Sara Spangelo

Applying Model Based Systems Engineering (MBSE) to a standard CubeSat

Model Based Systems Engineering (MBSE) is an emerging technology that is providing the next advance in modeling and systems engineering. MBSE uses Systems Modeling Language (SysML) as its modeling language. SysML is a domain-specific modeling language for systems engineering used to specify, analyze, design, optimize, and verify systems. An MBSE Challenge project was established to model a hypothetical FireSat satellite system to evaluate the suitability of SysML for describing space systems. Although much was learned regarding modeling of this system, the fictional nature of the FireSat system precluded anyone from actually building the satellite. Thus, the practical use of the model could not be demonstrated or verified. This paper reports on using MBSE and SysML to model a standard CubeSat and applying that model to an actual CubeSat mission, the Radio Aurora Explorer (RAX) mission, developed by the Michigan Exploration Lab (MXL) and SRI International.

Model based systems engineering (MBSE) applied to Radio Aurora Explorer (RAX) CubeSat mission operational scenarios

Small satellites are more highly resource-constrained by mass, power, volume, delivery timelines, and financial cost relative to their larger counterparts. Small satellites 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 satellite 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 satellite 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 satellite 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 satellite for representative mission scenarios. The modeling approach presented in this paper offers satellite 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.

Optimization-based scheduling for the single-satellite, multi-ground station communication problem

In this paper, we develop models and algorithms for solving the single-satellite, multi-ground station communication scheduling problem, with the objective of maximizing the total amount of data downloaded from space. With the growing number of small satellites gathering large quantities of data in space and seeking to download this data to a capacity-constrained ground station network, effective scheduling is critical to mission success. Our goal in this research is to develop tools that yield high-quality schedules in a timely fashion while accurately modeling on-board satellite energy and data dynamics as well as realistic constraints of the space environment and ground network. We formulate an under-constrained mixed integer program (MIP) to model the problem. We then introduce an iterative algorithm that progressively tightens the constraints of this model to obtain a feasible and thus optimal solution. Computational experiments are conducted on diverse real-world data sets to demonstrate tractability and solution quality. Additional experiments on a broad test bed of contrived problem instances are used to test the boundaries of tractability for applying this approach to other problem domains. Our computational results suggest that our approach is viable for real-world instances, as well as providing a strong foundation for more complex problems with multiple satellites and stochastic conditions.

Power Optimization of Solar-Powered Aircraft with Specified Closed Ground Tracks

This paper considers the optimization of flight trajectories for solar-powered aircraft. This work is unique relative to past work because flight path is constrained to repeatedly traverse a specified closed ground path. Constraints of this form are of interest in a variety of missions where the goal is to loiter near a fixed point on the ground. The performance index to be maximized is the average input power to the battery over each cycle of the ground path. It is advantageous to allow the periodic flight path to have altitude variations because during both ascent and descent there are opportunities to increase the angle of sun exposure to the aircraft solar array. A novel procedure for solving the related optimization problem is described that addresses the implementation of a difficult state constraint: the flight path must belong to the surface of the vertical cylinder whose base is the closed ground path. Results for a wide collection of optimization examples are described, which lead to an importan...

Periodic Energy-Optimal Path Planning for Solar-Powered Aircraft

[Abstract] 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 ight. We consider ascending and descending ight 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 identied 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 ight. Numerical simulation results are presented that help demonstrate the properties of the optimum trajectories.

Models and Tools to Evaluate Space Communication Network Capacity

This paper introduces models and tools to assess the communication capacity for highly dynamic and geographically diverse ground stations that loosely collaborate to provide increased satellite connectivity. Communication capacity is the total amount of information exchanged between a network of satellites and ground stations over a finite time period. We outline the major constraints on communication capacity which influence transmission capabilities from the satellite, ground station, and network perspectives. Orbit models are combined with engineering analysis software to compare the capacity of existing and future ground station networks. Simulation results from recent clustered satellite launches and representative ground networks are presented and the capacity properties are discussed. By studying network communication capacity, we find opportunities to optimize communication schedules across federated networks to simultaneously and autonomously support multiple satellites.

Enterprise modeling for CubeSats

Understanding the business aspect of a project or mission is of key importance in spacecraft systems engineering, including the mission cost, high level functions and objectives, workforce, hardware, and production of spacecraft. This is especially true for CubeSat missions, which typically deal with low costs, limited resources, low mass, low volume, and low power. Introducing enterprise modeling concepts to CubeSat missions allows for incorporation of analysis of cost, business processes, and requirements for the missions spacecraft and problem domain. The following describes an application of enterprise modeling to CubeSats.

Satellite Dynamics Simulator Development Using Lie Group Variational Integrator

Simulation technology is becoming increasingly crucial in the design and optimization of satellites due to the difficulties in testing and verifying system parameters on the ground. Computationally tractable and accurate methods are required in order to test satellite parameters in the complex and dynamic space environment. Although various satellite teams have developed simulation tools, many suffer from inaccurate numerical integrators, resulting in their simulations being of low fidelity for long duration simulations. This paper presents a MATLAB/Simulink-based simulator which includes high fidelity integration and modeling for accurate and relatively quick results. The simulator includes an energy-preserving variational integrator for both translational and rotational dynamics. A Lie Group Variational Integrator is used for the rotational dynamics, which enforces an orthogonality constraint for improved accuracy. This approach requires less computational time relative to other integration methods such as Runge-Kutta method for the same level of integration accuracy. The simulator includes perturbations to the orbital motion and attitude, including Earth oblateness, aerodynamic drag, solar pressure, gravity gradient, and residual dipole. The simulator also includes an advanced hysteresis model for improved modeling of magnetic attitude control systems. Simulation results are provided for a representative small satellite mission in low earth orbit with a passive magnetic stabilization control system. We compare the novel integration and hysteresis techniques to conventional simulators for long duration simulations for a realistic mission scenario.

Assessing the capacity of a federated ground station

We introduce models and tools to assess the communication capacity of dynamic ground station networks, in particular federated networks that are composed of geographically diverse and independent stations that loosely collaborate to provide increased satellite connectivity. Network capacity is the amount of information exchanged between a network of satellites and ground stations. The constraints on total network capacity which influence transmission capabilities are outlined, such as the satellite, ground station, and overall network parameters. Orbit propagators are combined with engineering analysis software to compare the capacity of existing and future ground station networks. Simulation results from recent clustered satellite launches are presented and discussed. By studying network capacity, we identify the potential for leveraging these federated networks to support multiple missions from multiple institutions. Future work is outlined, including the need to accurately model both satellite communication requirements, develop real time network analysis tools, and work towards developing dynamic optimization techinques for global autonomous networks.

Analytical modeling framework and applications for space communication networks

There is a growing number of resource-constrained small satellites that are currently performing and are proposed to accomplish novel science and technology missions. These missions seek to download large quantities of data to ground-station networks that currently have limited ability to support these missions. This limitation motivates the development of modeling and simulation tools to assess and optimize these mission scenarios. In this paper, we develop an extensible, analytical modeling framework for satellite operations. This framework captures dynamic states, subsystem functions, and interactions of the satellite with the external environment and ground-communication networks. This foundational framework enables assessment and optimization of complex space and ground networks under both deterministic and stochastic conditions. We apply this framework to develop a communication-focused model for an operational satellite mission. We implement the analytical model in a simulation environment and use ...