py mbp: Expose autodiff and symbolic scalar types

[EricCousineau-TRI]

Relevant Slack discussion:
https://drakedevelopers.slack.com/archives/C2CK4CWE7/p1555082817001300?thread_ts=1555024805.009600&cid=C2CK4CWE7

Thanks Russ and Michael!
Russ: do you mean something like this?

q = prog.NewContinuousVariables(plant.num_positions())
context = plant_sym.CreateDefaultContext()
plant_sym.SetPositions(context, q)```
If yes, here I get: `'System_[Expression]' object has no attribute 'SetPositions'`.

Check list:

• py math: Disentangle .eigen_geometry, .math, .autodiff, and .symbolic #11384 Remove the, uh, bad legacy dependencies that I left; currently we have: (--> representing depends-on)
  • .autodiff, .symbolic --> .math --> .common.eigen_geometry, but really we want
  • .math --> .common.eigen_geometry --> .autodiff, .symbolic
• py systems: Split and hoist general header utilities #11383 Start cleaning up value stuff
• py: Add numpy_compare testing utilities #11386 Consolidate testing utilities for NumPy matrix comparisons, esp. for extra dtypes
  • Overarching issue now tracked by py: Add NumPy testing utilities #11385, but just need PR to smooth out this work
• py eigen: Expose default scalars #11382 Expose dtypes for .common.eigen_geometry
• py math: Expose scalars for RotationMatrix, RollPitchYaw, RigidTransform #11563 Expose dtypes for .common.math
  • RotationMatrix first
  • RigidTransform, RollPitchYaw
• py multibody/math : Expose scalars for SpatialAcceleration, SpatialForce and SpatialVelocity #11590 Expose dtypes for .multibody.math
• py geometry : Expose scalars in geometry #11614 Expose dtypes for geometry
• py multibody/plant and multibody/tree: Expose scalar types #11633 Expose dtypes for .multibody.tree
• py multibody/plant and multibody/tree: Expose scalar types #11633 Expose dtypes for .multibody.plant

\cc @TobiaMarcucci @RussTedrake @hongkai-dai

[EricCousineau-TRI]

Added checklist. I'm going to tackle the first few items to figure out the general procedure and do some much-needed cleanup.
After binding .common.eigen_geometry, may request help from @m-chaturvedi.

\cc @jamiesnape

WIP Branch: master...EricCousineau-TRI:issue/11240-wip

[EricCousineau-TRI]

Per Slack convo, other suggestions for looking at scalar-type binding:
https://github.com/RobotLocomotion/drake/blob/2df723d/bindings/pydrake/systems/primitives_py.cc
https://github.com/RobotLocomotion/drake/blob/2df723d/bindings/pydrake/systems/framework_py_values.cc

This is a bit more advanced, so take it with a grain of salt:
https://github.com/RobotLocomotion/drake/blob/2df723d/bindings/pydrake/systems/framework_py_systems.cc

[EricCousineau-TRI]

Primary diff with scalar type change for eigen geometry: fc331ee

https://drake.mit.edu/python_bindings.html#differences-with-c-api

[mpetersen94]

Is there an eta for autodiff support of RigidTransform/RotationMatrix in python? I'm happy to help with the process if that would accelerate the timeline at all.

[m-chaturvedi]

I'm working on it. I need to write the relevant tests for it. I need to know from Eric which all methods need to be exposed other than RigidTransform and RotationMatrix. I'll try to finish it asap, so in a couple of days.
EDIT: Here, the PR: #11563

[EricCousineau-TRI]

Er, added my thumbs-up without answering!
To clarify, it would be best to bind all methods that are scalar-type depended, unless there are issues.
If there gets to be too much boiler-plate for instantiating unittest test cases, then it should be simple enough to simplify that, helping with aliases and all that.

[EricCousineau-TRI]

@mpetersen94 -- @m-chaturvedi just landed that PR. At present, the only thing not fully supported is RigidTransform_[T].translation() - but that should be resolved via #11575.

[gizatt]

(Posting at request of Hongkai / Eric) As I understand it this is blocking Python binding of StaticEquilibriumConstraint -- for timeline purposes, I'd love to have access to those bindings in a week or so, but I can adjust if that looks like it won't happen. Thanks!

[EricCousineau-TRI]

Per f2f, we will target next Friday, June 14th. Thanks!

[EricCousineau-TRI]

Per Slack convos, @m-chaturvedi is almost there; wrangling some issues with scalar type conversion with MBP+SG and matrix aliasing per #8116

[EricCousineau-TRI]

Done! Thanks @m-chaturvedi!

[EricCousineau-TRI]

(Even though #11575 is not yet resolved, can still fix that separately without needing this to be open.)