A modified Dubins method for optimal path planning of a Miniature Air Vehicle converging to a straight line path

Abstract

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

Optimal transition trajectory for waypoint following

“…In [13] an optimal path is computed to converge to a straight line starting from any initial configuration. Based on this result it can be shown that the γ-trajectory is the time-optimal trajectory that converges to the second waypoint segment starting from any start configuration on the first waypoint segment for γ ∈ [0, 1].…”

“…The proposed γ-trajectory takes minimum time to converge to the next waypoint segment starting from a point on the present waypoint segment. The trajectory generation is based on some results reported in rectilinear path convergence problem in [13]. A γ-trajectory is computed if the shortest distance between the waypoint and the trajectory is desired to be a certain value.…”

A modified dubins problem with partially restricted terminal conditions

“…Here, the final X position (X f ) is fixed and the final Y position (Y f ) is free. Dubins method was used for optimal path planning of miniature air vehicle converging to straight line in [4]- [6]. Way-point path following problems were discussed in [7], [8].…”

Towards autonomous airborne mapping of urban environments

“…fixed-wing UAVs) previously entailed [1]. The common problem of wind, manifesting as both opportunity and hindrance for many UAVs, has spawned many contributions in the past [4], [2].…”