Bayesian Optimisation for Safe Navigation under Localisation Uncertainty

In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.Comment: To appear in the proceedings of the 18th International Symposium on Robotics Research (ISRR 2017

Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard. While reasonable practical solutions have been advanced, they can often fail to find the best optima. Surprisingly, there is little theoretical analysis of this crucial problem in the literature. To address this, we derive a cumulative regret bound for Bayesian optimisation with Gaussian processes and unknown kernel hyper-parameters in the stochastic setting. The bound, which applies to the expected improvement acquisition function and sub-Gaussian observation noise, provides us with guidelines on how to design hyper-parameter estimation methods. A simple simulation demonstrates the importance of following these guidelines.Comment: 16 pages, 1 figur

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

ADMM-based Adaptive Sampling Strategy for Nonholonomic Mobile Robotic Sensor Networks

This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at unmeasured positions, which enables the sampling optimization problem to be formulated by the use of the log determinant of a predicted covariance matrix at next sampling locations. The control, movement and nonholonomic dynamics constraints of the mobile sensors are also considered in the adaptive sampling optimization problem. In order to tackle the nonlinearity and nonconvexity of the objective function in the optimization problem we first exploit the linearized alternating direction method of multipliers (L-ADMM) method that can effectively simplify the objective function, though it is computationally expensive since a nonconvex problem needs to be solved exactly in each iteration. We then propose a novel approach called the successive convexified ADMM (SC-ADMM) that sequentially convexify the nonlinear dynamic constraints so that the original optimization problem can be split into convex subproblems. It is noted that both the L-ADMM algorithm and our SC-ADMM approach can solve the sampling optimization problem in either a centralized or a distributed manner. We validated the proposed approaches in 1000 experiments in a synthetic environment with a real-world dataset, where the obtained results suggest that both the L-ADMM and SC- ADMM techniques can provide good accuracy for the monitoring purpose. However, our proposed SC-ADMM approach computationally outperforms the L-ADMM counterpart, demonstrating its better practicality.Comment: submitted to IEEE Sensors Journal, revised versio