Math & Kinematics

Inertia Tensor

The inertia tensor is a symmetric 3x3 matrix describing how a rigid body's mass is distributed about a reference point, determining the torque required for angular acceleration about any axis. Its eigenvectors define principal axes, and accurate link inertia values, specified in robot description formats like URDF, are required for dynamics computations, feedforward control, and physically plausible simulation.

Why it matters for physical AI

Wrong inertia parameters corrupt simulated dynamics and torque-level controllers alike, making inertial identification a quiet but critical ingredient of sim-to-real transfer and dynamic whole-body control.