Degrees of freedom

Each degree of freedom (DoF) is one number you need to describe a pose.

• A hinge joint, like the elbow bending, has 1 DoF: one angle.
• A ball joint, like the shoulder, can turn three ways: 3 DoF. Simulators often model it as three hinges in a row.
• A free body in space has 6 DoF: three for position ($x, y, z$) and three for orientation (roll, pitch, yaw).

A humanoid’s total is the 6 DoF of its pelvis floating in the world plus one per hinge:

$$n_{\text{DoF}} = 6 + n_{\text{hinges}}$$

The pelvis’s 6 have no motor (see underactuation under actuator). The body can only move them by pushing on the floor.

How many is enough

A real human has well over 200 DoF if you count every joint in the spine, hands and feet. Simulated humanoids pick a subset. More DoF give more realistic motion but more for the policy to learn, and more physics work per step. The choice depends on the task: grappling needs a flexible trunk and grip, standing and striking need the legs, hips, shoulders and feet.

In this project

The muscular body has 83 actuated joints, built for grappling later. The simple body v2 has 37 motors covering the waist, neck, clavicles, shoulders, elbows, wrists, hips, knees, ankles and toes. A first simple body without toes or clavicles was rejected by the coach: its rigid foot balanced on its front edge like a plank.