I am an engineer working on a steering system with many wheels. In order to steer correctly, the wheels must all be oriented perpendicular to a single point. So if the wheels were in a tight turn, their configuration might look something like this:
With the red dot representing the center steer point that all the wheels are perpendicular to. I track this point as the wheels make turns to ensure that they stay in sync, using a cartesian coordinate system. As the wheels are turned straighter, the steer point moves away from the wheels:
However, there is a problem when transitioning from a right turn to a left turn and vice versa. As the wheels approach parallel in such a turn, the steer point moves away from the wheels an infinite distance until the wheels are parallel, at which time there is not a valid steer point. As the wheels pass through parallel, the steer point jumps from infinity in one direction to the infinity 180° in the other direction.
This problem makes it impossible to smoothly track the steer point in the cartesian coordinate system. Is there a transform that I can use to another coordinate system that will allow me to track this steer point without the discontinuity?
Are there other tags I should use on this question? I'm not quite sure what branch of mathematics would be most applicable.