Considering the powered descent guidance problem for a spacecraft or launch vehicle - Early publications by Acikmese, et.al. used lossless convexification to solve the landing guidance problem using point mass dynamics.
Literature that dealt with the powered descent guidance problem using 6 DoF dynamics, also by Acikmese, et.al. proposed the use of successive convexification, with the reasons being that lossless convexification could not handle non-convex state and some classes of non-convex control constraints.
I have the following questions with respect to the above
1) Why is it that Lossless convexification cannot handle some classes of non-convex control constraints ? and what are those classes ? (e.g. the glideslope constraint)
2) What is it about lossless convexification that makes it unsuitable to operate on non-convex state constraints ,as opposed to successive convexification ?
2) Are there specific rotational formalisms ,e.g. quaternions, DCMs, Dual quaternions, MRPs, etc. that are inherently convex ? if so, how does one go about showing that they are convex ?
I would be much obliged if someone could answer these questions or atleast provide references that would aid in my understanding of the topic of convexification.
Thank you.
Hi Dr.Sagliano,
Thank you for responding. I apologize if my question wasnt clear.
my questions are as follows:
1) What exactly is the reason for using successive convexification over Lossless convexification?
2) Why is it that Lossless convexification cannot handle non-convex state constraints and some classes of non-convex control constraints ?
3) Are there attitude representations , e.g. Quaternions, Dual quaternions, that would make the problem convex ?
Dear Adhithya Babu,
A successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and it can handle nonlinear dynamics and non-convex state and control constraints. However lossless convexification cannot handle nonlinear dynamics. For the third question the answer is affirmative.
For more details and information about your questions I suggest you to see links and attached files on topic.
https://ieeexplore.ieee.org/document/8206363
http://depts.washington.edu/uwrainlab/wordpress/wp-content/uploads/2018/12/p3_main.pdf
https://www.researchgate.net/publication/220158360_Lossless_convexification_of_a_class_of_optimal_control_problems_with_non-convex_control_constraints
https://www.researchgate.net/publication/328256264_Spacecraft_Robot_Kinematics_Using_Dual_Quaternions
https://link.springer.com/article/10.1007/s40295-019-00181-4
https://pdfs.semanticscholar.org/d9bb/bc53c37fd6d6918794d4dbdc4b09d81c42f8.pdf
Best regards
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