Unmanned Aerial Vehicle Coordination on Closed Convex Paths in Wind

Abstract

I N THIS Note we consider the problem of motion coordination of an aerial robotic network in the presence of steady, uniform winds. We present application examples of multivehicle coordination and path planning methods. The control laws we employ are extensions of previous research results on particle coordination and minimum-time path planning in steady, uniform wind. In prior work most relevant to this Note, Lyapunov-based control laws are provided to drive a collective of vehicles to a symmetric pattern along a circular orbit [1], to coordinated patterns on convex curves [2], and to coordinated patterns in the presence of winds [3]. The development of minimum-time path planning algorithms is also relevant [4,5]. The vehicle coordination framework described here may serve as an intermediate layer between low-level vehicle control and highlevel mission planning. We assume that the control signal is the turn rate-of-change, which, in the case of a fixed-wing aircraft, may be controlled by regulating the bank angle.We also assume that the lowlevel controller (the autopilot) can execute the desired turn-rate commands. Similar vehicle models have been frequently used to design kinematic control laws to track targets with aerial vehicles [6– 9]. Coordinated steering laws were presented in [10], where it was shown that collective motion along parallel lines or around the same circle are the only relative equilibria if the particle steering laws depend only on relative positions and headings. Motivated by the need for coordination on curves of arbitrary shapes, Lyapunov-based control laws were presented in [11], in which relative arc lengths between particles were used for coordination, as opposed to relative phases. Leader–follower approaches have also been studied (see, for example, [12,13] and the references therein). The contributions of this Note are twofold: First, we extend an existing motion-coordination framework to the case in which the vehicles travel around strictly convex loops in the presence of a steady, uniform flowfield. Second, we present an approximation method that generates strictly convex curves from convex paths that may contain straight segments. The latter method is important to allow coordination on time-optimal paths, which frequently contain straight segments. This Note also includes simulation results focusing on two application examples: control-volume sampling and perimeter defense. In Sec. II we describe the motion-coordination algorithms. In Sec. III we present the curve-approximation method that enables coordinated control on approximately time-optimal paths. In Secs. IV and V we describe the application examples. Section VI summarizes this Note.