The goal of this work was to develop algorithms and software to generate a path that takes into account the direction of waves and wind as much as possible in order to mitigate potential damage to an autonomous underwater vehicle. A risk-based path planning algorithm to analyze real-world sensory data is combined with an enhanced sea surface model to generate a safe path.

The path planning method for sea surface vehicles prevents capsizing and bow-diving in a high sea state. A key idea is to use response amplitude operators (RAOs) or, in control terminology, the transfer functions from a sea state to a vessel’s motion, in order to find a set of speeds and headings that results in excessive pitch and roll oscillations. This information is translated to arithmetic constraints on the ship’s velocity, and are passed to a model predictive control (MPC)-based path planner to find a safe and optimal path that achieves specified goals. An obstacle avoidance capability is also added to the path planner.

A RAO is essentially a Bode plot that describes the frequency response of each of the six ship motions (i.e., roll, pitch, yaw, heave, sway, and surge) to a sea state (i.e., wave spectrum). A RAO is obtained from a linearized model of ship motions of a specific vessel hull shape at a specific speed and wave heading. Commercial software is available to compute RAOs based on computational fluid dynamics.

In order to enable online path planning, RAOs are pre-computed for all combinations of speed and wave heading at a certain interval, and are stored in memory. Then, during the online path planning, the RAOs are used to evaluate the maximum pitch and roll angles that are expected to occur when moving at a given speed and heading. This process is repeated on a discrete set of velocities, which is classified into safe and unsafe velocities by checking if the maximum pitch and roll angles are within pre-specified thresholds. Unsafe velocities are considered as obstacles in the velocity space, or velocity obstacles (VOs).VOs are translated into arithmetic constraints in the velocity space. The resulting constraints are typically non-convex.

The path planner is built upon the MPC. An optimal path planning problem with the non-convex velocity constraints obtained from the previous step is encoded into a mixed-integer linear programming (MILP). The MILP is solved online at each time step using the latest observation of the sea state in order to compute an optimal path.

This work was done by Masahiro Ono, Terrance L. Huntsberger, and Marco B. Quadrelli of Caltech for NASA’s Jet Propulsion Laboratory.

This software is available for commercial licensing. Please contact Dan Broderick at This email address is being protected from spambots. You need JavaScript enabled to view it.. Refer to NPO-49304.



This Brief includes a Technical Support Package (TSP).
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Safe Maritime Autonomous Path Planning in a High Sea State

(reference NPO49304) is currently available for download from the TSP library.

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