Optimal path planning in a constant wind with a bounded turning rate

Abstract

In this paper, we explore the problem of generating the optimal time path from an initial position and orientation to a final position and orientation in the two-dimensional plane for an aircraft with a bounded turning radius in the presence of a constant wind. Following the work of Boissonnat, we show using the Minimum Principle that the optimal path consists of periods of maximum turn rate or straight lines. We demonstrate, however, that unlike the no wind case, the optimal path can consist of three arcs where the length of the second arc is less than π. A method for generating the optimal path is also presented which iteratively solves the no wind case to intercept a moving virtual target.

Optimal path finding in direction, location, and time dependent environments

“…Unmanned aerial vehicle (UAV) routing is the predominant area of such applications, where researchers conduct an analysis of the effects of directional wind on the UAV optimal paths. In the majority of published work, the aircraft velocity and wind velocity are assumed to be constant, and the actual speed of the vehicle is equal to the sum of the two vectors [52,40]. This assumption imposes a very specific structure on the actual direction-dependent speed function and the minimum turning radius of an agent; we make no such restrictions in our forthcoming analysis.…”

“…The problem of optimal path finding for mini UAVs subjected to wind is similar in nature to the vessel routing problems, and has been extensively studied in recent years. The direction dependence of the speed function is introduced as a uniform wind vector field, which is added to a constant isotropic 'wind-free' speed of the airplane [40,41]. It is important to note that the resulting speed function has very distinct structure, and more specifically, the property of a convex polar plot.…”

Path Planning for a UAV Performing Reconnaissance of Static Ground Targets in Terrain

“…22 More recently it has been shown that in a constant wind field without obstacles, a shortest pose-to-pose path with bounded turning rate can be caclulated by transforming the final pose to a so-called virtual pose, applying the no-wind method, then transforming back. 4 Using these methods, pose-to-pose shortest path queries with no obstacles can be computed in constant time.…”

Guidance of Receiver Aircraft to Rendezvous with Tanker in the Presence of Wind

“…Ref. [10] explored the problem of finding the optimal path from an initial position and orientation to a final position and orientation for an aircraft with a limited turning radius in the presence of a constant wind. An iterative method for solving for the paths has also been presented and several examples of optimal paths in the presence of wind have been presented.…”