Spacecraft Dynamics and Trajectory Optimization

Researchers

Michael Marshall
Ashish Goel
Nicolas Lee
Sergio Pellegrino

Description

Traditionally, spacecraft have been designed as approximately rigid structures with flexible appendages like antennas or solar arrays. However, to increase performance, advanced material and structural systems are increasingly being utilized to develop new structural architectures for ultralight, packageable, and self-deployable spacecraft. These architectures trade structural rigidity in their deployed configurations against packaging efficiency in their stowed configurations in order to maximize the deployed aperture area that fits within existing launch vehicles. The increased flexibility in these ultralight, flexible spacecraft results in new challenges for efficient modeling, simulation, and control, and requires the development of new concepts of operation to maximize system performance on-orbit. Our research in spacecraft dynamics and trajectory optimization aims to address some of these challenges.

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In collaboration with the Caltech Space Solar Power Project, our research investigates concepts of operations for planar space solar power satellites. The baseline planar space solar power satellite architecture under consideration consists of lightweight, planar elements that integrate photovoltaic (PV) cells, direct current to microwave converters, and microwave patch antennas that radiate solar power to Earth. This baseline architecture is referred to as single-sided because it only incorporates a single PV surface and a single radio-frequency (RF) surface. However, as a consequence of planarity, the problems of orienting the spacecraft’s PV and RF surfaces are coupled, meaning any change to the PV surface’s orientation changes the RF surface’s orientation and vice versa. As a result, our research has investigated power-optimal guidance for planar space solar power satellites, i.e., the attitude trajectory that maximizes the power transmitted to a terrestrial receiving station throughout an orbit.

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This work has demonstrated how overall system performance for a planar space solar power satellite is intrinsically coupled to its orbit, both due to potential gaps in coverage over a terrestrial receiving station and due to changes in the geometry between the sun and the receiving station. Additionally, it has shown that dual-sided architectures, i.e., architectures with either two PV surfaces or two RF surfaces, are more advantageous than a comparable single-sided architecture for realizing an economically viable space solar power system. Dual-sided architectures typically transmit 50% more power per day than a comparable single-sided system. However, achieving this increased power transmission requires regular large attitude slew maneuvers which are complicated by possible control-structure interaction.

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Additional work has studied trajectory optimization for formation flying space solar power satellites. The size of a planar space solar power satellite’s deployed aperture is limited by the stowage volume in a launch vehicle. As a result, it is proposed to use formation flying space solar power satellites to increase the available on-orbit aperture size. Precise relative spatial positioning between satellites is required to operate the formation as a very large phased array. The optimal spacing between satellites is determined by the RF transmission frequency. In this area, our most recent efforts have involved the use of sequential convex optimization to solve a nonlinear constrained optimal control problem that determines the relative orbital dynamics that maximize the power transmitted by the formation. We have demonstrated the capability to design trajectories for formations of up to 16 spacecraft, but our ultimate goal is to address formations with tens or hundreds of spacecraft.

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Current work focuses on addressing challenges associated with slewing ultralight, flexible spacecraft on-orbit. Consequently, our research is investigating geometrically nonlinear finite element methods and model order reduction techniques suitable for addressing the challenges posed by efficiently simulating ultralight, flexible spacecraft dynamics. To date, our research has investigated model order reduction for a benchmark flexible multibody dynamics problem that combines geometrically nonlinear elastic deformations with large rigid body motions in order to challenge the state-of-the-art in model order reduction. This work extensively leverages proper orthogonal decomposition and a hyper-reduction method known as energy-conserving sampling and weighting, along with modern flexible multibody dynamics simulation techniques. Efforts to scale this work to address the challenges associated with slewing ultralight, flexible space solar power satellites are ongoing.

Publications:

  • Marshall, M. and Pellegrino, S. (2021). Reduced-order modeling for flexible spacecraft deployment and dynamics. SciTech 2021, AIAA.

  • Marshall, M., Goel, A., and Pellegrino, S. (2020). Power-optimal guidance for planar space solar power satellites. Journal of Guidance, Control and Dynamics 43(3): 518-535.

  • Marshall, M., Goel, A., and Pellegrino, S. (2019). Attitude maneuver design for planar space solar power satellite. 29th AAS/AIAA Space Flight Mechanics Meeting. Kaanapali, HI.

  • Goel, A., Chung, S.-J., and Pellegrino, S. (2017). Trajectory design of a spacecraft formation for space-based solar power using sequential convex programming. 9th International Workshop on Satellite Constellations and Formation Flying (IWSCFF). Boulder, CO.

  • Goel, A., Lee, N., and Pellegrino, S. (2017). Trajectory design of formation flying constellation for space-based solar power. IEEE Aerospace Conference, Big Sky, MN.