Motion planning is an essential aspect of robot autonomy, and as such it has been studied for decades, producing a wide range of planning methodologies. Path planners are generally categorised as either trajectory optimisers or sampling-based planners. The latter is the predominant planning paradigm as it can resolve a path efficiently while explicitly reasoning about path safety. Yet, with a limited budget, the resulting paths are far from optimal. In contrast, state-of-the-art trajectory optimisers explicitly trade-off between path safety and efficiency to produce locally optimal paths. However, these planners cannot incorporate updates from a partially observed model such as an occupancy map and fail in planning around information gaps caused by incomplete sensor coverage.
Autonomous exploration adds another twist to path planning. The objective of exploration is to safely and efficiently traverse through an unknown environment in order to map it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of the map. However, optimising over the entire space of trajectories is computationally intractable. Therefore, most exploration algorithms relax the general formulation by optimising a simpler one, for example finding the single next best view, resulting in suboptimal performance.
This thesis investigates methodologies for optimal and safe exploration over continuous paths. Contrary to existing exploration algorithms that break exploration into independent sub-problems of finding goal points and planning safe paths to these points, our holistic approach simultaneously optimises the coupled problems of where and how to explore. Thus, offering a shift in paradigm from next best view to next best path. With exploration defined as an optimisation problem over continuous paths, this thesis explores two different optimisation paradigms; Bayesian and functional.