Bayesian Optimisation for informative continuous path planning

Environmental monitoring with mobile robots requires solving the informative path planning problem. A key challenge is how to compute a continuous path over space and time that will allow a robot to best sample the environment for an initially unknown phenomenon. To address this problem we devise a layered Bayesian Optimisation approach that uses two Gaussian Processes, one to model the phenomenon and the other to model the quality of selected paths. By using different acquisition functions over both models we tackle the exploration-exploitation trade off in a principled manner. Our method optimises sampling over continuous paths and allows us to find trajectories that maximise the reward over the path. We test our method on a large scale experiment for modelling ozone concentration in the US, and on a mobile robot modelling the changes in luminosity. Comparisons are presented against information based criteria and point-based strategies demonstrating the benefits of our method.