New Cone-Rolling Principle and Its Application for the Underactuated Attitude Maneuver Optimization of a Rigid Body
Publication: Journal of Aerospace Engineering
Volume 34, Issue 1
Abstract
The global optimal solution for the underactuated attitude maneuver plays a significant role in the fields of spacecraft, robotics, and mechanics. This paper investigated the global optimal underactuated attitude maneuver by using angular velocity on a principal plane in the quaternion statement. The integral of angular velocity was considered as the performance criterion, and a correlation vector was introduced based on the coincidence of equations for the state and co-state. According to the Pontryagin minimum principle, it was concluded that the optimal angular velocity has the opposite direction as the correlation vector’s projection on the principal plane, thereby indicating that the optimal process is to roll the principal plane around a cone. The solution of the cone was obtained through two geometric constraints. One is that the angle between the correlation vector and the principal plane remains invariant; the other is that the trajectories of the correlation vector’s projection have the same length on the principal plane and the cone surface. The solution of the cone led to the analytical solution of the angular velocity and the control torque. For validation, the simulation results indicated that the optimal cost value obtained with the proposed cone-rolling solution, i.e., the integral of angular velocity, is lower than the suboptimal value obtained with the genetic algorithm. That is, the proposed cone-rolling principle–based global optimal analytical solution is reasonable and feasible.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
References
Behal, A., D. Dawson, E. Zergeroglu, and Y. Fang. 2002. “Nonlinear tracking control of an underactuated spacecraft.” J. Guidance Control Dyn. 25 (5): 979–985. https://doi.org/10.2514/2.4973.
Bullo, F., and A. D. Lewis. 2004. Geometric control of mechanical systems: Modeling, analysis, and design for simple mechanical control systems. New York: Springer. https://doi.org/10.1007/978-3-540-45730-5_8.
Chaturvedi, N. A., A. K. Sanyal, and N. H. McClamroch. 2011. “Rigid-body attitude control.” IEEE Control Syst. Mag. 31 (3): 30–51. https://doi.org/10.1109/MCS.2011.940459.
Colombo, L., D. Martín De Diego, and M. Zuccalli. 2010. “Optimal control of underactuated mechanical systems: A geometric approach.” J. Math. Phys. 51 (8): 083519. https://doi.org/10.1063/1.3456158.
Colombo, L., D. Martín de Diego, and M. Zuccalli. 2013. “Higher-order discrete variational problems with constraints.” J. Math. Phys. 54 (9): 093507. https://doi.org/10.1063/1.4820817.
Crouch, P. 1984. “Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models.” IEEE Trans. Autom. Control 29 (4): 321–331. https://doi.org/10.1109/TAC.1984.1103519.
Fantoni, I., R. Lozano, F. Mazenc, and K. Pettersen. 1999. “Stabilization of a nonlinear underactuated hovercraft.” In Proc., 38th IEEE Conf. on Decision and Control (Cat. No. 99CH36304), 2533–2538. New York: IEEE. https://doi.org/10.1109/CDC.1999.831309.
Ge, X., and L. Chen. 2009. “Optimal reorientation of underactuated spacecraft using genetic algorithm with wavelet approximation.” Acta Mech. Sin. 25 (4): 547–553. https://doi.org/10.1007/s10409-009-0246-6.
Ge, X.-S., and J. Lv. 2009. “Numerical algorithm for the attitude motion planning of an underactuated system of coupled rigid bodies spacecraft.” J. Astronaut. 30 (2): 645–651.
Gui, H., L. Jin, and S. Xu. 2013. “Attitude maneuver control of a two-wheeled spacecraft with bounded wheel speeds.” Acta Astronaut. 88 (Jul–Aug): 98–107. https://doi.org/10.1016/j.actaastro.2013.03.006.
Horri, N. M., and P. Palmer. 2012. “Practical implementation of attitude-control algorithms for an underactuated satellite.” J. Guidance Control Dyn. 35 (1): 40–45. https://doi.org/10.2514/1.54075.
