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Dead reckoning math

Paul Grayson 2013-12-12

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Where am I?

α

Δr cos α

Δr sin α

Δr

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Rotation and translation

α

Δx = Δr cos α

Δy = Δr sin α

Δr

Δα

For each encoder tick:

Calibrate Δr and Δα

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More efficient approximation

Δx = r cos α = r⋅c Δy = r sin α = r⋅s

Δc = cos(α+Δα) − cos(α)

= cos(α) cos(Δα) − sin(α) sin(Δα) - cos(α)

≈ −Δα sin(α) = −Δα⋅s

Δs = sin(α+Δα) - sin(α)

= sin(α) cos(Δα) + cos(α) sin(Δα) - sin(α)

≈Δα cos(α) = +Δα⋅c

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No trig necessary!