  Bayesian Optimisation has gained much popularity lately, as a global
optimisation technique for functions that are expensive to evaluate or unknown
a priori. While classical BO focuses on where to gather an observation next, it
does not take into account practical constraints for a robotic system such as
where it is physically possible to gather samples from, nor the sequential
nature of the problem while executing a trajectory. In field robotics and other
real-life situations, physical and trajectory constraints are inherent
problems. This paper addresses these issues by formulating Bayesian
Optimisation for continuous trajectories within a Partially Observable Markov
Decision Process (POMDP) framework. The resulting POMDP is solved using
Monte-Carlo Tree Search (MCTS), which we adapt to using a reward function
balancing exploration and exploitation. Experiments on monitoring a spatial
phenomenon with a UAV illustrate how our BO-POMDP algorithm outperforms
competing techniques.
