Initial design of low-thrust trajectories based on the Bezier curve-based shaping approach

Abstract

This paper presents a method to use the Bezier curve to rapidly generate three-dimensional low-thrust trajectories, which can provide a suitable initial approximation to be used for more accurate trajectory optimal control tools. Two missions, from Earth to Mars and the asteroid Dionysus, are considered to evaluate the performance of the method. In order to verify the advantages of this method, it is compared with the finite Fourier series method. Numerical results show that the Bezier method can get better performance index in shorter computation time compared with the finite Fourier series method. The applicability of the solution obtained by Bezier method is evaluated by introducing the obtained solution into the Gauss pseudospectral method as an initial guess. The simulation results show that the Bezier method can rapidly generate a very suitable three-dimensional initial trajectory for the optimal solver. This is very important for rapid evaluation of the feasibility of a large number of low-thrust flight schemes in the preliminary mission design stage.

Keywords

Preliminary mission analysis low-thrust trajectory approximation Bezier method shape-based fast computation

Get full access to this article

View all access options for this article.

References

Wang

Grant

. Minimum-fuel low-thrust transfers for spacecraft: a convex approach. IEEE Transac Aerosp Electron Syst 2018; 54: 2274–2290.

Tang

Jiang

. Fuel-optimal low-thrust trajectory optimization using indirect method and successive convex programming. IEEE Transac Aerosp Electron Syst 2018; 54: 2274–2290.

Zhao

Shang

Cui

, et al. Launch opportunity research for Earth-Mars low thrust trajectory. Proceedings of the 32nd Chinese control conference, Xi'an, China, 26–28 July, IEEE: Piscataway, NJ, 2013, pp. 2350–2355.

Xie

Zhang

, et al. Patched shaping approach to low-thrust multi-revolution transfer design. Proc IMechE, Part G: J Aerospace Engineering 2019; 233: 2663–2672.

Pan

. A quadratic homotopy method for fuel-optimal low-thrust trajectory design. Proc IMechE, Part G: J Aerospace Engineering 2019; 233: 1741–1757.

Shafieenejad

Novinzadeh

. Analytical solutions for two-point boundary value problems: optimal low-thrust orbit transfers. Proc IMechE, Part G: J Aerospace Engineering 2010; 224: 843–853.

Taheri

Abdelkhalik

. Fast initial trajectory design for low thrust restricted-three-body problems. J Guidance Control Dyn 2015; 38: 2146–2160.

Sun

Yuan

Fang

. Continuous low thrust trajectory optimization for preliminary design. Proc IMechE, Part G: J Aerospace Engineering 2016; 230: 921–933.

Petropoulos

Sims

. A review of some exact solutions to the planar equations of motion of a thrusting spacecraft. 2nd international symposium low thrust trajectories, Toulouse, France, 18–20 June 2002.

10.

McConaghy

Debban

Petropoulos

, et al. Design and optimization of low-thrust trajectories with gravity assists. J Spacecraft Rockets 2003; 40: 380–387.

11.

Izzo

. Lamberts problem for exponential sinusoids. J Guidance Control Dyn 2006; 29: 1242–1245.

12.

Roa

Pelaez

Senent

. New analytic solution with continuous thrust: generalized logarithmic spirals. J Guidance Control Dyn 2016; 36: 2336–2351.

13.

Wang

Zhang

. Multiobjective trajectory optimization for a suborbital spaceplane using directed search domain approach. Aerosp Sci Technol 2018; 77: 713–724.

14.

Zimmer

Ocampo

Bishop

. Reducing orbit covariance for continuous thrust spacecraft transfers. IEEE Transac Aerosp Electron Syst 2010; 46: 771–791.

15.

Novak

Vasile

. Improved shaping approach to the preliminary design of low-thrust trajectories. J Guidance Control Dyn 2011; 34: 128–147.

16.

Shafieenejad

Novinzadeh

Molazadeh

. Introducing a novel algorithm for minimum-time low-thrust orbital transfers with free initial condition. Proc IMechE, Part G: J Aerospace Engineering 2015; 229: 333–351.

17.

Petropoulos

Longuski

. Shape-based algorithm for the automated design of low-thrust gravity assist trajectories. J Spacecraft Rockets 2004; 41: 787–796.

18.

Zhang

Cao

. Coplanar ground-track adjustment using time difference. Aerosp Sci Technol 2016; 48: 21–27.

19.

Pascale

Vasile

. Preliminary design of low-thrust multiple gravity-assist trajectories. J Apacecraft Rockets 2006; 43: 1069–1076.

20.

Wall

Conway

. Shape-based approach to low-thrust rendezvous trajectory design. J Guidance Control Dyn 2009; 32: 95–101.

21.

Wall

. Shape-based approximation method for low-thrust trajectory optimization. AIAA/AAS astrodynamics specialist conference and exhibit, Honolulu, Hawaii, 18–21 August 2008, pp. 2008–6616.

22.

Xie

Zhang

. Simple shaping approximation for low-thrust trajectories between coplanar elliptical orbits. J Guidance Control Dyn 2015; 38: 2448–2455.

23.

Xie

Zhang

. Shaping approximation for low-thrust trajectories with large out-of-plane motion. J Guidance Control Dyn 2016; 39: 2776–2786.

24.

Gondelach

Noomen

. Hodographic-shaping method for low-thrust interplanetary trajectory design. J Spacecraft Rockets 2015; 52: 728–738.

25.

Zeng

Geng

. Shape-based analytic safe trajectory design for spacecraft equipped with low-thrust engines. Aerosp Sci Technol 2017; 62: 87–97.

26.

Peloni

Dachwald

Ceriotti

. Multiple near-earth asteroid rendezvous mission: solar-sailing options. Adv Sp Res 2018; 62: 2084–2098.

27.

Abdelkhalik

Taheri

. Approximate on-off low-thrust space trajectories using Fourier series. J Spacecraft Rockets 2012; 49: 962–965.

28.

Taheri

Abdelkhalik

. Initial three-dimensional low-thrust trajectory design. Adv Sp Res 2016; 57: 889–903.

29.

Taheri

Kolmanovsky

Atkins

. Shaping low-thrust trajectories with thrust-handling feature. Adv Sp Res 2018; 61: 879–890.

30.

Huo

Zhang

, et al. Initial trajectory design of electric solar wind sail based on finite Fourier series shape-based method. IEEE Transac Aerosp Electron Syst 2019; 55: 3674–3683.

31.

Huo

Mengali

Quarta

, et al. Electric sail trajectory design with Bezier curve-based shaping approach. Aerosp Sci Technol 2019; 88: 126–135.

32.

Janhunen

. Electric sail for spacecraft propulsion. J Propul Power 2004; 20: 763–764.

33.

Benson D. A gauss pseudospectral transcription for optimal control. PhD Thesis, MA Institute of Technology, Cambridge, 2005.

34.

Jiang

. Pseudospectral methods for trajectory optimization with interior point constraints: verification and applications. IEEE Transac Aerosp Electron Syst 2005; 49: 2005–2017.