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The endurance of unmanned aerial vehicles (UAVs) is a critical factor in expanding the scope of their applications. Extended flight times enable UAVs to undertake longer missions, cover larger areas and perform tasks such as persistent surveillance, data collection and search and rescue operations. Optimal trajectory planning is a cost-effective method to significantly enhance UAV endurance and performance by minimizing fuel consumption. This study introduces a novel numerical optimization framework to maximize UAV endurance. Specifically, we address the problem of determining optimal thrust and cruise angle of attack for a UAV in 2D space under specific initial, periodic and boundary conditions. By normalizing the free final time optimal control problem and employing Fourier collocation and quadrature, we transform it into a nonlinear programming problem. A key contribution of this work is accurately detecting and reconstructing the thrust history, including jump discontinuities, directly from Fourier pseudospectral data without smoothing techniques. The proposed method outperforms existing approaches in solving the periodic energy-optimal path planning problem for UAVs, as it effectively reconstructs the bang-bang thrust profile, facilitating rapid and efficient thrust adjustments essential for various flight maneuvers. Furthermore, the algorithm aligns with the UAV model, ensuring seamless integration into real-world control systems. The method’s independence from prediction horizon length, due to the use of Fourier collocation on the normalized interval $[0,2\pi ]$, is a notable advantage. This characteristic offers potential for future applications in various fields involving nonsmooth optimal control problems. This research generally provides a valuable tool for researchers and engineers working on UAV design and operation, paving the way for more efficient and effective UAV systems.

The flight conditions, small length scale, and low altitude flight of mini-UAVs lend them to the low Reynolds number of less than 300,000 in which the aircraft performance is significantly degraded. In such operating conditions, the aerodynamic performance of aircraft is critically dependent on its lifting surface which is the wing configuration and high-cambered airfoils are equipped to generate enough lift to keep the aircraft and its payload airborne at low operating speeds. However, the aerodynamic performance of airfoils at low Reynolds number is significantly degraded due to the early separation of flow. This results in higher form of drag and lower lift which leads to higher power required to generate thrust for the aircraft to overcome drag and remain airborne. Consequently, the range and endurance are significantly reduced. This paper investigates the interactive effects of different Alula deflection angles and span ratios on the aerodynamic efficiency of a three-dimensional (finite) swept back wing during cruise flight. A total of nine wing configurations are designed with different Alula deflection angles (4°, 13°, and 22°) and span ratios (5%, 10%, and 15%). Investigations are carried out using numerical simulations and wind tunnel experiments. Overall, an enhanced aerodynamic efficiency is achieved for wings equipped with Alula configuration at 13° deflection angle and 15% span ratio as well as 22° deflection angle and 5% span ratio, and they have 9.3% and 4.5% higher aerodynamic efficiency compared to the clean wing. The endurance of electric-powered mini-UAVs is exponentially proportional to aerodynamic efficiency. Hence, the resulting wing configurations from this research with improved aerodynamic efficiency have a promising effect on the endurance enhancement of UAVs during the cruise envelope of flight.