A complete analysis for deducing feasible formation maneuvers considering arbitrary formation geometry, and operational limits on speed and bank angle provides the motivation for the present work. This work first analyses the fundamental kinematic relationships to deduce a maneuver envelope for generic leader formation with an inner and an outer follower. This is followed by studies determining critical follower UAVs affecting leader’s maneuver. Based on a detailed analysis of the relationship between leader’s maneuver and followers’ physical constraints subject to the formation geometry, the work establishes in closed form a novel leader maneuver region as the main contribution. As expressed in the speed-turn radius space of the leader, the region provides a direct input for maneuver planning for fixed-UAV formations. 

• Challa, Vinay Reddy, and Ashwini Ratnoo. "On maneuverability of fixed-wing unmanned aerial vehicle formations." Journal of Guidance, Control, and Dynamics 44.7 (2021): 1327-1344. 

 (Link to the paper)

This work proposes a control law for generating a wide array of trochoid patterns. Following the proposed control law with a set of design parameters, a unicycle agent exhibits Andronov-Hopf bifurcation in speed-scaled angular velocity space. Resulting patterns traced by the agent are shown to be identical to the parametric form of trochoid curves. Bounds on the design parameters generating the desired class of patterns are deduced using the normal form and the central manifold theory. As a major highlight of this research, variation in a single design parameter is shown to generate four different classes each of hypotrochoid and epitrochoid patterns, respectively.

• P. Anjaly and A. Ratnoo, “Bifurcation-Based Control Law for Pattern Generation,” IEEE Control Systems Letters, vol. 3, no. 2, 2019, pp. 374-379.

 (Link to the paper)