FA-87908 / Inverse kinematics solvers / Member archive

Forearm Jacobian column uses the shoulder angle · case 03

Steps move the wrist in a direction that does not reduce the task error whenever q2 is non-zero.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [l1,l2,q1,q2,tx,ty,lam,maxstep], angles in degrees, maxstep in radians. Perform one damped least squares step dq = J^T (J J^T + lam^2 I)^-1 e with e = target - fk(q), scale dq so its Euclidean norm is at most maxstep, and return the updated [q1,q2] in degrees rounded to 4 places; a near-singular damped matrix (|det|<1e-12) returns "singular".

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
heavy damping	`[32.4429, 62.9881]`	`[31.2311, 68.0501]`	Failed

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