Chapter 3: URDF - Describing Humanoid Robot Bodies

Week 5, Part 1 of 13 | Estimated Time: 5-7 hours

In this chapter, you will learn to describe humanoid robot bodies using URDF (Unified Robot Description Format). By the end, you will have created a complete humanoid robot model that can be visualized in RViz2 and simulated in Gazebo.

Learning Objectives

By the end of this chapter, you will be able to:

Understand the structure and syntax of URDF files
Define links with visual and collision geometries
Specify joints (revolute, prismatic, fixed, continuous)
Model a simplified humanoid robot (torso, arms, legs, head)
Visualize URDF models in RViz2 with joint controls
Add sensor frames (camera, IMU mounting points)

1. Introduction to Robot Description Formats

What is URDF?

URDF (Unified Robot Description Format) is an XML format for describing robot structures. It defines:

Links: The rigid bodies (torso, arms, legs, head)
Joints: How links connect and move relative to each other
Visual geometry: What the robot looks like
Collision geometry: Simplified shapes for physics simulation
Inertial properties: Mass and moments of inertia

URDF vs SDF

Feature	URDF	SDF
Primary Use	ROS robot descriptions	Gazebo simulation
Closed Loops	Not supported	Supported
Sensors	Limited (via Gazebo plugins)	Native support
World Description	Robot only	Robot + environment
Format	Single XML file	Multiple files, includes

For this textbook, we use URDF because:

It's the standard for ROS 2 robot descriptions
Works with robot_state_publisher
Can be converted to SDF for Gazebo simulation

The Link-Joint Tree

Figure 3.1: Link-joint tree structure of a humanoid robot

2. URDF Fundamentals

Basic URDF Structure

<?xml version="1.0"?>
<robot name="my_robot">
  <!-- Materials (colors) -->
  <material name="blue">
    <color rgba="0.0 0.0 0.8 1.0"/>
  </material>

  <!-- Links -->
  <link name="base_link">
    <visual>...</visual>
    <collision>...</collision>
    <inertial>...</inertial>
  </link>

  <!-- Joints -->
  <joint name="joint1" type="revolute">
    <parent link="base_link"/>
    <child link="child_link"/>
    <origin xyz="0 0 0.1" rpy="0 0 0"/>
    <axis xyz="0 0 1"/>
    <limit lower="-1.57" upper="1.57" effort="10" velocity="1.0"/>
  </joint>

</robot>

Link Elements

A link describes a rigid body:

<link name="torso_link">
  <!-- What the robot looks like (for visualization) -->
  <visual>
    <origin xyz="0 0 0.25" rpy="0 0 0"/>
    <geometry>
      <box size="0.3 0.2 0.5"/>
    </geometry>
    <material name="blue"/>
  </visual>

  <!-- Simplified shape for collision detection -->
  <collision>
    <origin xyz="0 0 0.25" rpy="0 0 0"/>
    <geometry>
      <box size="0.3 0.2 0.5"/>
    </geometry>
  </collision>

  <!-- Physical properties for dynamics -->
  <inertial>
    <origin xyz="0 0 0.25" rpy="0 0 0"/>
    <mass value="10.0"/>
    <inertia ixx="0.1" ixy="0" ixz="0" iyy="0.1" iyz="0" izz="0.05"/>
  </inertial>
</link>

Geometry Types

<!-- Box: rectangular prism -->
<geometry>
  <box size="0.3 0.2 0.5"/>  <!-- width, depth, height -->
</geometry>

<!-- Cylinder: circular cross-section -->
<geometry>
  <cylinder radius="0.05" length="0.3"/>
</geometry>

<!-- Sphere: ball shape -->
<geometry>
  <sphere radius="0.1"/>
</geometry>

<!-- Mesh: custom 3D model -->
<geometry>
  <mesh filename="package://humanoid_description/meshes/torso.stl" scale="1 1 1"/>
</geometry>

Joint Types

Figure 3.2: URDF joint types

<!-- Revolute: rotation with limits (most common) -->
<joint name="shoulder_pan" type="revolute">
  <parent link="torso_link"/>
  <child link="upper_arm_link"/>
  <origin xyz="0.15 0 0.4" rpy="0 0 0"/>
  <axis xyz="0 0 1"/>  <!-- Rotation axis -->
  <limit lower="-3.14" upper="3.14" effort="100" velocity="1.0"/>
</joint>

