Continuous Exploitative Measurement Tra jectories Using Bayesian Optimisation

Abstract

Line-based sampling strategies aim to capture as much information as possible along a trajectory, whilst minimizing the trajectory's length. The current state of the art primarily contains exploration techniques that focus on uniformly sampling the measurement space. In this work, Bayesian optimization is used to create a novel exploitative line-based sampling strategy, that is able to guide the sampling process towards interesting regions.

Keywords

• Bayesian Optimization
• Line-Based Sampling
• Experiments

Introduction

Automated data collecting, using robots and drones, is omnipresent in both scienti c studies and engineering applications. In such a context, the length of the measurement trajectory is limited by battery restrictions or operating costs. As such, a line-based sampling strategy is used, which aims at minimising the trajectory length whilst maximising the information gained per step. The current state of the art primarily contains explorative techniques that uniformly sample the measurement space [ 1 ]. A model-driven approach allows the strategy to create a representation of the measurement space which can guide the sampling process towards interesting regions. In this work, Bayesian optimisation (BO) is used to create a line-based sampling strategy for global optimization that naturally deals with the exploration-exploitation trade o . Classic BO aims to nd the global optimum of the measurement space, using few data-points. This is typically quanti ed by evaluating an Acquisition Function (AF) over the entire space. Maximising the AF returns the sample location that has most potential to improve on the current global optimum. The maximum of the AF is iteratively acquired and recalculated in the search for the global Copyright 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

R. Delanghe et al. optimum. The advantage of using an AF is that it naturally deals with the exploration exploitation trade-o .

In this work, BO is used to create a Line-based Bayesian optimisation (LBO) strategy. The AF's maximum is used as a waypoint for the measurement probe. To reach this point, the probe moves in small steps, straight towards the waypoint and samples at every step until it is reached. At every step, it is allowed to deviate from its trajectory by some angle if this results in the sampling of a point with a higher acquisition score. The stepsize and angle of deviation are parameters of the strategy. This LBO strategy can only be used in convex spaces and is deterministic if the underlying BO is deterministic as well. 3

Experimentation, Results And Discussion

(a) RMSE Between estimated space and the ground truth. (b) Fraction of the maximum sampled value, compared to the global maximum

References

1. Van Steenkiste , T. , J. van der Herten , D. Deschrijver , and T. Dhaene . 2019 , Apr . ALBATROS: adaptive line-based sampling trajectories for sequential measurements . Engineering with Computers 35 ( 2 ): 537 - 550 .

2. H. Choset and P. Pignon , Coverage path planning: The boustrophedon cellular decomposition , in Field and service robotics , pp. 203 { 209 , Springer, 1998 .

3. MathWorks, peaks. https://nl.mathworks.com/help/matlab/ref/peaks.html.