Robotic Milking Arm: Teat-Tracking & Attachment

Sensing & Motion

Sensor noise 6 mm

Cow movement 10 mm

Arm speed 5

Attachment Cycle

Initializing…

Attached this cycle

0 / 4

Position uncertainty

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Success rate

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Cycles completed

How it works

A commercial milking robot cannot assume the udder sits still — the cow shifts weight, and a laser or ultrasonic sensor's single reading is noisy. The controller fuses repeated scans with a scalar recursive (Kalman) filter, updating a position estimate x̂ and its variance P after every measurement z:

K  = P / (P + R)          gain from current uncertainty P and sensor noise R
x̂' = x̂ + K·(z − x̂)       blend new measurement into the estimate
P' = (1 − K)·P             uncertainty shrinks with every scan

Once P drops below a lock threshold, the arm commits to x̂ as the attach target. The arm itself is a 2-link manipulator solved with closed-form inverse kinematics (law of cosines) rather than iterative search — given target distance d in the reach plane and link lengths L₁, L₂:

d  = √(r² + h²)                         r = horizontal offset, h = vertical offset
elbow angle    = acos((L1²+L2²−d²) / (2·L1·L2))
shoulder angle = atan2(h, r) + acos((L1²+d²−L2²) / (2·L1·d))

Sensor noise — the standard deviation R of each raw scan; higher noise needs more scans to converge, or leaves the final lock less certain.
Cow movement — the true teat position keeps drifting by a small sway while the estimate is being built and while the arm is en route, which is the main real-world source of attachment misses.
Arm speed — how fast the end effector chases the current estimate once it commits to move.
An attach only succeeds if the cup arrives within tolerance of the true, currently-swaying teat position — not just the last estimate — which is exactly the race real systems have to win.

Real-world relevance: automatic milking systems (e.g. Lely, DeLaval, GEA) use this laser-scan-plus-filter-plus-analytic-IK pipeline per teat, several times a day, per cow, unsupervised.

Teat cup / end effector Position estimate (Kalman) Unattached teat

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