Calibration is regression through physics. The inverse dynamics τ = RNEA(q, q̇, q̈; θ) predicts joint torques from motion, given parameters θ — masses, centers of mass, inertias, friction coefficients. A recording gives you thousands of (motion, torque) pairs, so fitting θ is least squares: minimize the squared error between predicted and measured torque. The classical trick notes that rigid-body dynamics is LINEAR in the inertial parameters, which solves part of the problem in one shot — but it cannot absorb nonlinear friction models, actuator effects, or chosen subsets of parameters. The gradient route can: run the dynamics on a scalar type that carries derivatives (a dual number), and every partial ∂τ/∂θ comes out exact to machine precision — no hand-derived derivative code, no finite-difference truncation. Three details make it robust. Masses, inertias, and friction coefficients must stay positive, so we optimize their logarithms — positivity by construction, and the chain rule of that reparameterization rides along in the dual seed. Coulomb friction has a sign() discontinuity at rest, so we smooth it with tanh(q̇/w) and the model stays differentiable through every zero crossing. And not every parameter is identifiable from every recording: a joint spinning about a vertical axis gives gravity no leverage on its link's mass, so the fit reports a per-parameter sensitivity — near zero means this data does not constrain that parameter, and its fitted value is not physical truth. This is why the field settled here: gradient-based system identification beats black-box search by one to two orders of magnitude, and it is the working role of differentiable simulation in 2026 practice — calibrate the model, then trust everything you build on it.