Jiang, Z.-P. 2002. “Global tracking control of underactuated ships by Lyapunov’s direct method.” Automatica 38 (2): 301–309. https://doi.org/10.1016/S0005-1098(01)00199-6.
Keshavarzian, H., and K. Daneshjou. 2019. “Modified under-actuated quadrotor model for forwarding flight in the presence of ground effect.” Aerosp. Sci. Technol. 89 (Jun): 242–252. https://doi.org/10.1016/j.ast.2019.04.001.
Li, J., S. Chen, C. Li, C. Gao, and W. Jing. 2019. “Adaptive control of underactuated flight vehicles with moving mass.” Aerosp. Sci. Technol. 85 (Feb): 75–84. https://doi.org/10.1016/j.ast.2018.12.003.
Liu, H., T. Huang, and D. G. Chetwynd. 2011. “An approach for acceleration analysis of lower mobility parallel manipulators.” J. Mech. Rob. 3 (1): 011013. https://doi.org/10.1115/1.4003271.
Liu, X., Z. Meng, and Z. You. 2018. “Adaptive collision-free formation control for under-actuated spacecraft.” Aerosp. Sci. Technol. 79 (Aug): 223–232. https://doi.org/10.1016/j.ast.2018.05.040.
Ma, G., Y. Zhuang, C. Li, and H. Huang. 2010. “Pseudospectral method for optimal motion planning of a rigid underactuated spacecraft.” In Proc., IEEE ICCA 2010, 684–688. New York: IEEE. https://doi.org/10.1109/ICCA.2010.5524248.
Mirshams, M., and M. Khosrojerdi. 2016. “Attitude control of an underactuated spacecraft using tube-based MPC approach.” Aerosp. Sci. Technol. 48 (Jan): 140–145. https://doi.org/10.1016/j.ast.2015.09.018.
Mirshams, M., and M. Khosrojerdi. 2017. “Attitude control of an underactuated spacecraft using quaternion feedback regulator and tube-based MPC.” Acta Astronaut. 132 (Mar): 143–149. https://doi.org/10.1016/j.actaastro.2016.11.033.
Ortega, R., and M. W. Spong. 2000. “Stabilization of underactuated mechanical systems via interconnection and damping assignment.” IIFAC Proc. Vol. 33 (2): 69–74. https://doi.org/10.1016/S1474-6670(17)35549-0.
Petersen, C. 2016. “Advances in underactuated spacecraft control.” Doctoral dissertation, Aerospace Engineering, Univ. of Michigan.
Spong, M. W. 1998. “Underactuated mechanical systems.” In Control problems in robotics and automation, 135–150. New York: Springer. https://doi.org/10.1007/BFb0015081.
Trivailo, P. M., F. Wang, and H. Zhang. 2009. “Optimal attitude control of an accompanying satellite rotating around the space station.” Acta Astronaut. 64 (2–3): 89–94. https://doi.org/10.1016/j.actaastro.2008.05.018.
Wang, B., Z. Meng, C. Jia, and P. Huang. 2019. “Anti-tangle control of tethered space robots using linear motion of tether offset.” Aerosp. Sci. Technol. 89 (Jun): 163–174. https://doi.org/10.1016/j.ast.2019.03.060.
Wang, D., J. Zhao, and C. Hu. 2014. “Time-optimal attitude maneuver for underactuated spacecraft based on pseudospectral method.” In Proc., 2014 IEEE Chinese Guidance, Navigation and Control Conf., 1067–1072. New York: IEEE. https://doi.org/10.1109/CGNCC.2014.7007353.
Zhang, J., K. Ma, and G. Meng. 2014. “Controllability analysis and attitude path planning of underactuated spacecraft systems.” Aerosp. Sci. Technol. 33 (1): 76–81. https://doi.org/10.1016/j.ast.2014.01.003.
Information & Authors
Information
Published In
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jan 16, 2020
Accepted: Jul 29, 2020
Published online: Sep 30, 2020
Published in print: Jan 1, 2021
Discussion open until: Feb 28, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.