Port stochastic scenarios

[jwnimmer-tri]

The Drake developers at TRI have the following capabilities in our internal repositories:

• specify random distributions and transforms in C++, Python, and YAML,
• specify constraints on pose, generalized position, and vector direction in C++, Python, and YAML,
• populate these values into a simulation's initial conditions and diagram-level constraints.

In principle, we are happy to share it, but making it public takes time and we have not yet prioritized it. Please upvote it by adding a "thumbs up" reaction to this comment if you want us to know that you are keen.

Here's an illustration of how it could be used to specify a simulation:

# An example scenario for acrobot, with randomness.
one_example:
  controller_params: !UniformVector
    min: [4, 40, 4, 0.9e3]
    max: [6, 60, 6, 1.1e3]
  initial_state: !UniformVector
    min: [1.1, -0.1, -0.1, -0.1]
    max: [1.3, 0.1, 0.1, 0.1]
  t_final: 30.0
  tape_period: 0.05

[hzyjerry]

I am very interested in this for my research. Would love to see progress on it :)
Also happy to chat more and potentially contribute.

[jwnimmer-tri]

Bumping to high because Russ wants #13282 and this is a prereq.

[jwnimmer-tri]

I believe everything we need is now available on master, without restriction. I still some a few clean-ups to follow up, but the feature should be fully operable now.