# Low-Thrust Transfer to Quasi-Synchronous Martian Elliptic Orbit via Nonlinear Feedback Control
## 5 Concluding Remarks  
This research identifies a specific repeating-ground-track, quasi-synchronous orbit as a viable option for Martian constellations tailored to the continuous coverage of high-latitude regions. The orbit at hand is flown nine times in 5 nodal days. Coverage analysis reveals that two satellites are sufficient to ensure continuous global coverage at high latitudes. The maximum revisit time increases as the latitude decreases and can eventually be reduced by including additional satellites. Low-thrust propulsion, in conjunction with nonlinear orbit control, is proposed as a convenient option to perform the orbit transfer from the initial 4-sol orbit. In this framework, orbit dynamics about Mars are modeled with the inclusion of the most relevant perturbations, i.e., several harmonics of the areopotential, together with the gravitational pull due to the Sun as a third body. A saturated feedback law for the low-thrust magnitude and direction--with an upper bound on magnitude--is introduced and is proven to enjoy global stability properties. In particular, some sufficient conditions for the asymptotic convergence toward the operational conditions are presented. These conditions include the perturbing acceleration term and lead to identifying three types of transfer arcs: (a) maximum-thrust arcs, (b) time-varying, intermediate-thrust arcs, and (c) coast arcs. Specifically, this research extends the range of application of nonlinear orbit control to elliptic orbits with some prescribed, time-varying orbit elements. Monte Carlo simulations are run, assuming either nominal or nonnominal flight conditions, i.e., stochastic failures of the propulsion system, imperfect estimation of the orbit perturbations, or dispersed initial conditions, representative of possible injection errors at the planetary capture. The numerical results demonstrate that the low-thrust transfer strategy based on nonlinear orbit control is effective and needs a limited amount of propellant. Moreover, the feedback control law at hand does not require any offline reference trajectory; therefore, it is effective  
Figure 21: Monte Carlo analysis 2: propellant mass consumption.  
Figure 20: Monte Carlo analysis 2: time of convergence.  
as an autonomous real-time guidance strategy, even in the presence of nonnominal flight conditions. A possible, though challenging, extension of nonlinear orbit control can be represented by the inclusion of the final position (along the operational orbit) in the target set. This would represent a valuable addition, very useful in challenging mission scenarios, such as orbit rendezvous.  
Conceptualization, M.P. ([PERSON]); methodology, R.S., M.P. ([PERSON]) and M.P. ([PERSON]); software, R.S. and M.P. ([PERSON]); validation, M.P. ([PERSON]); formal analysis, R.S., M.P. ([PERSON]) and M.P. ([PERSON]); investigation, R.S., M.P. ([PERSON]) and M.P. ([PERSON]); data curation, R.S. and M.P. ([PERSON]); writing--original draft preparation, R.S. and M.P. ([PERSON]); writing--review and editing, R.S. and M.P. ([PERSON]); visualization, R.S. and M.P. ([PERSON]); supervision, M.P. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data needed to reproduce the results are contained in the paper.  
The authors declare no conflict of interest.