Successive Convexification for On-board Scheduling of Spacecraft Rendezvous Missions
Authors:   ISAE-SUPAERO, Toulouse, France, Claudet Thomas , Labroquère Jérémie , Sanfedino Francesco , Alazard Daniel 
Published: January 2024

Spacecraft rendezvous (RDV) are space missions in which a first satellite, called servicer, or chaser, has to reach another spacecraft, known as the client, or target. This has numerous applications, such as for on-orbit servicing, e.g. refueling and repairing of active satellites [1], assembly and manufacturing of large structures in space [2], active debris removal [3], asteroids deflection [4], and military purposes.
One of the primary challenges of spacecraft rendezvous is the need for highly accurate guidance systems. Optimal trajectories are sought from the far-range to the close proximity to minimize fuel consumption or time. Another important aspect is the use of propulsion systems to maneuver the spacecraft such as electric or chemical thrusters. This choice depends on the specific mission requirements and constraints, such as the required delta-v, and the available power and propellant.
In addition to these technical challenges, spacecraft rendezvous also requires careful planning and coordination. This can include developing detailed mission plans and procedures, as well as conducting simulations and ground testing to verify that the spacecraft and systems will perform as expected. Overall, spacecraft rendezvous is a complex and challenging task that demands a combination of advanced technology and careful planning.
However, within an ever-demanding world of commercial and military space operations, autonomy is and will be playing a key role in maximizing profits and guaranteeing sovereignty. To this end, novel approaches of embedded optimization are found to reduce the need for communication with the ground, allowing for greater responsiveness in front of evolving or uncertain environments, thus leading to mission success [5, 6, 7].
This Ph.D. work stems from the RAPTOR (Robotic and Artificial intelligence Processing Test on Representative Target) project, uniting academia and industry, and aiming at providing disruptive solutions to spacecraft rendezvous. The final paper proposes an approach for modeling scheduling constraints using the successive convexification framework. This method can handle integer constraints and greatly reduce computational complexity from exponential to polynomial, making it suitable for on-board computations. This approach implements convexified if-else constraints to handle a variety of operations such as hold points or propulsion switches between chemical and electric firings. On the attitude side, target line-of-sight and nadir-pointing antennas during communication windows are enforced. Further, in the case of electric propulsion, a coupled approach considers proper alignment of the chaser’s attitude to produce the desired delta-v.
This application allows the authors to demonstrate the interest of the proposed modeling approach in realistic scenarios with on-board autonomous time constraints. For instance, the convergence of the algorithm in finite time is discussed. A 6-DOF fuel-optimal trajectory is generated which satisfies linear initial / target states constraints and verifies both translational and attitude equations with quaternions. Second-order cone programming and state-triggered constraints supports this base to demonstrate the effectiveness of the proposed method.
References:
[1] Tsiotras, P., & De Nailly, A. (2005). Comparison between peer-to-peer and single-spacecraft refueling strategies for spacecraft in circular orbits. In Infotech@ Aerospace (p. 7115).
[2] Zhihui, X. U. E., Jinguo, L. I. U., Chenchen, W. U., & Yuchuang, T. O. N. G. (2021). Review of in-space assembly technologies. Chinese Journal of Aeronautics, 34(11), 21-47.
[3] Kawamoto, S., Ohkawa, Y., Okamoto, H., Iki, K., Okumura, T., Katayama, Y., ... & Ohnishi, M. (2017, April). Current status of research and development on active debris removal at JAXA. In 7th European Conference on Space Debris (SDC7).
[4] Cheng, A. F., Atchison, J., Kantsiper, B., Rivkin, A. S., Stickle, A., Reed, C., ... & Ulamec, S. (2015). Asteroid impact and deflection assessment mission. Acta Astronautica, 115, 262-269.
[5] Blazquez, E. (2021). Rendezvous optimization and GNC design for proximity operations on cis-lunar near rectilinear halo orbits (Doctoral dissertation, Toulouse, ISAE).
[6] Malyuta, D., Reynolds, T., Szmuk, M., Mesbahi, M., Acikmese, B., & Carson, J. M. (2019). Discretization performance and accuracy analysis for the rocket powered descent guidance problem. In AIAA Scitech 2019 Forum (p. 0925).
[7] Malyuta, D., Reynolds, T., Szmuk, M., Acikmese, B., & Mesbahi, M. (2020). Fast trajectory optimization via successive convexification for spacecraft rendezvous with integer constraints. In AIAA Scitech 2020 Forum (p. 0616).