### Optimal Control for Proximity Operations and Docking

Lee, Dae-Ro;Pernicka, Henry

• 발행 : 2010.09.15
• 13 3

#### 초록

This paper proposes optimal control techniques for determining translational and rotational maneuvers that facilitate proximity operations and docking. Two candidate controllers that provide translational motion are compared. A state-dependent Riccati equation controller is formulated from nonlinear relative motion dynamics, and a linear quadratic tracking controller is formulated from linearized relative motion. A linear quadratic Gaussian controller using star trackers to provide quaternion measurements is designed for precision attitude maneuvering. The attitude maneuvers are evaluated for different final axis alignment geometries that depend on the approach distance. A six degrees-of-freedom simulation demonstrates that the controllers successfully perform proximity operations that meet the conditions for docking.

#### 키워드

Optimal control;Proximity operations and docking;State-dependent Riccati equation controller;Linear quadratic tracking controller;Linear quadratic Gaussian controller

#### 참고문헌

1. Alba-Flores, R. and Barbieri, E. (2006). Real-time infinite horizon linear-quadratic tracking controller for vibration quenching in flexible beams. IEEE International Conference on Systems, Man and Cybernetics, Taipei, Taiwan. pp. 38-43.
2. Bach, R. and Paielli, R. (1993). Linearization of attitudecontrol error dynamics. IEEE Transactions on Automatic Control, 38, 1521-1525. https://doi.org/10.1109/9.241567
3. Budiyono, A. and Wibowo, S. S. (2007). Optimal tracking controller design for a small scale helicopter. Journal of Bionic Engineering, 4, 271-280. https://doi.org/10.1016/S1672-6529(07)60041-9
4. Cimen, T. (2008). State-Dependent Riccati Equation (SDRE) control: a survey. Proceedings of the 17th International Federation of Automatic Control (IFAC) World Congress, Seoul, Korea. pp. 3761-3775.
5. Cloutier, J. R. (1997). State-dependent Riccati equation techniques: an overview. Proceedings of the American Control Conference, Albuquerque, NM. pp. 932-936.
6. Crassidis, J. L. and Junkins, J. L. (2004). Optimal Estimation of Dynamic Systems. Boca Raton: Chapman & Hall/CRC.
7. Fehse, W. (2003). Automated Rendezvous and Docking of Spacecraft. Cambridge: Cambridge Univeristy Press.
8. Gonnaud, J. L. and Pascal, V. (1999). ATV guidance, navigation and control for rendezvous with ISS. Proceedings of the 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems, Noordwijk, the Netherlands. p. 501.
9. Lee, D. and Pernicka, H. (2009). Vision-based relative state estimation using the unscented Kalman filter. Spaceflight Mechanics Meeting, Savannah, GA. Paper No. 09-166.
10. Lefferts, E. J., Markley, F. L., and Shuster, M. D. (1993). Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics, 5, 417-429.
11. Lewis, F. L. and Syrmos, V. L. (1995). Optimal Control. 2nd ed. New York: Wiley.
12. Madonna, R. G. (1997). Orbital Mechanics. Original ed. Malabar, FL: Krieger Pub. Co. pp. 105-107.
13. Nagata, T., J. Modi, V., and matsuo, H. (2001). Dynamics and control of flexible multibody systems: Part II: simulation code and parametric studies with nonlinear control. Acta Astronautica, 49, 595-610. https://doi.org/10.1016/S0094-5765(01)00010-8
14. Naidu, D. S. (2003). Optimal Control Systems. Boca Raton, FL: CRC Press.
15. National Aeronautics and Space Administration (NASA). (May 15, 2006). Overview of the DART mishap investigation results (for public release).
16. Olszewski, O. J. (1990). Automated terminal guidance for a shuttle rendezvous to space station freedom. AIAA Guidance, Navigation and Control Conference, Portland, OR. pp. 377-388.
17. Paielli, R. A. and Bach, R. E. (1993). Attitude control with realization of linear error dynamics. Journal of Guidance, Control, and Dynamics, 16, 182-189. https://doi.org/10.2514/3.11444
18. Pearson, D. J. (1989). Shuttle rendezvous and proximity operations. Proceedings of the CNES International Symposium on Space Dynamics, Paris. pp. 833-851.
19. Prussing, J. E. and Conway, B. A. (1993). Orbital Mechanics. New York: Oxford University Press.
20. Rumford, T. (2002). Demonstration of Autonomous Rendezvous Technology (DART) project summary. Core Technologies for Space Systems Conference, Colorado Springs, CO.
21. Schaub, H. and Junkins, J. L. (2003). Analytical Mechanics of Space Systems. Reston, VA: American Institute of Aeronautics and Astronautics.
22. Stansbery, D. T. and Cloutier, J. R. (2000). Position and attitude control of a spacecraft using the state-dependent Riccati equation technique. Proceedings of the American Control Conference, Chicago, IL. pp. 1867-1871.
23. Sznaier, M. and Suarez, R. (2001). Suboptimal control of constrained nonlinear systems via receding horizon state dependent Riccati equations. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL. pp. 3832-3837.
24. Vallado, D. A. and McClain, W. D. (2001). Fundamentals of Astrodynamics and Applications. 2nd ed. Boston: Kluwer Academic Publishers. pp. 524-537.
25. Walker, S. R., LoPresti, J. A., and Schrock, M. B. (2005). Space shuttle Rbar pitch maneuver for thermal protection system inspection. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA. AIAA 2005-5983.
26. Wertz, J. R. and Bell, R. (2003). Autonomous rendezvous and docking technologies-status and prospects. Space Systems Technology and Operations Conference, SPIE AeroSense Symposium, Orlando, FL. Paper No. 5088-5083.
27. Wie, B. (1998). Space Vehicle Dynamics and Control. Reston, VA: American Institute of Aeronautics and Astronautics. pp. 365-369.
28. Xin, M., Balakrishnan, S. N., and Stansbery, D. T. (2004). Spacecraft position and attitude control with ${\theta}$-D technique. 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV. AIAA 2004-2540.
29. Zimpfer, D., Kachmar, P., and Tuohy, S. (2005). Autonomous rendezvous, capture and in-space assembly: past, present and future. 1st Space Exploration Conference: Continuing the Voyage of Discovery, Orlando, FL. AIAA 2005-2523.

#### 피인용 문헌

1. Nonlinear Control for Proximity Operations Based on Differential Algebra vol.38, pp.11, 2015, https://doi.org/10.5139/IJASS.2010.11.3.206