Abstract
The power-limited solar electric propulsion system is considered more practical in mission design. An accurate mathematical model of the propulsion system, based on experimental data of the power generation system, is used in this paper. An indirect method is used to deal with the time-optimal and fuel-optimal control problems, in which the solar electric propulsion system is described using a finite number of operation points, which are characterized by different pairs of thruster input power. In order to guarantee the integral accuracy for the discrete power-limited problem, a power operation detection technique is embedded in the fourth-order Runge-Kutta algorithm with fixed step. Moreover, the logarithmic homotopy method and normalization technique are employed to overcome the difficulties caused by using indirect methods. Three numerical simulations with actual propulsion systems are given to substantiate the feasibility and efficiency of the proposed method.
Similar content being viewed by others
Notes
Data available online at https://ssd.jpl.nasa.gov/dat/ELEMENTS.NUMBR [retrieved 22 February 2017].
References
Bertrand, R., Epenoy, R.: New smoothing techniques for solving bang-bang optimal control problems—numerical results and statistical interpretation. Optim. Control Appl. Methods 197, 171–197 (2002). https://doi.org/10.1002/oca.709
Bhaskaran, S., Riedel, J., Synnott, S., Wang, T.: The Deep Space 1 autonomous navigation system: a post-flight analysis. In: Pap. AIAA, pp. 1–11 (2000). https://doi.org/10.2514/6.2000-3935
Brophy, J.R., Noca, M.: Electric propulsion for solar system exploration. J. Propuls. Power 14, 700–707 (1998). https://doi.org/10.2514/2.5332
Chen, Y., Baoyin, H., Li, J.: Power-limited solar electric propulsion trajectory optimization. In: 1st IAA Conference on Dynamics and Control of Space System, Porto, Portugal, pp. 1545–1551 (2012)
Chi, Z., Yang, H., Chen, S., Li, J.: Homotopy method for optimization of variable-specific-impulse low-thrust trajectories. Astrophys. Space Sci. 362, 216 (2017). https://doi.org/10.1007/s10509-017-3196-7
Dankanich, J.W.: Low-thrust mission design and application. In: 46th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., vol. 6857 (2010). https://doi.org/10.2514/6.2010-6857
Gao, Y., Kluever, C.A.: Engine-switching strategies for interplanetary solar-electric-propulsion spacecraft. J. Spacecr. Rockets 42, 765–767 (2005). https://doi.org/10.2514/1.14973
Jewitt, D., Agarwal, J., Weaver, H., Mutchler, M., Larson, S.: Episodic ejection from active asteroid 311P/Panstarrs. Astrophys. J. 798, 109 (2015). https://doi.org/10.1088/0004-637X/798/2/109
Jiang, F., Baoyin, H., Li, J.: Practical techniques for low-thrust trajectory optimization with homotopic approach. J. Guid. Control Dyn. 35, 245–258 (2012). https://doi.org/10.2514/1.52476
Jiang, F., Tang, G., Li, J.: Improving low-thrust trajectory optimization by adjoint estimation with shape-based path. J. Guid. Control Dyn. 40, 3282–3289 (2017). https://doi.org/10.2514/1.G002803
Landau, D., Chase, J., Randolph, T., Timmerman, P., Oh, D.: Electric propulsion system selection process for interplanetary missions. J. Spacecr. Rockets 48, 467–476 (2011). https://doi.org/10.2514/1.51424
Li, H., Chen, S., Baoyin, H.: J2-perturbed multitarget rendezvous optimization with low thrust. J. Guid. Control Dyn. 41, 1–7 (2017). https://doi.org/10.2514/1.G002889
Marcos, C.D.F., Marcos, R.D.F.: Asteroid (469219) 2016 HO3, the smallest and closest Earth quasi-satellite. Mon. Not. R. Astron. Soc. 3456, 3441–3456 (2016). https://doi.org/10.1093/mnras/stw1972
