Convex optimisation approach to constrained fuel optimal control of spacecraft in close relative motion. Issue 9 (1st May 2018)

• Record Type: Journal Article
• Authors: Massioni, Paolo; Massari, Mauro
• Is Part Of: Advances in space research. Volume 61:Issue 9(2018)
• Page Start: 2366
• Page End: 2376
• Publication Date: 2018-05-01
• Subjects: Fuel optimal control -- Constrained optimal control -- Close relative motion -- Convex optimisation -- Sum of squares; Space sciences -- Periodicals; Astronautics -- Periodicals; Geophysics -- Periodicals; 500.505
• DOI: 10.1016/j.asr.2018.02.020
• Languages: English
• ISSNs: 0273-1177

Abstract

Highlights: A solution method is proposed for spacecraft fuel optimal control problems. The method is suitable for spacecraft close motion dynamics. The method turns the problem into a convex optimisation (no local optima). Applications examples are shown for close motion in circular and elliptical orbits. Abstract: This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.