<!-- Continuous: unlimited rotation (wheels) -->
<joint name="wheel_joint" type="continuous">
  <parent link="base_link"/>
  <child link="wheel_link"/>
  <axis xyz="0 1 0"/>
</joint>

<!-- Prismatic: linear sliding -->
<joint name="gripper_slide" type="prismatic">
  <parent link="hand_link"/>
  <child link="finger_link"/>
  <axis xyz="1 0 0"/>
  <limit lower="0" upper="0.05" effort="10" velocity="0.1"/>
</joint>

<!-- Fixed: no relative motion -->
<joint name="camera_mount" type="fixed">
  <parent link="head_link"/>
  <child link="camera_link"/>
  <origin xyz="0.05 0 0.05" rpy="0 0 0"/>
</joint>

3. Building a Humanoid Torso and Arms

Let's build our humanoid robot step by step, starting with the torso and arms.

The Base and Torso

<?xml version="1.0"?>
<robot name="humanoid" xmlns:xacro="http://www.ros.org/wiki/xacro">

  <!-- Materials -->
  <material name="blue">
    <color rgba="0.2 0.2 0.8 1.0"/>
  </material>
  <material name="gray">
    <color rgba="0.5 0.5 0.5 1.0"/>
  </material>
  <material name="white">
    <color rgba="0.9 0.9 0.9 1.0"/>
  </material>

  <!-- Base Link (pelvis) -->
  <link name="base_link">
    <visual>
      <origin xyz="0 0 0" rpy="0 0 0"/>
      <geometry>
        <box size="0.25 0.3 0.15"/>
      </geometry>
      <material name="gray"/>
    </visual>
    <collision>
      <origin xyz="0 0 0" rpy="0 0 0"/>
      <geometry>
        <box size="0.25 0.3 0.15"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="5.0"/>
      <inertia ixx="0.05" ixy="0" ixz="0" iyy="0.05" iyz="0" izz="0.03"/>
    </inertial>
  </link>

  <!-- Torso Link -->
  <link name="torso_link">
    <visual>
      <origin xyz="0 0 0.2" rpy="0 0 0"/>
      <geometry>
        <box size="0.3 0.25 0.4"/>
      </geometry>
      <material name="blue"/>
    </visual>
    <collision>
      <origin xyz="0 0 0.2" rpy="0 0 0"/>
      <geometry>
        <box size="0.3 0.25 0.4"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0 0 0.2" rpy="0 0 0"/>
      <mass value="15.0"/>
      <inertia ixx="0.3" ixy="0" ixz="0" iyy="0.3" iyz="0" izz="0.15"/>
    </inertial>
  </link>

  <!-- Torso Joint (connects base to torso) -->
  <joint name="torso_joint" type="fixed">
    <parent link="base_link"/>
    <child link="torso_link"/>
    <origin xyz="0 0 0.075" rpy="0 0 0"/>
  </joint>

Adding Arms

  <!-- ========== LEFT ARM ========== -->

  <!-- Left Shoulder Link -->
  <link name="l_shoulder_link">
    <visual>
      <geometry>
        <sphere radius="0.05"/>
      </geometry>
      <material name="gray"/>
    </visual>
    <collision>
      <geometry>
        <sphere radius="0.05"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.5"/>
      <inertia ixx="0.001" ixy="0" ixz="0" iyy="0.001" iyz="0" izz="0.001"/>
    </inertial>
  </link>

  <!-- Left Shoulder Pan Joint -->
  <joint name="l_shoulder_pan_joint" type="revolute">
    <parent link="torso_link"/>
    <child link="l_shoulder_link"/>
    <origin xyz="0.17 0 0.35" rpy="0 0 0"/>
    <axis xyz="0 0 1"/>
    <limit lower="-2.0" upper="2.0" effort="50" velocity="2.0"/>
  </joint>

