Application of Optimal Control Theory to Dynamic Soaring of Seabirds

Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft

“…There are two common approaches to the modelling of dynamic soaring, namely, those proposed by Zhao and Qi [20] and Sachs and Bussotis [21]. The latter utilizes Cartesian coordinates, while the former uses spherical coordinates.…”

“…According to the geometric relationship shown in Figure 2, we transform the equations above to the following equations in Cartesian coordinates by vx = vcosθcosψ, vy = vcosθsinψ and vz =vsinθ, where vx, vy, and vz denote the velocities of the aircraft along the respective axes. The problem formulation and modeling procedures adopted in this study are similar to those of some relevant previous works [16,21,23,36]. The aircraft is under the action of its weight, aerodynamics, and inertial force.…”

“…Although the optimization method affords an optimal means of generating a Rayleigh Cycle [18][19][20][21][22][23][24][25][26][27][28], the computation procedure, as noted above, is too time-consuming for real-time applications. Hence, we used a state machine to imitate the four phases of the Rayleigh cycle of an albatross, namely, the upwind climb, high-altitude turn, downwind dive, and low-altitude turn phases.…”

“…Figure 7 indicates that the optimal lift coefficient C L for an albatross is approximately 0.1. The lift coefficient corresponding to the maximum lift-to-drag ratio can be calculated using [21] as C D0 /n = 1.32…”

“…Zhao [19,20] used NPSOL, a numerical optimization software, to minimize the dynamic soaring cycles of unpowered aircraft and powered aircraft. Sachs [21,22] also solved the optimal control problem of dynamic soaring and computed the minimum shear wind strength under certain conditions. Deittert et al [23] utilized the differential flatness property to determine the optimal trajectory for cross-country flight.…”