Class 05 - Q&A

[ivanightingale]

This is the discussion thread for Class 5. Please feel free to ask any questions here.

I'll post a few questions here too so you can check if you understood the topic. Please provide your answer as a reply. Note that this will count as your attendance (I believe).

[ivanightingale]

Can you explain what direct transcription is, and what collocation is? How are they related?

[klamike]

These are both techniques used when making an infinite dimensional problem finite, so we can actually solve it. Direct transcription is what it sounds like -- directly discretize the problem using some integrator. Typically this only gives a good model of the dynamics very close to the discretization points. Collocation is a kind of direct transcription where to improve the accuracy between the discretization points we impose additional constraints on the residual at intermediate points.

[klamike]

Folks may be interested in InfiniteOpt which is a very nice modeling language for infinite-dimensional problems... check their docs for how they do transcription https://infiniteopt.github.io/InfiniteOpt.jl/stable/

[ivanightingale]

@klamike Another point about collocation is it in general specifically refers to using splines to represent trajectories.

[ivanightingale]

What are some sources of nonlinearity in dynamics that show up in robotics applications?

[ivanightingale]

What are some pros and cons of the Hermite-Simpson collocation?

[ivanightingale]

Can you explain, on a high level, how differential dynamic programming works, given an initial guess of the trajectories?

[andrewrosemberg]

I am very curious to understand the theoretical and practical differences between the KKT linearization used in Sequential Quadratic Programming (SQP) and the version of Differential Dynamic Programming (DDP) that employs LQR as a subproblem.