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 flnal 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 …. A method for generating the optimal path is also presented which iteratively solves the no wind case to intercept a moving virtual target. I. Introduction Optimal path planning is an important problem for robotics and unmanned vehicles. In this paper, we explore a method for flnding the shortest path from an initial position and orientation to a flnal position and and orientation in the two-dimensional plane for an aircraft with a bounded turning radius in the presence of a constant wind. This work was motivated by our group’s work with our ∞eet of small autonomous aircraft. Each modifled Sig Rascal aircraft ∞ies under the combined control of an ofi-the-shelf Piccolo avionics package for low level control and an onboard PC104 computer for higher level tasks. These aircraft ∞y at a nominal speed of 20 m/s, and wind speeds of over 5 m/s have been encountered during ∞ight testing. The problem described above was flrst solved in the case of no wind by Dubins using geometric arguments 8