  <!-- Left Upper Arm Link -->
  <link name="l_upper_arm_link">
    <visual>
      <origin xyz="0.1 0 0" rpy="0 1.5708 0"/>
      <geometry>
        <cylinder radius="0.04" length="0.2"/>
      </geometry>
      <material name="blue"/>
    </visual>
    <collision>
      <origin xyz="0.1 0 0" rpy="0 1.5708 0"/>
      <geometry>
        <cylinder radius="0.04" length="0.2"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0.1 0 0" rpy="0 0 0"/>
      <mass value="2.0"/>
      <inertia ixx="0.01" ixy="0" ixz="0" iyy="0.01" iyz="0" izz="0.005"/>
    </inertial>
  </link>

  <!-- Left Shoulder Lift Joint -->
  <joint name="l_shoulder_lift_joint" type="revolute">
    <parent link="l_shoulder_link"/>
    <child link="l_upper_arm_link"/>
    <origin xyz="0 0 0" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
    <limit lower="-1.5" upper="1.5" effort="50" velocity="2.0"/>
  </joint>

  <!-- Left Forearm Link -->
  <link name="l_forearm_link">
    <visual>
      <origin xyz="0.1 0 0" rpy="0 1.5708 0"/>
      <geometry>
        <cylinder radius="0.035" length="0.2"/>
      </geometry>
      <material name="blue"/>
    </visual>
    <collision>
      <origin xyz="0.1 0 0" rpy="0 1.5708 0"/>
      <geometry>
        <cylinder radius="0.035" length="0.2"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0.1 0 0" rpy="0 0 0"/>
      <mass value="1.5"/>
      <inertia ixx="0.008" ixy="0" ixz="0" iyy="0.008" iyz="0" izz="0.004"/>
    </inertial>
  </link>

  <!-- Left Elbow Joint -->
  <joint name="l_elbow_joint" type="revolute">
    <parent link="l_upper_arm_link"/>
    <child link="l_forearm_link"/>
    <origin xyz="0.2 0 0" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
    <limit lower="0" upper="2.5" effort="30" velocity="2.0"/>
  </joint>

  <!-- Left Hand Link -->
  <link name="l_hand_link">
    <visual>
      <origin xyz="0.04 0 0" rpy="0 0 0"/>
      <geometry>
        <box size="0.08 0.06 0.03"/>
      </geometry>
      <material name="white"/>
    </visual>
    <collision>
      <origin xyz="0.04 0 0" rpy="0 0 0"/>
      <geometry>
        <box size="0.08 0.06 0.03"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0.04 0 0" rpy="0 0 0"/>
      <mass value="0.5"/>
      <inertia ixx="0.001" ixy="0" ixz="0" iyy="0.001" iyz="0" izz="0.001"/>
    </inertial>
  </link>

  <!-- Left Wrist Joint -->
  <joint name="l_wrist_joint" type="revolute">
    <parent link="l_forearm_link"/>
    <child link="l_hand_link"/>
    <origin xyz="0.2 0 0" rpy="0 0 0"/>
    <axis xyz="1 0 0"/>
    <limit lower="-1.5" upper="1.5" effort="10" velocity="2.0"/>
  </joint>

  <!-- Right arm is similar but mirrored (y-axis negated) -->

4. Building Bipedal Legs with Joint Limits

Leg Structure

Humanoid legs require careful attention to:

Joint limits: Prevent impossible poses
Joint axes: Match human biomechanics
Inertial properties: Affect balance in simulation

  <!-- ========== LEFT LEG ========== -->

  <!-- Left Hip Link -->
  <link name="l_hip_link">
    <visual>
      <geometry>
        <sphere radius="0.05"/>
      </geometry>
      <material name="gray"/>
    </visual>
    <collision>
      <geometry>
        <sphere radius="0.05"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="1.0"/>
      <inertia ixx="0.002" ixy="0" ixz="0" iyy="0.002" iyz="0" izz="0.002"/>
    </inertial>
  </link>

  <!-- Left Hip Yaw Joint -->
  <joint name="l_hip_yaw_joint" type="revolute">
    <parent link="base_link"/>
    <child link="l_hip_link"/>
    <origin xyz="0 0.1 -0.075" rpy="0 0 0"/>
    <axis xyz="0 0 1"/>
    <limit lower="-0.5" upper="0.5" effort="100" velocity="2.0"/>
  </joint>

