Modelling sand ripples in mine countermeasure simulations by means of stochastic optimal control

TL;DR

The paper tackles coverage path planning for autonomous mine countermeasure missions in seabed environments where sand ripples degrade mine detection. It extends a stochastic optimal control CPP framework by introducing a ripple-domain multiplier via a two-dimensional domain function and a directional Ripple term, orienting planned trajectories perpendicular to ripples. The objective remains to minimize the survey time $T_f$ while enforcing an expected residual risk constraint $\mathbb{E}[q(T_f)]$, computed through Monte Carlo integration of the survival probability $e^{-\int_0^{T_f} \gamma(\mathbf{x}(\tau),\boldsymbol{\omega}) d\tau}$. Results for up to two vehicles show ripple-aware planning increases both mission duration and computation time but produces more realistic, scalable trajectories; the framework remains extensible and points to speed-ups via quasi-Monte Carlo methods and general domain shapes. These findings improve the fidelity of MCM simulations in heterogeneous seabed conditions and provide a foundation for more efficient, ripple-aware mission planning.

Abstract

Modelling and simulating mine countermeasures (MCM) search missions performed by autonomous vehicles equipped with a sensor capable of detecting mines at sea is a challenging endeavour. In this work, we present a novel way to model and account for sand ripples present on the bottom of the ocean while calculating trajectories for the autonomous vehicles by means of a stochastic optimal control framework. It is known from the scientific literature that these ripples impact the sea mine detection capabilities of the autonomous vehicles.

Figures (5)

• Figure 1: Schematic view the two-dimensional rectangular function (left) and two dimensional rectangular function on the domain $\Omega = \left[5,25\right]^2$ (right).
• Figure 2: The ripple function for ripples at $135^\text{o}$.
• Figure 3: Delimitation of the ripple zone. Sand ripples are present in the upper-left triangle at $135^\text{o}$ and depicted by the red dotted line.
• Figure 4: Trajectories and residual MCM risks, see Tab. \ref{['Tab:res_1S']}, for the results of the different cases as defined in Tab. \ref{['Tab:cases']}. The red color represents the zone that has been surveyed by the sensor, while the blue zone has not been surveyed. The detection probability of a mine by the sensor in the red zone is 1.0 or 100 % and 0 % in the blue zone. The black line represents the trajectory of the autonomous vehicle.
• Figure 5: Trajectories and residual MCM risks, see Tab. \ref{['Tab:res_2S']}, for the results of the different cases as defined in Tab. \ref{['Tab:cases']}. The red color represents the zone that has been surveyed by the combined sensors, while the blue zone has not been surveyed. The detection probability of a mine by the combined sensors in the red zone is 1.0 or 100 % and 0 % in the blue zone. The black lines represent the trajectories of the autonomous vehicles.