Controls
Readouts
The update is q ← q + J♯(q)(y* − φ(q)) with J♯ = (JᵀJ + ρI)⁻¹Jᵀ (Spring 2026 deck 03 p.56 with K = I, D = ρI). ρ = 0 is Gauss-Newton; ρ > 0 is damped Gauss-Newton (Levenberg–Marquardt methods adapt ρ); the gradient-descent option replaces J♯ by αJᵀ with Armijo. Ghost arms are the iterates; the chart is log₁₀ of the residual ‖φ(q) − y*‖ per iteration.
Default state: the unreachable target (0.75, 0.05) with plain Gauss-Newton. Press Run: the steps blow up as the arm straightens (det J → 0). Then raise ρ, or tick Armijo, and Run again: the arm settles on the boundary, pointing at the target.
One proposed joint-position change
Start at q⁽⁰⁾ = (30°, 45°). The target is y* = (0.50, 0.20) m. Angles in the calculation use radians.
Predict whether a step that reaches the target in the local model will also reach it when checked with forward kinematics.
| Tip position | x [m] | y [m] |
|---|---|---|
| Initial | ||
| Local prediction | ||
| FK check |
| Distance [m] | Cost [m²] | |
|---|---|---|
| Initial | ||
| Local prediction | ||
| FK check |
Distance = ‖tip − target‖.
Cost = ½ × distance².
The FK check evaluates the proposed joint angles in the robot's kinematic model. It is not a physical measurement or a motion simulation. No damping or line search is used.
Open the iterative solver from the same starting pose when the next sections introduce it.