FA-88284 / Inverse kinematics solvers / Member archive

Back-reach shoulder elevation uses the unsigned radius · case 04

Over-the-back solutions come out mirrored in front of the robot.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [d1,a2,a3,px,py,pz,reach,elbow]: base yaw t1, shoulder t2, elbow t3 with shoulder height d1. reach "front" uses t1=atan2(py,px) and r=hypot(px,py); "back" turns t1 by 180 degrees and uses -r. With s=pz-d1, cos t3=(r^2+s^2-a2^2-a3^2)/(2 a2 a3); beyond +/-(1+1e-12) is "unreachable", else clamp. elbow "up" takes sin t3<=0. t2=atan2(s,r)-atan2(a3 sin t3, a2+a3 cos t3). Angles in degrees wrapped to [-180,180), rounded 4.

Why this case matters

Inverse kinematics code turns task-space goals into joint commands; a wrong branch, sign, limit or update order sends a real arm to the wrong pose.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
back third quadrant	`[63.4349, 28.1439, -104.4775]`	`[63.4349, -103.6664, -104.4775]`	Failed

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