  <!-- Left Thigh Link -->
  <link name="l_thigh_link">
    <visual>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.35"/>
      </geometry>
      <material name="blue"/>
    </visual>
    <collision>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <geometry>
        <cylinder radius="0.05" length="0.35"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <mass value="5.0"/>
      <inertia ixx="0.06" ixy="0" ixz="0" iyy="0.06" iyz="0" izz="0.02"/>
    </inertial>
  </link>

  <!-- Left Hip Pitch Joint -->
  <joint name="l_hip_pitch_joint" type="revolute">
    <parent link="l_hip_link"/>
    <child link="l_thigh_link"/>
    <origin xyz="0 0 0" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
    <limit lower="-1.5" upper="0.5" effort="150" velocity="2.0"/>
  </joint>

  <!-- Left Shin Link -->
  <link name="l_shin_link">
    <visual>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <geometry>
        <cylinder radius="0.04" length="0.35"/>
      </geometry>
      <material name="blue"/>
    </visual>
    <collision>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <geometry>
        <cylinder radius="0.04" length="0.35"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0 0 -0.175" rpy="0 0 0"/>
      <mass value="3.0"/>
      <inertia ixx="0.04" ixy="0" ixz="0" iyy="0.04" iyz="0" izz="0.01"/>
    </inertial>
  </link>

  <!-- Left Knee Joint -->
  <joint name="l_knee_joint" type="revolute">
    <parent link="l_thigh_link"/>
    <child link="l_shin_link"/>
    <origin xyz="0 0 -0.35" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
    <limit lower="0" upper="2.5" effort="100" velocity="2.0"/>
    <!-- Knee only bends backward! -->
  </joint>

  <!-- Left Foot Link -->
  <link name="l_foot_link">
    <visual>
      <origin xyz="0.05 0 -0.025" rpy="0 0 0"/>
      <geometry>
        <box size="0.2 0.1 0.05"/>
      </geometry>
      <material name="white"/>
    </visual>
    <collision>
      <origin xyz="0.05 0 -0.025" rpy="0 0 0"/>
      <geometry>
        <box size="0.2 0.1 0.05"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0.05 0 -0.025" rpy="0 0 0"/>
      <mass value="1.0"/>
      <inertia ixx="0.002" ixy="0" ixz="0" iyy="0.004" iyz="0" izz="0.005"/>
    </inertial>
  </link>

  <!-- Left Ankle Joint -->
  <joint name="l_ankle_joint" type="revolute">
    <parent link="l_shin_link"/>
    <child link="l_foot_link"/>
    <origin xyz="0 0 -0.35" rpy="0 0 0"/>
    <axis xyz="0 1 0"/>
    <limit lower="-0.8" upper="0.8" effort="50" velocity="2.0"/>
  </joint>

Joint Limit Guidelines for Humanoids

Joint	Typical Range	Notes
Hip Yaw	±30°	Internal/external rotation
Hip Pitch	-90° to +30°	Flexion/extension
Hip Roll	±30°	Abduction/adduction
Knee	0° to +150°	Only bends backward
Ankle Pitch	±45°	Dorsiflexion/plantarflexion
Ankle Roll	±30°	Inversion/eversion
Shoulder Pan	±120°	Horizontal swing
Shoulder Lift	±90°	Raise/lower
Elbow	0° to +150°	Only bends one way
Wrist	±90°	Rotation

5. Adding a Sensor Head

Head with Camera and IMU Frames

  <!-- ========== HEAD ========== -->

  <!-- Head Link -->
  <link name="head_link">
    <visual>
      <origin xyz="0 0 0.075" rpy="0 0 0"/>
      <geometry>
        <sphere radius="0.1"/>
      </geometry>
      <material name="white"/>
    </visual>
    <collision>
      <origin xyz="0 0 0.075" rpy="0 0 0"/>
      <geometry>
        <sphere radius="0.1"/>
      </geometry>
    </collision>
    <inertial>
      <origin xyz="0 0 0.075" rpy="0 0 0"/>
      <mass value="3.0"/>
      <inertia ixx="0.015" ixy="0" ixz="0" iyy="0.015" iyz="0" izz="0.015"/>
    </inertial>
  </link>

