Body Construction Logic and Hierarchical

This section provides a clear and structured overview of how bodies are organized in MuJoCo, and how their child elements (joint, geom, site, camera, light) relate to them. No element attributes are explained here—only conceptual structure and hierarchy.

---

1. Body: The Fundamental Spatial Unit in MuJoCo

• Each body represents a local coordinate frame with a position (pos) and orientation (quat).

• The entire scene forms a tree starting from worldbody, where each body is nested inside its parent.

• All child elements define their transforms relative to the coordinate system of their parent body.

In short: 👉 MuJoCo scenes are built as a tree of bodies, each serving as a spatial reference node.

---

2. Types of Child Elements Under a Body

A body may contain several types of child elements:

Element	Structural Role
joint	Defines motion between the body and its parent
geom	Defines physical/visual geometry
site	A reference point used for sensing, targeting, or marking
camera	A view frame attached to the body
light	A light source attached to the body

---

3. Relationship Between Body and Joint

3.1 Joint connects a body to its parent

• Every body (except worldbody) may contain 0 or more joints.

• A joint specifies the degree of freedom (DOF) with respect to the parent body.

3.2 Joint defines body mobility

• A body with joints is movable.

• A body without joints is fixed relative to its parent.

3.3 Multiple joints

• Multiple joints combine in sequence, forming compound motion.

---

4. Relationship Between Body and Geom

4.1 Geom attaches geometry to a body

• Each geom is positioned and oriented relative to the parent body.

• A body may have multiple geoms to define:

  • Collision geometry

  • Visual mesh

  • Mass and inertia contribution

4.2 Complex shapes

A single link can be represented by multiple geoms combined.

---

5. Relationship Between Body and Site

5.1 Site is a reference point

• A site carries no mass and has no physical role.

• Common uses include:

  • End-effector targets

  • Task/goal markers

  • Sensor mounting points

  • IK target frames

5.2 Site transforms with the body

Its world transform = body transform × site local transform.

---

6. Relationship Between Body and Camera

6.1 Camera is defined in the body’s frame

• A camera’s position and orientation are based on the body it is attached to.

• This enables:

  • Head-mounted cameras

  • Hand-eye cameras

  • Vehicle onboard cameras

6.2 Cameras do not affect physics

They only define viewpoints.

---

7. Relationship Between Body and Light

7.1 Light behaves similarly to a camera

• Attached to a body and moves with it.

• Useful for:

  • Robot-mounted flashlights

  • Vehicle headlights

  • Moving scene lights

7.2 Light affects rendering only

It does not influence physical simulation.

---

8. Example: Body Hierarchy Structure

worldbody
└── body (A)
    ├── joint (A_joint)
    ├── geom (A_geom1)
    ├── geom (A_geom2)
    ├── site (A_site)
    ├── camera (A_camera)
    ├── light (A_light)
    └── body (B)
        ├── joint (B_joint)
        ├── geom (B_geom)
        └── body (C)

Summary:

• Bodies form the tree structure

• Joints define motion relationships

• Geoms / sites / cameras / lights are spatial attachments

9. Summary

MuJoCo uses bodies as the core hierarchical unit of a scene. Each body defines a local coordinate system and may contain joints, geoms, sites, cameras, and lights. Bodies connect to parent bodies through joints to form the kinematic tree, while the other child elements attach spatially to the body to define geometry, reference frames, vision, and lighting. This architecture forms a complete structure for physical simulation, rendering, and observation.