FA-88335 / Inverse kinematics solvers / Member archive

Adaptive gain numerator uses the squared error norm · case 05

The step gain ignores how well the predicted motion aligns with the error.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [l1,l2,q1,q2,tx,ty]: one Jacobian-transpose step for a planar 2R arm with the error-optimal gain alpha = <e, J J^T e> / <J J^T e, J J^T e>, dq = alpha J^T e. When <J J^T e, J J^T e> < 1e-15 return ["stationary", q1, q2]. Otherwise return ["step", alpha (6 decimals), q1 and q2 updated in degrees (4 decimals)].

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
moderate error	`["step", 0.070435, 32.5652, 61.4771]`	`["step", 0.263207, 39.5859, 65.5199]`	Failed

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