Shortest Path for the Dubins Car

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0.25

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min

3

In 1957, Lester Eli Dubins proved that the shortest path between two

(x,y,θ)

coordinates for a forward-moving vehicle with a minimum turning radius

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min

is composed entirely of no more than three circular arcs of radius

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min

or straight lines.

In this Demonstration, the starting position of the blue car is green and its end position (the goal) is red. You can drag two locators, one for the red car's

(x,y)

position and the other for the red car's orientation

θ

. The sliders let you vary the minimum turning radius

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min

or move the blue car from the start to the goal.