Add a "Planar" Floating Base Type

[liangfok]

Motivation

We want to simulate mobile robots capable of holonomic motion but don't want to model all of the complex contact interactions between the omni-directional wheels and the ground. The current integrators in C++ Drake result in very high reaction forces from these contacts, resulting in the need to run simulations at excessively small time steps, which results in very low real-time factors. By switching to a dedicated floating base type that only restricts lateral movement along the Z-axis, and rotational movement around the X and Y axes, we can eliminate all contact forces with the ground and thus speed up simulations.

Implementation

See drake-distro/systems/plants/joints/DrakeJoint.h.

[sherm1]

:+1: A planar joint should be in every multibody toolbox -- it has many uses. For simplified ground contact it can only be used if you can be sure there will be no Z-axis liftoff.

In many cases we can recover the contact forces even with the planar joint in place -- they are represented by the joint's reaction forces which can be calculated almost for free.

[jwnimmer-tri]

@liangfok Should this be reassigned to @amcastro-tri?

[liangfok]

Yes, I think that's a good idea. @amcastro-tri, feel free to escalate to @sherm1 if you're not the right person for this.

[sherm1]

Definitely something for the new MultibodyTree, not a retrofit for RBTree. However, this joint is easily emulated now in RBTree using a sequence of two prismatic and one revolute joint, using two dummy massless bodies to serve as intermediate frames.

[jwnimmer-tri]

The same work-around applies for MultibodyPlant -- we'll close this until someone wants to advocate that the work-around is unsatisfactory.