  <!-- Neck Joint -->
  <joint name="neck_pan_joint" type="revolute">
    <parent link="torso_link"/>
    <child link="head_link"/>
    <origin xyz="0 0 0.425" rpy="0 0 0"/>
    <axis xyz="0 0 1"/>
    <limit lower="-1.5" upper="1.5" effort="20" velocity="2.0"/>
  </joint>

  <!-- Camera Link -->
  <link name="camera_link">
    <visual>
      <geometry>
        <box size="0.03 0.08 0.02"/>
      </geometry>
      <material name="gray"/>
    </visual>
    <collision>
      <geometry>
        <box size="0.03 0.08 0.02"/>
      </geometry>
    </collision>
    <inertial>
      <mass value="0.1"/>
      <inertia ixx="0.0001" ixy="0" ixz="0" iyy="0.0001" iyz="0" izz="0.0001"/>
    </inertial>
  </link>

  <!-- Camera Mount (fixed) -->
  <joint name="camera_joint" type="fixed">
    <parent link="head_link"/>
    <child link="camera_link"/>
    <origin xyz="0.08 0 0.1" rpy="0 0 0"/>
  </joint>

  <!-- Camera Optical Frame (for image data) -->
  <link name="camera_optical_link"/>

  <joint name="camera_optical_joint" type="fixed">
    <parent link="camera_link"/>
    <child link="camera_optical_link"/>
    <!-- Rotate to match ROS optical frame convention (Z forward, X right, Y down) -->
    <origin xyz="0 0 0" rpy="-1.5708 0 -1.5708"/>
  </joint>

  <!-- IMU Link -->
  <link name="imu_link">
    <visual>
      <geometry>
        <box size="0.02 0.02 0.01"/>
      </geometry>
      <material name="gray"/>
    </visual>
    <inertial>
      <mass value="0.05"/>
      <inertia ixx="0.00001" ixy="0" ixz="0" iyy="0.00001" iyz="0" izz="0.00001"/>
    </inertial>
  </link>

  <!-- IMU Mount (in torso) -->
  <joint name="imu_joint" type="fixed">
    <parent link="torso_link"/>
    <child link="imu_link"/>
    <origin xyz="0 0 0.2" rpy="0 0 0"/>
  </joint>

</robot>

6. Visualization with RViz2

Launch File for Visualization

#!/usr/bin/env python3
"""
Physical AI & Humanoid Robotics Textbook
Module 1, Chapter 3: URDF Visualization Launch
"""

import os
from launch import LaunchDescription
from launch_ros.actions import Node
from launch.substitutions import Command
from ament_index_python.packages import get_package_share_directory


def generate_launch_description():
    # Get URDF file path
    urdf_file = os.path.join(
        get_package_share_directory('humanoid_description'),
        'urdf',
        'humanoid.urdf'
    )

    # Read URDF content
    with open(urdf_file, 'r') as f:
        robot_description = f.read()

    # Robot State Publisher
    robot_state_publisher = Node(
        package='robot_state_publisher',
        executable='robot_state_publisher',
        parameters=[{'robot_description': robot_description}],
        output='screen'
    )

    # Joint State Publisher GUI
    joint_state_publisher_gui = Node(
        package='joint_state_publisher_gui',
        executable='joint_state_publisher_gui',
        name='joint_state_publisher_gui'
    )

    # RViz2
    rviz_config = os.path.join(
        get_package_share_directory('humanoid_description'),
        'rviz',
        'display.rviz'
    )

    rviz = Node(
        package='rviz2',
        executable='rviz2',
        arguments=['-d', rviz_config],
        output='screen'
    )

    return LaunchDescription([
        robot_state_publisher,
        joint_state_publisher_gui,
        rviz
    ])

Running the Visualization

# Install dependencies
sudo apt install ros-jazzy-joint-state-publisher-gui ros-jazzy-robot-state-publisher

# Launch visualization
ros2 launch humanoid_description display.launch.py

You should see:

RViz2 window with the humanoid robot model
Joint State Publisher GUI with sliders for each joint
Moving the sliders updates the robot pose in real-time

7. URDF Best Practices for Simulation

Inertial Properties

For stable physics simulation:

