DDP reformulation question

[FreyJo]

Hi Giulio,

I addressed both things that you pointed out in the last comment in the pull request.

@valenorf

Still, I notice strange behavior using DDP. When I leave keep_x0=True, I have a timing in some closed loop iter. of 0.001ms, and sometimes spikes to 0.008ms (even in this case, the robot does not walk as nicely as with sqp. But I feel something is missing). This strong variability in timing does not seem to happen with the variable keep_x0=False. (time is more or less consistent during the different calls, but the robot falls. This is for the case x0 is a variable itself, like in robust MPC I guess.)

How do you use the DDP solver in closed loop?
I think that actually, we did not really test it yet.
If you formulate your problem with translate_to_feasibility_problem(keep_x0=False), it is not possible right now to update the initial state. Or how did you do that?
Thus, you basically always solve the same problem over and over, if you keep_x0=False, which should then give you a very consistent timing.
On the other hand, your initial state update probably is correct when you set keep_x0=True and the differences in runtime correspond to the solver requiring a varying number of iterations. I suggest printing the solver statistics to evaluate this.

I think, we should set up a minimal example with closed loop DDP in acados for reference!