Towards Analytic Informative Path Planning

Abstract

Informative path planning algorithms are used to guide agents in carrying out observation actions to best learn about their environment. Prior information, predictive modelling and operational constraints are some of the considerations that go into this engineering problem. This thesis take a head on, analytic Bayesian approach towards the problem with aims to reduce the dependence on prior assumptions and to improve the adaptability of autonomous information gathering algorithms.

First, conjugate priors are used to construct Bayesian sensor models. These keep the Bayesian update step in closed-form, giving more readily applicable solutions and algebraic context for numeric approximations that go beyond such forms.

These sensor models are then integrated into stochastic processes that model the quantity of interest across the environment. Further, a novel alternative to Gaussian processes is derived using the semi conjugate prior to the multivariate Gaussian distribution. This allows for a Conjugate prior over the covariance matrix of the Gaussian process while also permitting observations that have independent Gaussian noise. In a novel finding, the covariance of this proposed model is more stable than that of a canonical noisy t processes and its covariance converges to the that of the ground truth when given the true mean and kernel function.

These models are then integrated into informative path planning algorithms using Monte Carlo Tree search driven by the mutual information of each stochastic process. The algorithms were then tested on a series of potassium density maps over New South Wales Australia. The theoretical properties of each model were demonstrated on the data set, with t processes performing equally or better than Gaussian processes depending on the priors used.