Always include <inertial> elements - Required for Gazebo
Use realistic mass values - Affects dynamics
Calculate moments of inertia - Use formulas or estimation tools

# Calculating inertia for a box (Python)
def box_inertia(mass, x, y, z):
    """Calculate inertia tensor for a box."""
    ixx = (1/12) * mass * (y**2 + z**2)
    iyy = (1/12) * mass * (x**2 + z**2)
    izz = (1/12) * mass * (x**2 + y**2)
    return ixx, iyy, izz

# Example: 10 kg box, 0.3 x 0.2 x 0.5 meters
ixx, iyy, izz = box_inertia(10.0, 0.3, 0.2, 0.5)
# ixx=0.242, iyy=0.283, izz=0.108

Collision Geometry

Use simpler shapes than visual geometry
Convex hulls are faster than meshes
Box > Cylinder > Sphere > Mesh (in computational cost)

<!-- Visual: detailed mesh -->
<visual>
  <geometry>
    <mesh filename="package://humanoid/meshes/hand_detailed.stl"/>
  </geometry>
</visual>

<!-- Collision: simple box approximation -->
<collision>
  <geometry>
    <box size="0.08 0.06 0.03"/>
  </geometry>
</collision>

Joint Configuration

<!-- Good: explicit limits and dynamics -->
<joint name="elbow_joint" type="revolute">
  <parent link="upper_arm"/>
  <child link="forearm"/>
  <origin xyz="0.25 0 0" rpy="0 0 0"/>
  <axis xyz="0 1 0"/>
  <limit lower="0" upper="2.5" effort="30" velocity="2.0"/>
  <dynamics damping="0.5" friction="0.1"/>
</joint>

8. Common Errors and Solutions

Error: "Link has no collision geometry"

Cause: Missing collision element in link.

Solution: Add collision geometry to all links:

<link name="my_link">
  <visual>...</visual>
  <collision>  <!-- Add this! -->
    <geometry>
      <box size="0.1 0.1 0.1"/>
    </geometry>
  </collision>
</link>

Error: "Inertia matrix not positive definite"

Cause: Invalid inertia values (often zeros or negatives).

Solution: Use realistic inertia values:

<inertial>
  <mass value="1.0"/>
  <inertia ixx="0.01" ixy="0" ixz="0" iyy="0.01" iyz="0" izz="0.01"/>
</inertial>

Error: "Robot model not showing in RViz"

Cause: Fixed frame not set or TF not being published.

Solution:

Set "Fixed Frame" to base_link in RViz
Ensure robot_state_publisher is running
Check URDF is valid: check_urdf humanoid.urdf

Error: "Joint moves in wrong direction"

Cause: Incorrect axis definition.

Solution: Verify axis matches intended rotation:

<axis xyz="0 1 0"/>  <!-- Rotates around Y axis -->

Error: "Model explodes in Gazebo"

Cause: Unrealistic mass/inertia or missing collision geometry.

Solution:

Verify all links have proper inertial elements
Check joint limits are set
Add damping to joints
Use smaller simulation timesteps

9. Exercises

Exercise 3.1: Build a Simple Robot Arm (Difficulty: Basic)

Objective: Create a 3-DOF robot arm URDF.

Instructions:

Create a new URDF file robot_arm.urdf
Define links: base, link1, link2, link3, end_effector
Use revolute joints between links
Add visual geometry (cylinders for links)
Visualize in RViz2

Expected Outcome: 3-joint arm visible in RViz with working joint controls.

Exercise 3.2: Add Sensor Frames (Difficulty: Intermediate)

Objective: Add LiDAR and depth camera frames to the humanoid.

Instructions:

Add a LiDAR link mounted on the torso
Add a depth camera link on the head (beside the existing camera)
Use fixed joints for mounting
Define appropriate optical frames
Verify frame relationships with ros2 run tf2_tools view_frames

Expected Outcome: TF tree shows sensor frames correctly attached.

Exercise 3.3: Complete Humanoid with 10+ Links (Difficulty: Advanced)

Objective: Complete the humanoid URDF with both arms and legs.

