# Streamlines for Motion Planning in Underwater Currents

## TL;DR

This paper introduces a novel sampling-based motion planning method for underwater vehicles that efficiently computes reachability and cost over long distances by leveraging stream functions and streamlines within complex ocean currents.

## Contribution

The paper presents a new approach using stream functions to efficiently connect points in flow fields, enabling long-range planning in complicated underwater currents.

## Key findings

- Method supports planning over hundreds of kilometres.
- Demonstrated with real current data along Australia's east coast.
- Avoids exhaustive control space search.

## Abstract

Motion planning for underwater vehicles must consider the effect of ocean currents. We present an efficient method to compute reachability and cost between sample points in sampling-based motion planning that supports long-range planning over hundreds of kilometres in complicated flows. The idea is to search a reduced space of control inputs that consists of stream functions whose level sets, or streamlines, optimally connect two given points. Such stream functions are generated by superimposing a control input onto the underlying current flow. A streamline represents the resulting path that a vehicle would follow as it is carried along by the current given that control input. We provide rigorous analysis that shows how our method avoids exhaustive search of the control space, and demonstrate simulated examples in complicated flows including a traversal along the east coast of Australia, using actual current predictions, between Sydney and Brisbane.