Upgrade Drake to latest release 1.20.0

[jwnimmer-tri]

Closes #296.

See also #293.

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This change is 

[jwnimmer-tri]

+@EricCousineau-TRI for review, please.

[EricCousineau-TRI]

, thanks! \cc @IanTheEngineer @calderpg-tri

Reviewed 1 of 1 files at r1, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @jwnimmer-tri)

[jwnimmer-tri]

I think the one of the builds keeps timing out. I'm not sure if I should keep retrying it, but I'll give it another go.

[EricCousineau-TRI]

I've filed #295 to try and fix the caching issues as you've mentioned a ways back.
I will test locally using ./run_all_tests.sh, and then force merge if that works out.

[jwnimmer-tri]

We'll probably have Drake v1.20 tagged before CI is ready here, in which case I'll plan to rework this to pin v1.20 instead.

[jwnimmer-tri]

Hah, our posts crossed in the wind.

I guess I don't mind whether we land this with 1.19 now or wait a couple hours for 1.20.

[EricCousineau-TRI]

Ah, probably good to just wait out v1.20.0. I'll let my local tests continue to run, just in case.

EDIT: Tests pass locally.

[jwnimmer-tri]

Pushed up to 1.20 now.

[EricCousineau-TRI]

Local testing passed w/ newer v1.20.0 push - merging!