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Unformatted text preview: pN +1 . We
let hi = (pi )3 , the z coordinate of the knot point; these are the heights of the knot points (above
sealevel, say). For your convenience, these knot points are equidistant, i.e., pi+1 − pi 2 = d for all
i. (The points give an arclength parametrization of the road.) We let si > 0 denote the (constant)
vehicle speed as it moves along road segment i, from pi to pi+1 , for i = 1, . . . , N , and sN +1 ≥ 0
denote the vehicle speed after it passes through knot point pN +1 . Our goal is to minimize the total
time to traverse the road, which we denote T .
We let fi ≥ 0 denote the total fuel burnt while traversing the ith segment. This fuel burn is turned
into an increase in vehicle energy given by ηfi , where η > 0 is a constant that includes the engine
eﬃciency and the energy content of the fuel. While traversing the ith road segment the vehicle is
subject to a drag force, given by CD s2 , where CD > 0 is the coeﬃcient of drag, which results in an
i
energy loss dCD s2 .
i
We...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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