Dynamics, Numerical Optimization and Control of Dynamic Soaring Maneuvers for a Morphing Capable Unmanned Aerial Vehicle

Abstract

Dynamic soaring is a versatile maneuver executed to acquire energy available in the atmospheric wind shears. For UAVs, dynamic soaring maneuvers have mostly been confined in literature to fixed configurations. In order to analyze the extent to which dynamic soaring is influenced by different morphologies, an innovative concept of integrating dynamic soaring with morphing capabilities is introduced in this research. Through simulations, two major studies were performed. One of them analyzed the impact of span morphology and the other of sweep morphology on dynamic soaring parameters. An Unmanned Air Vehicle (UAV) with standard wing-tail configuration is considered. The aerodynamic modeling is based on empirical estimation procedure duly validated with numerical Vortex Lattice Method (VLM). Three-dimensional point-mass UAV equations of motion and nonlinear wind gradient profile are used to model the flight dynamics. The trajectory optimization problem is formulated as an optimal control problem using hp-adaptive Guassian quadrature collocation technique. Optimal soaring trajectories are generated for both morphologies. Parametric characterization of the key performance parameters is performed to determine the optimal platform configuration during various phases of the maneuver. The comparison of morphing ability during flight is compared with its fixed-wing counterpart. Simulation results demonstrate the benefits of extending soaring maneu- vers to morphing configurations and its viability for onboard utilization. Results indicate 15% lesser required wind shear by the proposed span morphology and 14% lesser required wind shear by the proposed sweep morphology, in comparison to their respective fixed wing counterparts. This shows that the morphing UAV can perform dynamic soaring in an environment, where fixed configuration UAVs might not, because of lesser available wind shears. Apart from this, span morphology reduced drag by 15%, lift requirement by 11% and angle of attack requirement by 20%, whereas increased the maximum velocity by 6.2%, normalized energies by 9% and improved loitering parameters (approximately 10%), in comparison to fixed span configurations. Similarly, sweep morphology guaranteed 20% drag reduction, 16% lesser angle of attack requirement and improved loitering performance over the fixed sweep configurations. The stability analysis of the nonlinear system along the optimal trajectory is then performed utilizing both linear (Floquet theory) and nonlinear (Contraction theory) techniques. Stability of dynamic soaring orbits is important since the trajectories can get disturbed by a strong gust or crosswinds causing the UAV to veer off-course. Although control system can be designed, a stable orbit can reduce the control effort and power. The problem of analyzing stability is treated from the context of a periodic coefficient system. The stability analysis revealed that a closed-loop control is necessary as the system dynamics are inherently unstable. A geometric nonlinear controllability analysis of UAV under dynamic soaring conditions is then performed. To achieve such an objective, the state-of-theart mathematical tools of nonlinear controllability are utilized. The controllability of a flying vehicle along that optimal soaring trajectory is analyzed. More im- portantly, the geometric nonlinear controllability characteristics of generic flight dynamics is analyzed in the presence and absence of wind shear to provide a controllability explanation for the role of wind shear in the physics of dynamic soaring flight. It is found that the wind shear is instrumental in ensuring controllability as it allows the UAV attitude controls (pitch and roll) to play the role of thrust in controlling the flight path angle. The presented analysis represents a controllability-based mathematical proof for the energetics of flight physics. Keywords: Numerical Optimization; Dynamical Systems; Differential Equations; Trajectory Optimization; Non-linear Dynamics; Wind Shear; Morphing; Stability Analysis; Floquet Analysis; Contraction Analysis; ; Differential Geomtery; Numerical Simulations.