- Volume 11 Issue 4
This paper proposes a linear system control algorithm with collision avoidance in multiple satellites. Consideration of collision avoidance is augmented by adding a weighting term in the cost function of the original tracking problem in linear quadratic control (LQC). Because the proposed algorithm relies on a similar solution procedure to the original LQC, its inherent advantages, including gain-robustness and optimality, are preserved. To confirm and visualize the derived algorithm, a simple example of two-vehicle motion in the two-dimensional plane is illustrated. In addition, the proposed collision avoidance control is applied to satellite formation flying, and verified by numerical simulations.
Collision avoidance;Linear quadratic control;Tracking problem;Satellite formation flying
- Anderson, B. D. O. and Moore, J. B. (1990). Optimal Control: Linear Quadratic Methods. Englewood Cliffs: Prentice Hall.
- Bellman, R. E. (1952). On the theory of dynamics programming. Proceeding of the National Academy of Sciences, California, pp. 716-719.
- Clohessy, W. H. and Wiltshire, R. S. (1960). Terminal guidance system for satellite rendezvous. Journal of the Aerospace Science, 27, 653-658. https://doi.org/10.2514/8.8704
- Dorato, P., Abdallah, C. T., and Cerone, V. (1995). Linear-Quadratic Control: an Introduction. Englewood Cliffs: Prentice Hall.
- Fravolini, M. L., Ficola, A., Napolitano, M. R., Campa, G., and Perhinschi, M. G. (2003). Development of modeling and control tools for aerial refueling for UAVs. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, pp. AIAA 2003-5798.
- Gribble, J. J. (1993). Linear quadratic Gaussian/loop transfer recovery design for a helicopter in low-speed flight. Journal of Guidance, Control, and Dynamics, 16, 754-761. https://doi.org/10.2514/3.21077
- Hadaegh, F. Y., Ghavimi, A. R., Singh, G., and Quadrelli, M. (2000). A centralized optimal controller for formation flying spacecraft. International Conference of Intelligence and Technology.
- Lim, H., Bang, H., and Kim, H. (2005). Sliding mode control for the configuration of satellite formation flying using potential functions. International Journal of Aeronautical and Space Sciences, 6, 56-63. https://doi.org/10.5139/IJASS.2005.6.2.056
- Lovren N. and Tomic, M. (1994). Analytic solution of the Riccati equation for the homing missile linear-quadratic control problem. Journal of Guidance, Control, and Dynamics, 17, 619-621. https://doi.org/10.2514/3.21242
- McCambish, S. B. Romano M., Nolet, S., Edwards C. M., and Miller, D. W. (2009). Flight testing of multiple-spacecraft control on SPHERES during close-proximity operations. Journal of Guidance, Control, and Dynamics, 46, 1202-1213.
- Plumlee, J. H. and Bevly, D. M. (2004). Control of a ground vehicle using quadratic programming based control allocation techniques. Proceeding of the American Control Conference, Boston, MA, 4704-4709
- Psiaki, M. L. (2001). Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation. Journal of Guidance, Control, and Dynamics, 24, 386-394. https://doi.org/10.2514/2.4723
- Ridgely, D. B., Banda, S. S., McQuade, T. E., and Lynch, P. J. (1987). Linear-quadratic-Gaussian with loop-transfer recovery methodology for an unmanned aircraft. Journal of Guidance, Control, and Dynamics, 10, 82-89. https://doi.org/10.2514/3.20184
- Slater, G. L., Byram, S. M., and Williams, T. W. (2006). Collision avoidance for satellites in formation flight. Journal of Guidance, Control, and Dynamics, 29, 1140-1146. https://doi.org/10.2514/1.16812
- Speyer, J. L. (1979). Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem. IEEE Transactions and Automatic Control, 24, 262-269. https://doi.org/10.1109/TAC.1979.1101973
- Xing, G. Q., Parvez, S. A., and Folta, D. (2000). Design and implementation of synchronized autonomous orbit and attitude control for multiple spacecraft formation using GPS measurement feedback. Advances in the Astronautical Sciences, 105I, 115-134.
- Wang, S. and Schaub, H. (2008). Spacecraft collision avoidance using coulomb forces with separation distance and rate feedback. Journal of Guidance, Control, and Dynamics, 31, 740-750. https://doi.org/10.2514/1.29634
- Wiener, N. (1948). Cybernetics. New York: John Wiley.
- Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance vol.26, pp.1, 2017, https://doi.org/10.1088/1674-1056/26/1/014502
- An Online Tilt Estimation and Compensation Algorithm for a Small Satellite Camera vol.19, pp.1, 2018, https://doi.org/10.1007/s42405-018-0024-4