Lolla, T.; Ueckermann, M.P.; Yigit, K.; Haley, P.J.; Lermusiaux, P.F.J., 2012, Path planning in time dependent flow fields using level set methods, 2012 IEEE International Conference on Robotics and Automation (ICRA), 166-173, 14-18 May 2012,
We develop and illustrate an efficient but rigorous
methodology that predicts the time-optimal paths of ocean
vehicles in dynamic continuous flows. The goal is to best
utilize or avoid currents, without limitation on these currents
nor on the number of vehicles. The methodology employs a
new modified level set equation to evolve a wavefront from
the starting point of vehicles until they reach their desired
goal locations, combining flow advection with nominal vehicle
motions. The optimal paths of vehicles are then computed
by solving particle tracking equations backwards in time.
The computational cost is linear with the number of vehicles
and geometric with spatial dimensions. The methodology is
applicable to any continuous flows and many vehicles scenarios.
Present illustrations consist of the crossing of a canonical
uniform jet and its validation with an optimization problem,
as well as more complex time varying 2D flow fields, including
jets, eddies and forbidden regions.