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Path Following

Path Following. Frenet Frame. Look ahead to point on curve. Auxiliary curves for ‘look-at’ and ‘up’. v = w x u. w = P’(u). u = P’(u) x P’’(u). P’’(u). Path Following. Frenet Frame - local coordinate system at a point on curve. Use w as direction vector Use v as up vector.

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Path Following

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  1. Path Following Frenet Frame Look ahead to point on curve Auxiliary curves for ‘look-at’ and ‘up’

  2. v = w x u w = P’(u) u = P’(u) x P’’(u) P’’(u) Path Following Frenet Frame - local coordinate system at a point on curve Use w as direction vector Use v as up vector

  3. Path Following - Y is ‘up’

  4. Path Following - curvature is ‘up’

  5. Path Following - bank into curvature

  6. Path Following - bank into curvature

  7. Curvature continuity Frenet Frame P”(u)=0 may not be defined may not be continuous

  8. y up • Up vector to stay upright, use vector: • perpendicular to tangent • in plane with global y-axis Look ahead to point on curve Using the tangent for direction can be too jerky Looking n points ahead can smooth out direction

  9. Define “look-at” vector using auxiliary curve

  10. Define “up” vector using auxiliary curve

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