FA-88205 / Inverse kinematics solvers / Member archive

Self-motion term bypasses the null-space projector · case 05

Joint centering moves the end effector off the task.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [lengths(3), q(3 deg), target, qc(3 deg), k]: planar 3R arm, position task only. One step dq = J+ e + (I - J+ J) z, J+ = J^T (J J^T)^-1, e = target - fk(q), z = k*(qc-q) in radians. Return the updated q in degrees rounded to 4, or "singular" when |det(J J^T)|<1e-12.

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
unequal links	`[80.493, -203.2751, 169.3338]`	`[87.5837, -214.0176, 178.4237]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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