py systems: Enable / show example of doing convertible VectorSystem

[EricCousineau-TRI]

From @RussTedrake's pain points:

RuntimeError: The object named [] of type drake::pydrake::(anonymous)::Impl::PyVectorSystem does not support ToAutoDiffXd.

There are examples of doing scalar convertible types here:
https://github.com/RobotLocomotion/drake/tree/ffaa013/bindings/pydrake/systems/test/scalar_conversion_test.py#L12

However, I should inspect how hard it is to allow intermediate C++ base classes (e.g. VectorSystem) to do scalar conversion through this shindig. If it's messy / boilerplatey, will consider just reimplementing the intermediate in Python or what not.
Either one shouldn't be that hard.

[RussTedrake]

Thanks! My "pain point" request has two parts. (1) just being able to convert subclasses of VectorSystem... which I think is just a matter of declaring the ScalarConverter versions of the constructor, etc(?), and (2) getting rid of the boilerplate around the python system conversion.

EDIT(eric): Moved pain point (2) to #10755.

[EricCousineau-TRI]

I would like this issue to focus on the first pain point, will create a separate one for the second. Thanks!

[EricCousineau-TRI]

User ran into this pain point again on StackOverflow: https://stackoverflow.com/questions/57512465/class-implementation-in-python

Upon revisiting this, though, it seems like it may be more complicated: VectorSystem overloads depend on reference semantics between C++ Eigen matrices and Python NumPy arrays, which is still not supported (#8116).

That issue is a still be nebulous due to the NumPy version requirements + potential for segfaults.

Proposed solutions:

• First try to make the error message encountered a little more tractable for users.
• Briefly see what's involved in the dtype stuff - knowing that it may open a can of worms.
• Try out @jwnimmer-tri's suggestion in making a pure Python sugar class, and ditch overloading of the C++ VectorSystem in Python.
  • Caveat here is any analysis that is constrained to VectorSystem; I should see what methods those are.

[jwnimmer-tri]

Caveat here is any analysis that is constrained to VectorSystem; I should see what methods those are.

TTBOMK nothing uses the type of a VectorSystem to infer facts. It should always just be asking quacks-like questions as in "Is this System SISO", etc.

Or in other words, I would be happy to break any code that uses the runtime type of a VectorSystem to infer facts.

[jwnimmer-tri]

Per #20989 (comment), we should disprefer VectorSystem in the first place, so there's no point in gold-plating its Python bindings.