Trajectory optimization of multirotor agricultural UAVs

Multirotor agricultural unmanned aerial vehicles (UAVs) are perceived as one of the key enablers for precision agriculture (PA) in near future. UAVs capture images with much higher resolution compared to satellites and airplanes because of the low altitude remote sensing (≤ 400 ft above ground level in the USA). UAVs also provide better operational and temporal flexibility to react quickly to undesirable weather events. The sensitivity of the image capturing devices (thermal and multispectral) to exhaust gases makes gas powered UAVs practically unusable for PA's scouting or sensing tasks. Therefore, agricultural UAVs are typically electric powered using lithiumion polymer (Li-Po) batteries. However, the endurance of Li-Po battery pack imposes severe constraints on the operational time span of an electric UAV during an agricultural mission. Hence, optimal path planning is critical for maximizing farm field area coverage and minimizing operational cost for image acquisition per flight. Our research contribution focuses on the trajectory optimization of multirotor UAVs in multi-phase optimal control framework with field area coverage and energy as two separate performance indexes to be maximized and minimized respectively. The mathematical relationship between the thrust produced and power consumed by a UAV is derived using momentum theory for the climb, cruise, and descent phases. Finally, the two optimal control problems formulated are numerically solved using pseudospectral method for an actual UAV product: DJI Phantom 4.0 quadcopter.