Bayesian Optimisation for Planning under Uncertainty

Abstract

Under an increasing demand for data to understand critical processes in our world, robots have become powerful tools to automatically gather data and interact with their environments. In this context, this thesis addresses planning problems where limited prior information leads to uncertainty about the outcomes of a robot's decisions. The methods are based on Bayesian optimisation (BO), which provides a framework to solve planning problems under uncertainty by means of probabilistic modelling. As a first contribution, the thesis provides a method to find energy-efficient paths over unknown terrains. The method applies a Gaussian process (GP) model to learn online how a robot's power consumption varies as a function of its configuration while moving over the terrain. BO is applied to optimise trajectories over the GP model being learnt so that they are informative and energetically efficient. The method was tested in experiments on simulated and physical environments. A second contribution addresses the problem of policy search in high-dimensional parameter spaces. To deal with high dimensionality the method combines BO with a coordinate-descent scheme that greatly improves BO's performance when compared to conventional approaches. The method was applied to optimise a control policy for a race car in a simulated environment and shown to outperform other optimisation approaches. Finally, the thesis provides two methods to address planning problems involving uncertainty in the inputs space. The first method is applied to actively learn terrain roughness models via proprioceptive sensing with a mobile robot under localisation uncertainty. Experiments demonstrate the method's performance in both simulations and a physical environment. The second method is derived for more general optimisation problems. In particular, this method is provided with theoretical guarantees and empirical performance comparisons against other approaches in simulated environments.