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Unread 25-10-2013, 14:46
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Ether Ether is offline
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Geometry & Trig Quiz



Let XY be a standard (right-handed) Cartesian coordinate system fixed with respect to the field surface.

The center-of-geometry[1] of a 4-wheel crab-drive[2] robot is sitting at coordinates (X0,Y0) and its orientation (longitudinal axis) is "alpha" radians clockwise from the +Y axis.

All 4 wheels are turned to a steering angle "beta" radians clockwise from the longitudal axis of the robot.

The trackwidth of the robot is "W" and the wheelbase is "L".

Find the new steering angle "sigma" necessary to drive the robot in a straight line so that its center-of-geometry is located at point (X1,Y1).


Notes:

[1] "center of geometry" in this context means the center of the rectangle formed by the locations of the 4 wheels

[2] "crab drive" in this context means all 4 wheels are steered to the same angle and are driven at the same speed





Last edited by Ether : 25-10-2013 at 16:36.
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