Application of quasi-Monte Carlo in Mine Countermeasure Simulations with a Stochastic Optimal Control Framework

TL;DR

This paper integrates quasi-Monte Carlo methods into a stochastic optimal control framework to optimize autonomous mine countermeasure missions, achieving faster computations and flexible domain handling.

Contribution

It introduces a novel combination of quasi-Monte Carlo schemes with relaxation strategies for efficient and adaptable autonomous vehicle trajectory optimization in mine detection.

Findings

Rank-1 Lattice scheme doubles speed compared to Monte Carlo

Relaxation strategy improves residual risk satisfaction

Method extends to convex quadrilateral domains

Abstract

Modelling and simulating mine countermeasures search missions performed by autonomous vehicles equipped with a sensor capable of detecting mines at sea is a challenging endeavour. The output of our stochastic optimal control implementation consists of an optimal trajectory in a square domain for the autonomous vehicle such that the total mission time is minimized for a given residual risk of not detecting sea mines. We model this risk as an expected value integral. We found that upon completion of the simulation, the user requested residual risk is usually not satisfied. We solved this by implementing a relaxation strategy which consists of incrementally increasing the square search domain. We then combined this strategy with different quasi-Monte Carlo schemes used for solving the integral. We found that using a Rank-1 Lattice scheme yields a speedup up to a factor two with respect to the Monte Carlo scheme. We also present an implementation which allows us to compute a trajectory in a convex quadrilateral domain, as opposed to a square domain, and combine it with our relaxation strategy.