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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 sea-level, say). For your convenience, these knot points are equidistant, i.e., pi+1 − pi 2 = d for all i. (The points give an arc-length 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.

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