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http://www4.cs.umanitoba.ca/~jacky/Teaching/Courses/74.795-LocalVision/ReadingList/fox97dynamic.pdf
The basic math for collision avoidance is ghastly to say the least,
and much of what has been written deals with much slower moving
robots, mainly because most ultrasonic rangefinders will only work to
around ten meters or so, lots of variables such as
air density/temperature/humidity/target size,velocity,direction of travel /aspect ratio and so on.
At the speeds you desire to achieve, well your onboard computer would
have less than a second to build a "mental" picture of its enviroment
then decided what action to take, an array of sensors might do it, just,
provided the vehicle did not skid to much when the brakes activate hard.
A scanning laser rangefinder... not easy to to build but a pair of them working together would give slightly better results.
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It all really depends upon your budget, in recent months big names have thrown a lot "sponsorship" to talented teams, the results.....
Well you can read all about it the DARPA website.