible operations to be used online while sacrificing as little accuracy as possible. Grid maps suffer from large storage requirements, however, provide no freedom to choose an optimal set of data to store. Nicholas is interested in developing spare approximations for infinite dimensional occupancy map updates, allowing their use in the field.
simultaneous localisation and mapping
Simultaneous localisation and mapping (SLAM), as the name implies is the procedure of simultaneously mapping an environment and estimating a robot’s location. Contradictory to the name, most SLAM algorithms are a recursive operation, first the pose is updated then the environment is mapped. Nicholas is interested in researching a joint probability distribution containing both a robot’s pose (position and orientation) and an infinite dimensional occupancy field, providing a means to update both simultaneously.