FA-88232 / Inverse kinematics solvers / Member archive

Damping is applied outside the singular zone · case 02

Well-conditioned poses get damped because (1-w/w0)^2 is positive for w>w0.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [l1,l2,q1,q2,vx,vy,w0,lam0]: resolved-rate step for a planar 2R arm. Manipulability w=|l1 l2 sin q2|. Damping lam^2 = 0 when w>=w0, else lam0^2 (1-w/w0)^2. Solve (J^T J + lam^2 I) qdot = J^T v; if that matrix determinant is below 1e-12 return ["singular", w]. Return [status, qdot1, qdot2] in degrees per second, status "damped" when lam^2>0 else "exact".

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
negative elbow well conditioned	`["damped", 5.2116, -12.3508]`	`["exact", 9.4468, -19.8957]`	Failed

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