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Orbital rendezvous performance comparison of differential geometric and ZEM/ZEV feedback guidance algorithms

Abstract

In this paper, the performance of two distinct classes of feedback guidance algorithms is evaluated for a spacecraft rendezvous problem utilizing a continuous low-thrust propulsion system. They are the DG (Differential Geometric) and ZEM/ZEV (Zero-Effort-Miss/Zero- Effort-Velocity) feedback guidance algorithms. Even though these two guidance algorithms do not attempt to minimize the onboard fuel consumption or ΔV directly, the ΔV requirement is used as a measure of their orbital rendezvous performance for various initial conditions and a wide range of the rendezvous time (within less than one orbital period of the target vehicle). For the DG guidance, the effects of its guidance parameter and terminal time on the closed-loop performance are evaluated by numerical simulations. For the ZEM/ZEV guidance, its nearfuel- optimality is further demonstrated for a rapid, short-range orbital rendezvous, in comparison with the corresponding open-loop optimal solutions. Furthermore, the poor ΔV performance of the ZEM/ZEV guidance for a slow, long-range orbital rendezvous is remedied by simply adding an initial drift phase. The ZEM/ZEV feedback guidance algorithm and its appropriate variants are then shown to be a simple practical solution to a non-impulsive rendezvous problem, in comparison with the DG guidance as well as the open-loop optimal guidance.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61673135 and 61603114).

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Correspondence to Bong Wie.

Additional information

Pengyu Wang received his B.S. degree in automation from Harbin Engineering University, China, in 2015, and M.S. degree in control science and engineering from Harbin Institute of Technology, China, in 2017. He is now a Ph.D. candidate at Harbin Institute of Technology focusing on the development and application of control theories in aerospace problems, including Mars pinpoint landing, spacecraft rendezvous, and missile impact-time guidance, etc.

Yanning Guo received his Ph.D. degree in control science and engineering from Harbin Institute of Technology, China, in 2012, and was a visiting scholar at Iowa State University in 2010–2011. Currently, he is an associate professor at Harbin Institute of Technology, and specializes in optimal control, sliding-mode control, as well as visual navigation and localization.

Bong Wie is a professor of aerospace engineering at Iowa State University. He is the founding director of the Asteroid Deflection Research Center established in 2008 at Iowa State University. He received his M.S. and Ph.D. degrees in aeronautics and astronautics from Stanford University in 1978 and 1981, respectively. In 2006, the AIAA (American Institute of Aeronautics and Astronautics) presented Prof. Wie with the Mechanics and Control of Flight Award for his innovative research on advanced control of complex spacecraft such as agile imaging satellites, solar sails, and large space structures.

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Wang, P., Guo, Y. & Wie, B. Orbital rendezvous performance comparison of differential geometric and ZEM/ZEV feedback guidance algorithms. Astrodyn 3, 79–92 (2019). https://doi.org/10.1007/s42064-018-0037-6

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Keywords

  • differential geometric guidance
  • ZEM/ZEV feedback guidance
  • orbital rendezvous
  • initial drift phase