Reducing the Risk of Orbit Transfer in Low-thrust Missions

1. Iman Alizadeh University of California, Irvine Reducing the Riskof Orbit Transfer in Low-thrust Missions Image from http://dawn.jpl.nasa.gov/multimedia/images/vestaorbit_300.jpg

2. Motivation • Designing Space missions with low-cost. • Low-thrust propulsion technology are very efficient Image Credit: NASA/JPL Image Credit: NASA/JPL

3. Motivation • Designing Space missions with low-cost. • Low-thrust propulsion technology are very efficient BUT Time of powered flight is long Very low control authority T/W < 0.01 Risk of failure (continues thrust) Image Credit: JAXA

4. Low-thrust challenges • In multi-body environments trajectories are very sensitive to perturbations ( Launch errors, temporary engine loss, …) • Stability is critical for low-thrust missions in multi body environments.

5. Problem statement • Current trajectory design methods do not take the risk from loss of control into account. • Sensitivity analysis is preformed by Monte Carlo simulation around the reference trajectory which is computationally expensive. • Provide methods to reduce the sensitivity and increase the life-time of low-thrust trajectories.

6. Outline of Presentation • Modeling • Indirect stability improvement • Direct stability improvement • Conclusions and future works

7. 3-Body Dynamics Circular Restricted Three Body Problem Jacobi constant

8. 3-Body Dynamics Equilibrium points, periodic orbits and invariant manifolds

9. Trajectory Optimization Problem CRTBP dynamics J= maximizing payload at final time Solution: shooting method

10. LEO to Lyapunov transfer in the Earth-Moon system

11. Stability in the powered flight :Indirect approach • How to reduce sensitivity of the reference trajectory to loss of control?

12. Indirect method:Desensitizing the reference trajectory

13. Comparison of two optimal thrust profiles

14. Deviation from the reference trajectory for 1 day loss of control Remains small in case of loss of control

15. Stability in the powered flight :Direct approach • How to improve the life-time characteristics of an optimal trajectory? • Important to address planetary protection requirements

16. Lyapunov-Laypunov Transfer in theJupiter-Europa system

17. Life-time computation

18. Direct method:Inverse Dynamics 1- Design an optimal retargeting trajectory for the initial condition. 2- Integrate the fuel-optimal retargeting trajectory backward in time. 3- extract the required control to traverse the backward integrated path.

19. Modified trajectories andthrust profile

20. Improved life-time

21. Conclusions Improving robustness of low-thrust trajectories to loss of control systematically by: • Minimizing the angle between controlled and uncontrolled vector field. • Back-propagating an optimal retargeting trajectory and extract control using inverse dynamics. • The proposed methods are computationally less expensive than traditional approaches.

22. Future Works • Considering the constant specific impulse engines for the transfers. • Investigation of the optimality of the inverse dynamics. • Design of robust guidance scheme to account for engine performance degradation.

23. Thank YOU !