Math & Kinematics
Gauss-Newton
Gauss-Newton is an iterative algorithm for nonlinear least-squares problems that approximates the Hessian using only first-order Jacobian information, solving a linearized normal-equation system at each step. It converges rapidly near solutions where residuals are small, and its damped variant, Levenberg-Marquardt, adds regularization for robustness. In robotics it is the standard solver core for bundle adjustment, factor-graph SLAM, camera calibration, and inverse kinematics.
Why it matters for physical AI
Most geometric estimation a robot performs, from calibrating its cameras to building maps, reduces to nonlinear least squares; Gauss-Newton-family solvers are the numerical engine making these computations fast enough for online use.
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Put these concepts to work on real hardware
Axol is a dual-arm robot built for physical AI — teleoperate it, collect demonstrations, and deploy learned policies out of the box.