Inertial Parameters

The set of values describing how heavy a rigid body is, where its center of mass sits, and how hard it is to rotate about each axis.

Inertial parameters describe the mass distribution of each rigid link in a robot, commonly given as 10 numbers: mass m (1 value), center-of-mass position c, or equivalently the first mass moment m·c (3 values), and the inertia tensor I (a 3×3 symmetric matrix with 6 independent entries, describing how hard the body is to rotate about each axis). Robot description files like URDF and MJCF store exactly these numbers in each link's inertial field. Kinematics only deals with geometry, but the moment dynamics enters the picture — gravity compensation, inverse dynamics, torque control, physics simulation — inertial parameters become essential. Values exported straight from CAD often diverge from the real hardware, since cables, screws, and other small parts get left out, so dynamic parameter identification is typically needed afterward, along with checks for physical consistency, such as positive mass and a positive-definite inertia tensor. Inaccurate inertial parameters are one source of the sim-to-real gap, and domain randomization commonly perturbs link mass to compensate.

ExampleA link's inertial tag in URDF includes mass, origin (center-of-mass position), and the six values ixx, ixy, ixz, iyy, iyz, izz of the inertia tensor. legged_gym provides an added_mass_range parameter that randomly adds or removes mass from the torso during training.

Also called

Mass Properties

Related

Mass Matrix · Inertia Tensor · Center of Mass (CoM) · Dynamic Parameter Identification · Unified Robot Description Format · Dynamics Randomization

Sources

Modern Robotics (Lynch & Park) preprint PDF, Ch. 4 URDF 与 Ch. 8 动力学 (Chinese)
Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification (Wensing, Kim, Slotine)
legged_gym: legged_robot_config.py