Floating Base

A robot whose torso isn't bolted to the ground and instead has its own 6 degrees of freedom of free motion.

An arm bolted to a table has a fixed base — the base doesn't move, so joint angles alone describe its configuration. A humanoid's, quadruped's, or drone's torso (the base) isn't attached to the world, so on top of its joints, 6 more degrees of freedom are needed to describe the torso's own position and orientation in space — this is what's meant by a floating base. Modeling it usually means inserting a virtual “free joint” between the world and the torso: MuJoCo calls it a free joint, with position given by 7 numbers (3D position plus a 4D unit quaternion) and velocity given by 6 numbers (3D linear velocity plus 3D angular velocity). The difficulty is that these 6 degrees of freedom have no motor driving them directly — the torso can only be pushed indirectly through the feet's contact forces with the ground, which makes it underactuated. As a result, controlling a floating-base robot is inseparable from contact forces, friction cones, and state estimation, and the torso's pose has to be estimated from an IMU and leg odometry.

ExampleIn the Unitree G1 model from the MuJoCo Menagerie, the root body pelvis carries a freejoint named floating_base_joint, so the first 7 values of qpos are the pelvis position and quaternion, with the individual joint angles following after.

Also called

Free Joint, Free-Flyer Joint

Related

Generalized Coordinates · Underactuation · Centroidal Dynamics · Whole-Body Control · State Estimation · MJCF (MuJoCo XML Format)

Sources

MuJoCo Documentation - Overview (joint types, free joint)
MuJoCo Menagerie - unitree_g1/g1.xml
Underactuated Robotics (MIT) - Multi-Body Dynamics