Martinon, P., Gergaud, J.: Using switching detection and variational equations for the shooting method. Optim. Control Appl. Methods 28, 95–116 (2007). https://doi.org/10.1002/oca.794
Mengali, G., Quarta, A.A.: Fuel-optimal, power-limited rendezvous with variable thruster efficiency. J. Guid. Control Dyn. 28, 1194–1199 (2005). https://doi.org/10.2514/1.12480
Oshima, K., Campagnola, S., Yanao, T.: Global search for low-thrust transfers to the Moon in the planar circular restricted three-body problem. Celest. Mech. Dyn. Astron. 128, 303–322 (2017). https://doi.org/10.1007/s10569-016-9748-2
Quarta, A.A., Mengali, G.: Minimum-time space missions with solar electric propulsion. Aerosp. Sci. Technol. 15, 381–392 (2011). https://doi.org/10.1016/j.ast.2010.09.003
Quarta, A.A., Izzo, D., Vasile, M.: Time-optimal trajectories to circumsolar space using solar electric propulsion. Adv. Space Res. 51, 411–422 (2013). https://doi.org/10.1016/j.asr.2012.09.012
Rayman, M.D., Williams, S.N.: Design of the first interplanetary solar electric propulsion mission. J. Spacecr. Rockets 39, 589–595 (2002). https://doi.org/10.2514/2.3848
Russell, R.P.: Primer vector theory applied to global low-thrust trade studies. J. Guid. Control Dyn. 30, 460–472 (2007)
Senent, J., Ocampo, C., Capella, A.: Low-thrust variable-specific-impulse transfers and guidance to unstable periodic orbits. J. Guid. Control Dyn. 28, 280–290 (2005). https://doi.org/10.2514/1.6398
Soulas, G., Domonkos, M., Patterson, M.: Wear test results for the NEXT ion engine. In: 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, EPSC2003-4863, Huntsville, Alabama, USA (2003)
Woo, B., Coverstone, V.L., Hartmann, J.W., Cupples, M.: Trajectory and system analysis for outer-planet solar electric propulsion missions. J. Spacecr. Rockets 42(3), 510–516 (2005). https://doi.org/10.2514/1.7011
Woo, B., Coverstone, V.L., Cupples, M.: Application of solar electric propulsion to a comet surface sample return mission. J. Spacecr. Rockets 43, 1225–1230 (2006). https://doi.org/10.2514/1.23371
Yang, H., Baoyin, H.: Fuel-optimal control for soft landing on an irregular asteroid. IEEE Trans. Aerosp. Electron. Syst. 51, 1688–1697 (2015). https://doi.org/10.1109/TAES.2015.140295
Yang, H., Li, J., Baoyin, H.: Low-cost transfer between asteroids with distant orbits using multiple gravity assists. Adv. Space Res. 56, 837–847 (2015). https://doi.org/10.1016/j.asr.2015.05.013
Yang, H., Bai, X., Baoyin, H.: Rapid generation of time-optimal trajectories for asteroid landing via convex optimization. J. Guid. Control Dyn. 40, 628–641 (2017). https://doi.org/10.2514/1.G002170
Zhang, P., Li, J., Baoyin, H., Tang, G.: A low-thrust transfer between the Earth-Moon and Sun-Earth systems based on invariant manifolds. Acta Astronaut. 91, 77–88 (2013). https://doi.org/10.1016/j.actaastro.2013.05.005
Zhang, P., Li, J., Gong, S.: Fuel-optimal trajectory design using solar electric propulsion under power constraints and performance degradation. Sci. China, Phys. Mech. Astron. 57, 1090–1097 (2014). https://doi.org/10.1007/s11433-014-5477-2
Zhang, C., Topputo, F., Bernelli-Zazzera, F., Zhao, Y.-S.: Low-thrust minimum-fuel optimization in the circular restricted three-body problem. J. Guid. Control Dyn. 38, 1501–1510 (2015). https://doi.org/10.2514/1.G001080
Acknowledgement
This work is supported by the National Natural Science Fund of China (Grants 11672146 and 11572166).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chi, Z., Li, H., Jiang, F. et al. Power-limited low-thrust trajectory optimization with operation point detection. Astrophys Space Sci 363, 122 (2018). https://doi.org/10.1007/s10509-018-3344-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-018-3344-8