Instructions:

Start with the torso and head from Section 3
Add left arm (shoulder, upper arm, forearm, hand)
Add right arm (mirrored from left)
Add left leg (hip, thigh, shin, foot)
Add right leg (mirrored from left)
Set realistic joint limits
Add proper inertial properties
Test in RViz2 and verify all joints work

Expected Outcome: Full humanoid with 15+ links and 12+ movable joints.

Summary

In this chapter, you learned:

URDF is an XML format for describing robot structures with links and joints
Links define rigid bodies with visual, collision, and inertial properties
Joints connect links and define their relative motion (revolute, prismatic, fixed, continuous)
Humanoid robots require careful attention to joint limits matching human biomechanics
Sensor frames are attached using fixed joints with proper optical frame conventions
RViz2 with robot_state_publisher and joint_state_publisher_gui allows interactive visualization
Best practices for simulation include realistic inertia, simple collision geometry, and joint dynamics

Key Terms

Term	Definition
URDF	Unified Robot Description Format - XML format for robot structure
Link	A rigid body in the robot kinematic tree
Joint	Connection between two links defining their relative motion
Visual Geometry	3D shape used for rendering the robot
Collision Geometry	Simplified shape for physics collision detection
Inertial	Mass and moment of inertia properties for dynamics
TF	Transform library - tracks coordinate frame relationships
robot_state_publisher	Node that publishes TF transforms from joint states

What's Next

In Chapter 4, you will learn to bridge AI systems with ROS 2 control. You will create custom messages, build action servers for complex behaviors, and implement a command interpreter that prepares you for the VLA systems in Module 4.

Physical AI & Humanoid Robotics Textbook - Module 1, Chapter 3 ROS 2 Jazzy | Ubuntu 22.04 | Python 3.10+

Learning Objectives​

1. Introduction to Robot Description Formats​

What is URDF?​

URDF vs SDF​

The Link-Joint Tree​

2. URDF Fundamentals​

Basic URDF Structure​

Link Elements​

Geometry Types​

Joint Types​

3. Building a Humanoid Torso and Arms​

The Base and Torso​

Adding Arms​

4. Building Bipedal Legs with Joint Limits​

Leg Structure​

Joint Limit Guidelines for Humanoids​

5. Adding a Sensor Head​

Head with Camera and IMU Frames​

6. Visualization with RViz2​

Launch File for Visualization​

Running the Visualization​

7. URDF Best Practices for Simulation​

Inertial Properties​

Collision Geometry​

Joint Configuration​

8. Common Errors and Solutions​

Error: "Link has no collision geometry"​

Error: "Inertia matrix not positive definite"​

Error: "Robot model not showing in RViz"​

Error: "Joint moves in wrong direction"​

Error: "Model explodes in Gazebo"​

9. Exercises​

Exercise 3.1: Build a Simple Robot Arm (Difficulty: Basic)​

Exercise 3.2: Add Sensor Frames (Difficulty: Intermediate)​

Exercise 3.3: Complete Humanoid with 10+ Links (Difficulty: Advanced)​

Summary​

Key Terms​

What's Next​

Learning Objectives

1. Introduction to Robot Description Formats

What is URDF?

URDF vs SDF

The Link-Joint Tree

2. URDF Fundamentals

Basic URDF Structure

Link Elements

Geometry Types

Joint Types

3. Building a Humanoid Torso and Arms

The Base and Torso

Adding Arms

4. Building Bipedal Legs with Joint Limits

Leg Structure

Joint Limit Guidelines for Humanoids

5. Adding a Sensor Head

Head with Camera and IMU Frames

6. Visualization with RViz2

Launch File for Visualization

Running the Visualization

7. URDF Best Practices for Simulation

Inertial Properties

Collision Geometry

Joint Configuration

8. Common Errors and Solutions

Error: "Link has no collision geometry"

Error: "Inertia matrix not positive definite"

Error: "Robot model not showing in RViz"

Error: "Joint moves in wrong direction"

Error: "Model explodes in Gazebo"

9. Exercises

Exercise 3.1: Build a Simple Robot Arm (Difficulty: Basic)

Exercise 3.2: Add Sensor Frames (Difficulty: Intermediate)

Exercise 3.3: Complete Humanoid with 10+ Links (Difficulty: Advanced)

Summary

Key Terms

What's Next