Question

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 ?

3,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 ?


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Answer 1

Answer:

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.