Figure out why convergence is more difficult with human scaled parameters.

[moorepants]

• [x] See if convergence for the n-pendulum problem is faster if I set the parameters to the original numerical values. I need to determine if it is actually the change in parameter values that affects this or if I've changed something else in my code that affected this.
• [x] Explore scaling the constraints and objective.
• [ ] Try SNOPT?

[tvdbogert]

It is just difficult, or (so far) impossible to get convergence?

[moorepants]

I just got the Park/Kuo model running. I'm also having this issue. For example, if my initial guess is the known state trajectories and the known continuous gains, it took around 2000 iterations to find the solution. It does find the correct solution, but at some point in history I was able to find the correct solution for the n-pendulum problem with far fewer iterations. I'm also having trouble converging at all for different initial gain guesses (random, zeros, ones).

[moorepants]

I just confirmed that the parameter id problem converges in under 100 iterations after switching back to my original numerical parameter set for the n-link pendulum which was masses and links are 1.0 kg and 1 m respectively. I'm not sure why this would effect things so much.

[tvdbogert]

Have you experimented with varying the time step for direct collocation? The smaller pendulum has faster dynamics, so may need smaller step size to converge equally well. Other than that I would have no idea.

[moorepants]

Yeh, I've used smaller steps. I think I'll need to systematically go through various things. This is discouraging though...

[tvdbogert]

It's such a dramatic difference in performance of the optimization. Important to understand what the critical factor is. Yes, systematic exploration of in-between cases seems to be the only option.

[moorepants]

Ton suggested trying a regularization term in the cost function.

• sum of squares of all unknowns
• integral of second derivative of states squared (smoothness)

These should have small weighting terms.

[moorepants]

Think about scaling:

• Scale constraints by bodyweight
• Maybe scale the objective to be close to 1
• https://projects.coin-or.org/Ipopt/wiki/HintsAndTricks

[moorepants]

Some useful links for scaling:

• http://list.coin-or.org/pipermail/ipopt/2013-June/003416.html
• http://www.gams.com/dd/docs/solvers/conopt.pdf
• Betts has a nice section in his book on scaling.
• http://arxiv.org/pdf/1301.7283v1.pdf
• https://projects.coin-or.org/Ipopt/wiki/HintsAndTricks

[moorepants]

@tvdbogert Good news. The gains for human quiet standing problem range from 0 to 1000. The state trajectories are all in the realm of -0.5 to 0.5, so they are fine in terms of scaling. I scaled the gains in the problem formulation such that they are all 0.5. Problem now converges in 31 iterations. The paper can move forward!

[tvdbogert]

So it was the scaling! Very nice and very useful to know how important this is.

[moorepants]

Fixed both examples:

• 006b3031760e10
• 4a75e1374111db0d