Time-optimal path planning in dynamic flows using level set equations: realistic applications

Abstract

The level set methodology for time-optimal path planning is employed to predict collision-free and fastest time trajectories for swarms of underwater vehicles deployed in the Philippine Archipelago region. To simulate the multiscale ocean flows in this complex region, a data-assimilative primitive-equation ocean modeling system is employed with telescoping domains that are interconnected by implicit two-way nesting. These data-driven multiresolution simulations provide a realistic flow environment, including variable large-scale currents, strong jets, eddies, wind-driven currents and tides. The properties and capabilities of the rigorous level set methodology are illustrated and assessed quantitatively for several vehicle types and mission scenarios. Feasibility studies of all-to-all broadcast missions, leading to minimal time transmission between source and receiver locations, are performed using a large number of vehicles. The results with gliders and faster propelled vehicles are compared. Reachability studies, i.e. determining the boundaries of regions that can be reached by vehicles for exploratory missions, are then exemplified and analyzed. Finally, the methodology is used to determine the optimal strategies for fastest time pickup of deployed gliders by means of underway surface vessels or stationary platforms. The results highlight the complex effects of multiscale flows on the optimal paths, the need to utilize the ocean environment for more efficient autonomous missions and the benefits of including ocean forecasts in the planning of timeoptimal paths.

Energy efficient path planning for a marine surface vehicle considering heading angle

“…Using the configuration space, a graph search algorithm can be easily adopted, as the vehicle can be regarded as one grid point in the overall grid map. The shape of the vehicle is assumed to be a streamlined and slender mono-hull body with an order of magnitude longer length overall (LOA) than the beam or draft (Newman, 1977).…”

“…The edge cost is determined based on information about the current and next node to be traveled. The total forces on the vehicle due to environmental effects can be precisely calculated using a potential theory (Newman, 1977) based on the concept of the velocity potential of the water particle; however this requires too much computational load. The ship resistance solution is an appropriate alternative to handle this problem.…”

Optimal Planning and Sampling Predictions for Autonomous and Lagrangian Platforms and Sensors in the Northern Arabian Sea

“…Gliders were piloted in a yo-yo pattern (1,000 m dives in four to five hours) and their reachability was computed accordingly (e.g., Lolla et al, 2014a). Figure 2b illustrates such a glider reachability forecast overlaid on a 2 m mesoscale vorticity forecast.…”

“…The corresponding time-optimal path can then be extracted from the dynamic reachability front prediction by solving a particle backtracking ordinary differential equation (ODE; Lolla et al, 2014b). These equations were applied to gliders and AUVs for reachability and path planning, and coordinated path planning of swarms, in realistic current simulations (Lolla et al, 2014a(Lolla et al, , 2015. They were theoretically extended to anisotropic motions and to fully three-dimensional paths, including planning for floats or other vehicles with constrained relative motions.…”

Autonomous & adaptive oceanographic front tracking on board autonomous underwater vehicles

“…As a result, environmentally adaptive autonomous sampling methods are still in the development and testing phases for the smaller AUV groups. For general reviews on oceanic adaptive sampling and path planning, we refer to [2]- [11]. Related works on adaptive front tracking and onboard routing include [12]- [17].…”