A.3.3.CC:5.4 - A velocity restriction leaves a configuration question open

For an ideal car rolling in a plane without lateral wheel slip, let (x,y) be the point halfway between the rear wheels and theta the chassis orientation. Let v be this point’s velocity component along the chassis’s forward direction. Then

xdot = v cos(theta), ydot = v sin(theta),

so sin(theta) xdot - cos(theta) ydot = 0. At theta = 0 the rear reference point has ydot = 0.

This equation constrains a velocity at a configuration. It does not impose a fixed y coordinate: a stationary car at another y satisfies the same velocity condition with v = 0. Whether a car can reach a selected parking position from its current one also depends on steering, obstacles and an allowed sequence of motions. Preserve those as a planning question instead of deleting the position from the configuration description.