This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the controlled attitude trajectory avoids undesired regions defined by an inequality constraint. In addition, we develop an adaptive update law that enables attitude stabilization in the presence of unknown disturbances. The attitude dynamics and the proposed control systems are developed on the special orthogonal group such that singularities and ambiguities of other attitude parameterizations, such as Euler angles and quaternions are completely avoided. The effectiveness of the proposed control system is demonstrated through numerical simulations and experimental results.
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Recommended by Associate Editor Sing Kiong Nguang under the direction of Editor PooGyeon Park. This research has been supported in part by NSF under the grants CMMI-1243000, CMMI-1335008, and CNS-1337722.
Shankar Kulumani is a PhD Candidate in the Department of Mechanical and Aerospace Engineering at George Washington University. He received his bachelor’s degree in Astronautical Engineering from the US Air Force Academy in 2009 and his master’s degree in Aeronautical and Astronautical Engineering from Purdue University in 2013. His current research interests include the application of geometric mechanics and control to aerospace systems.
Taeyoung Lee is an associate professor of Department of Mechanical and Aerospace Engineering at the George Washington University. He received his doctoral degree in Aerospace Engineering and his master’s degree in Mathematics at the University of Michigan in 2008. His research interests include computational geometric mechanics and control of complex systems.
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Kulumani, S., Lee, T. Constrained geometric attitude control on SO(3). Int. J. Control Autom. Syst. 15, 2796–2809 (2017). https://doi.org/10.1007/s12555-016-0607-4
- Adaptive control
- attitude control
- special orthogonal group