It is known that collocation (or shooting) enforces exact dynamic satisfaction at collocation nodes, so dynamics can violate inbetween. Also, violation can be caused by approximating using polynomials.
Is there a way to post analyse the accuracy of dynamic satisfaction, like using a higher order interpolation.
About QP formulation
I’ve been looking into the race_cars example these days
I think the QPs are formulated as
min (s-s_ref)^2 + p(\delta z)^2
with \delta z some slacks for constraints, and p is some penalty weight.
Basically, trying to be as close as possible to s_ref (some large progress that actually impossible), and penalise constraint violation.
So the cost can be driven lower by violating constraints, but the postive part is all sub QPs will be feasible.
Which brings to another question:
Why it does not seem favourable to have restoration in actual embeded system, is that purely due to memory usage concern, or there are some other reasons?
I have no experience with embeded, but just out of cuiosity. Or there are other reasons for making strictly feasible QPs?
Regarding 1., you can use an acados integrator to easily simulate the solution that you obtained with a more accurate integration scheme
Regarding 2., if you use the solver SQP in acados, all QP subproblems need to be feasible, otherwise the solver will raise an error. You can try the solver SQP_WITH_FEASIBLE_QP which should be able to handle infeasible QPs (by internally reformulating them with slacks). This solver is not very thoroughly tested though.
Yes, post simulation is the exsiting route, I think what you mean is post sim with more steps, since the highest stage is 4?
But I think it might not necesarilly show the real accuracy of the sim during the solve?
If say later on I will move to some rather difficult problem and try to analyze failures, are there any suggestions about how to debug, saying dig deeper to see whether it is a solver issue or transcription issue?
And I think the SQP_WITH_FEASIBLE_QP, the feasible one is basically an l1-penalty restoration?
