# Albatross-Like Utilization of Wind Gradient for Unpowered Flight of Fixed-Wing Aircraft
## 1 Introduction  
An aircraft usually consumes a large amount of energy during flight. There is, however, the question of whether an aircraft can fly indefinitely without carrying a power source. This might be realizable if a method could be developed for the aircraft to continuously extract energy from its environment. A wind field in which the wind gradient varies with the altitude is known to contain a large amount of energy [1; 2; 3]. In addition, albatrosses have been observed to soar for long periods without flapping their wings [4; 5; 6; 7]. [PERSON] was perhaps the first to discuss the problem relevant to albatrosses soaring in a horizontal but non-uniform wind field [8]. This type of flight involves the extraction of energy from a wind gradient and is referred to as dynamic soaring. The phenomenon of dynamic soaring has attracted the interest of many scholars. The technique utilized by an albatross to obtain extra airspeed for soaring is referred to as the Rayleigh cycle [9] and is illustrated in Figure 1. [PERSON] [10] showed that wind speed increases with the altitude, which generally occurs over the sea where albatrosses fly. Different researchers have observed birds to understand their soaring mechanics [11; 12; 13], and theories regarding their utilization of wind gradient have been developed. [PERSON] [14] used a two-dimensional model to investigate two types of complete soaring flight cycles in a logarithmic wind velocity profile. [PERSON] [15]obtained a three-dimensional mass point dynamics equation for obtaining non-diving flight. In addition, [PERSON] [16], [PERSON] et al. [17], and [PERSON] et al. [18] analyzed the energy transformation in wind-gradient-based flight from a physics viewpoint. With the development of computer science, the use of numerical algorithms has become a popular approach to determine the optimal trajectory under a wind gradient. [PERSON] [19; 20] used NPSOL, a numerical optimization software, to minimize the dynamic soaring cycles of unpowered aircraft and powered aircraft. [PERSON] [21; 22] also solved the optimal control problem of dynamic soaring and computed the minimum shear wind strength under certain conditions. [PERSON] et al. [23] utilized the differential flatness property to determine the optimal trajectory for cross-country flight. [PERSON] et al. [24] used the GPOPS-II optimal control software for trajectory computation. There have been several other studies on the optimization of dynamic soaring [25; 26; 27; 28; 29]. Recent improvements were achieved in the practical application of dynamic soaring. [PERSON] et al. [30; 31] proposed an algorithm for determining the flight direction for the quickest energy harvest. [PERSON] et al. [32] and [PERSON] et al. [33] proposed a method for estimating the wind field for trajectory design. [PERSON] et al. [34] presented a nonlinear model of a predictive control strategy for trajectory determination for energy extraction. [PERSON] et al. [35] controlled a simulated glider based on a set of Takagi-Sugeno-Kang fuzzy rules to exploit wind gradient energy. Although these contributions improved the sophistication of the concept of dynamic soaring, this was accompanied by a more complicated practical implementation process. In contrast, [PERSON] et al. [36] and [PERSON] [37] proposed a simple method for generating a guidance strategy for autonomous dynamic soaring. This involved the division of the Rayleigh cycle into four sections, the characteristics of which were determined by simple equations. [PERSON] and [PERSON] [38] also developed a dynamic soaring plan in which the Dubins path was used to improve the computational efficiency. They showed that dynamic soaring could be achieved using modern technology. However, their strategy has the shortcoming of involving numerous control parameters, which makes practical implementation cumbersome. In the present study, we followed the simplification route of [PERSON] et al.