Planning and executing optimal non-entangling paths for tethered underwater vehicles

In this paper, we present a method to improve the navigation of tethered underwater vehicles by computing optimal paths that prevent their tethers from becoming entangled in obstacles. To accomplish this, we define the Non-Entangling Travelling Salesperson Problem (NE-TSP) as an extension of the Travelling Salesperson Problem with a non-entangling constraint. We compute the optimal solution to the NE-TSP by constructing a Mixed Integer Programming model, leveraging homotopy augmented graphs to plan an optimal trajectory through a set of inspection points, while maintaining a non-entangling guarantee. To avoid the computational expense of computing an optimal solution to the NE-TSP, we also introduce several methods to compute near-optimal solutions. In a set of simulated trials, our method was able to plan optimal non-entangling paths through a variety of environments. These results were then validated in a set of pool and field trials using a Seabotix vLBV300 underwater vehicle. The paths generated by our method were then compared to human-generated paths.