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This paper considers energy-optimal path planning in a loitering mission for solar-powered unmanned aerial vehicles (UAVs) which collect solar energy from the sun to power their flight. We consider ascending and descending flight maneuvers in a periodic mission constrained to the surface of a vertical cylinder. The coupling of the aircraft kinematic and energetic models is treated in a novel scheme that implements both the periodic and cylindrical constraints. Optimum trajectories are identified by specifying the heading angle and altitude by periodic splines. Given the periodic splines, we are able to solve for the other aircraft parameters, including the aerodynamic, propulsive, and energetic properties of the aircraft. In an example problem, trajectories are obtained that generate better energy properties than those given by constant altitude circular flight. Numerical simulation results are presented that help demonstrate the properties of the optimum trajectories.

Abstract-Small spacecraft are more highly resource-constrained by mass, power, volume, delivery timelines, and financial cost relative to their larger counterparts. Small spacecraft are operationally challenging because subsystem functions are coupled and constrained by the limited available commodities (e.g. data, energy, and access times to ground resources). Furthermore, additional operational complexities arise because small spacecraft components are physically integrated, which may yield thermal or radio frequency interference.In this paper, we extend our initial Model Based Systems Engineering (MBSE) framework developed for a small spacecraft mission by demonstrating the ability to model different behaviors and scenarios.We integrate several simulation tools to execute SysML-based behavior models, including subsystem functions and internal states of the spacecraft. We demonstrate utility of this approach to drive the system analysis and design process. We demonstrate applicability of the simulation environment to capture realistic spacecraft operational scenarios, which include energy collection, the data acquisition, and downloading to ground stations.The integrated modeling environment enables users to extract feasibility, performance, and robustness metrics. This enables visualization of both the physical states (e.g. position, attitude) and functional states (e.g. operating points of various subsystems) of the spacecraft for representative mission scenarios.The modeling approach presented in this paper offers spacecraft designers and operators the opportunity to assess the feasibility of vehicle and network parameters, as well as the feasibility of operational schedules. This will enable future missions to benefit from using these models throughout the full design, test, and fly cycle. In particular, vehicle and network parameters and schedules can be verified prior to being implemented, during mission operations, and can also be updated in near real-time with operational performance feedback.