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Fix ackermann odometry equation
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christophfroehlich committed Dec 30, 2023
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4 changes: 2 additions & 2 deletions steering_controllers_library/doc/userdoc.rst
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Expand Up @@ -213,12 +213,12 @@ The calculation of :math:`\phi` from two angle measurements of the steering axle
If there is no slip and the measurements are ideal,

.. math::
\phi = \arctan\left(\frac{l + w_f/2 \tan(\phi_{left})}{\tan(\phi_{left})}\right) = \arctan\left(\frac{l - w_f/2 \tan(\phi_{right})}{\tan(\phi_{right})}\right)
\phi = \arctan\left(\frac{l\tan(\phi_{left})}{l + w_f/2 \tan(\phi_{left})}\right) = \arctan\left(\frac{\tan(l\phi_{right})}{l - w_f/2 \tan(\phi_{right})}\right)
holds. But to get a more robust solution, we take the average of both , i.e.,

.. math::
\phi = 0.5 \left(\arctan\left(\frac{l + w_f/2 \tan(\phi_{left})}{\tan(\phi_{left})}\right) + \arctan\left(\frac{l - w_f/2 \tan(\phi_{right})}{\tan(\phi_{right})}\right)\right).
\phi = 0.5 \left(\arctan\left(\frac{l\tan(\phi_{left})}{l + w_f/2 \tan(\phi_{left})}\right) + \arctan\left(\frac{\tan(l\phi_{right})}{l - w_f/2 \tan(\phi_{right})}\right)\right).
Ackermann steering with traction
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