I. Introduction
There has been a spurt of interest in recent years in the area of unmanned aerial vehicle (UAV) formation control and obstacle avoidance. Many interesting applications of formation flying have been studied. Examples include forest fire monitoring [1], radar deception [2], and surface-to-air missile (SAM) jamming [3]. Main considerations in formation flying include how to come together and maintain a formation and how to achieve collision/obstacle avoidance. Obstacle avoidance in a 2-D environment has been studied earlier [4], [5]. In [4], the concept of rapidly exploring random trees (RRT) originally investigated in [6] was used to find dynamically feasible obstacle-free paths. After obtaining an obstacle-free path, a reactive path planner was used to avoid pop-up obstacles. This generates trajectories that are not taxing for the vehicle, i.e., the trajectories involve less turns. As the main idea is to track a path generated a priori and avoid pop-up obstacles as they appear, this scheme does not guarantee a shortest distance path always. Also, the RRT scheme requires larger computation times than the method proposed in this brief. In [5], mixed integer linear programming (MILP) was used to design dynamically feasible trajectories for obstacle avoidance. However, the MILP scheme requires larger computation capabilities when compared to the scheme proposed in this study. Furthermore, the 2-D approach presented in this brief gives the shortest distance paths.