Maliput lane smoothness research

[Agustin Alba Chicar]

Research on the smoothness of the roads and the Maliput's API needs in terms of the spec. from it define a start point geometry implementation to create non straight roads and junctions between them. Confirm with drake's dev team.

[Agustin Alba Chicar]

After some interaction with drake's team, these are the conclusions:

• C1 restrictions implies continuity at all the points and tangent continuity at all points. Tolerances can be retrieved by calling: linear_tolerance() and angular_tolerance().
• straight lines are not enough to cover C1 restrictions. Arcs, splines, bezier and clothoids should suffice.
• When creating a map, straight lines and arcs can do a good job but when fitting points to a geometry (for example from an OSM or RNDF map description) the problems may become more complex and polynomial approach might be the way to go.
• Euler spirals or clothoids are real road curves, so getting an implementation of them may be desirable.
• At this moment there is no support for Bezier or Splines but it's thought to be implemented in the following weeks (Bezier curves).

[Agustin Alba Chicar]

We are going to use Splines from ignition::math and test on a separate branch of Ekumen's Drake fork the implementation using something similar dragway.