Yilmaz, N.K., C. Evangelinos, P.F.J. Lermusiaux and N. Patrikalakis, 2008. Path Planning of Autonomous Underwater Vehicles for Adaptive Sampling Using Mixed Integer Linear Programming. IEEE Transactions, Journal of Oceanic Engineering, 33 (4), 522-537. doi: 10.1109/JOE.2008.2002105.
The goal of adaptive sampling in the ocean is to predict
the types and locations of additional ocean measurements that
would be most useful to collect. Quantitatively, what is most useful
is defined by an objective function and the goal is then to optimize
this objective under the constraints of the available observing network.
Examples of objectives are better oceanic understanding, to
improve forecast quality, or to sample regions of high interest. This
work provides a new path-planning scheme for the adaptive sampling
problem. We define the path-planning problem in terms of
an optimization framework and propose a method based on mixed
integer linear programming (MILP). The mathematical goal is to
find the vehicle path that maximizes the line integral of the uncertainty
of field estimates along this path. Sampling this path can improve
the accuracy of the field estimates the most. While achieving
this objective, several constraints must be satisfied and are implemented.
They relate to vehicle motion, intervehicle coordination,
communication, collision avoidance, etc. The MILP formulation is
quite powerful to handle different problem constraints and flexible
enough to allow easy extensions of the problem. The formulation
covers single- and multiple-vehicle cases as well as singleand
multiple-day formulations. The need for a multiple-day formulation
arises when the ocean sampling mission is optimized for
several days ahead. We first introduce the details of the formulation,
then elaborate on the objective function and constraints, and
finally, present a varied set of examples to illustrate the applicability
of the proposed method.