[Madison]

After briefly glancing at the rules, it seems to me that you'd want to retrofit an existing vehicle to complete this challenge. They say that it's a course that could be accomodated by any commercial four wheel drive vehicle, so I'd start by acquiring one of those. Convert it to a gasoline/electric hybrid and throw in oodles of solar cells.

Install an onboard computer system that is capable of controlling the trucks acceleration, braking, and steering. Also interface it with the vehicles existing sensors so that mechanical problems can be detected.

For navigation, I'd expect that you'd need two-levels of systems to accomplish this task. The first, larger level would be global positioning system based and would be used to locate the vehicle in the most general sense. If the course is provided in advance, program the system to proceed through a series of waypoints along the route. If the course isn't provided in advance, or if only their waypoints are provided with no information about road conditions, turns, etc., it's much harder.
The second level of navigation would have to be used for local navigation. That is, you'd need a battery of sensors (maybe ground radar) that could detect and map out the surrounding terrain. The onboard computer would then need to extrapolate a route from that data based on where it is and where it needs to go, and then decide a way after accounting for ease to cross certain terrain versus time to cross other terrain.

Anyway, that's where I'd start. It's definitely not an easy undertaking and would require quite a bit of capital. But, if I were given the chance, I'd give it a shot.