Skip to main content

Chapter 2.3: Physics Simulation

Learning Objectives​

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

  • Configure physics engine parameters for realistic simulation
  • Understand collision detection and response mechanisms
  • Optimize simulation performance and stability
  • Model complex physical interactions for humanoid robots
  • Troubleshoot common physics simulation issues

Introduction​

Physics simulation is the cornerstone of realistic robot simulation, enabling accurate modeling of forces, collisions, and movements that occur in the real world. For humanoid robots, which must interact with complex environments and perform dynamic movements, accurate physics simulation is crucial for developing and testing control algorithms before deployment on real hardware.

In this chapter, we'll explore the physics simulation capabilities of Gazebo, focusing on how to configure and optimize physics parameters for humanoid robotics applications. We'll cover collision detection, contact modeling, and techniques for achieving both realistic behavior and computational efficiency.

Physics Engine Fundamentals​

Understanding the Physics Pipeline​

Gazebo's physics simulation follows this pipeline:

  1. Collision Detection: Identifying when objects come into contact
  2. Contact Processing: Calculating forces and torques at contact points
  3. Integration: Updating positions and velocities based on applied forces
  4. Constraint Solving: Ensuring joint constraints and other restrictions are maintained

Time Stepping and Real-time Performance​

The physics simulation operates in discrete time steps:

<physics type="ode">
  <!-- Maximum simulation step size in seconds -->
  <max_step_size>0.001</max_step_size>
  
  <!-- Desired real-time factor (1.0 = real-time, >1.0 = faster than real-time) -->
  <real_time_factor>1.0</real_time_factor>
  
  <!-- Update rate in Hz (1/dt) -->
  <real_time_update_rate>1000.0</real_time_update_rate>
</physics>

Key Considerations:

  • Smaller step sizes increase accuracy but require more computation
  • Real-time factor affects how fast the simulation runs relative to wall-clock time
  • Update rate should match your control loop frequency for consistency

Collision Detection and Geometry​

Collision Geometry Types​

Gazebo supports various collision geometries, each with trade-offs:

<link name="collision_example">
  <!-- Simple shapes (fastest) -->
  <collision name="box_collision">
    <geometry>
      <box>
        <size>1 1 1</size>
      </box>
    </geometry>
  </collision>
  
  <!-- Mesh-based collisions (most accurate but slowest) -->
  <collision name="mesh_collision">
    <geometry>
      <mesh>
        <uri>package://my_robot/meshes/complex_shape.dae</uri>
      </mesh>
    </geometry>
  </collision>
  
  <!-- Convex hull approximation (balance of accuracy and performance) -->
  <collision name="convex_collision">
    <geometry>
      <mesh>
        <uri>package://my_robot/meshes/convex_hull.dae</uri>
      </mesh>
    </geometry>
  </collision>
</link>

Multiple Collision Elements​

For complex shapes, use multiple collision elements:

<link name="complex_link">
  <!-- Approximate with multiple simple shapes -->
  <collision name="main_collision">
    <geometry>
      <cylinder>
        <radius>0.1</radius>
        <length>0.5</length>
      </cylinder>
    </geometry>
  </collision>
  
  <collision name="top_collision">
    <geometry>
      <sphere>
        <radius>0.1</radius>
      </sphere>
    </geometry>
    <pose>0 0 0.3 0 0 0</pose>
  </collision>
  
  <collision name="bottom_collision">
    <geometry>
      <sphere>
        <radius>0.1</radius>
      </sphere>
    </geometry>
    <pose>0 0 -0.3 0 0 0</pose>
  </collision>
</link>

Contact Modeling​

Friction Parameters​

Friction is crucial for realistic humanoid locomotion:

<collision name="foot_collision">
  <geometry>
    <box>
      <size>0.2 0.1 0.05</size>
    </box>
  </geometry>
  <surface>
    <friction>
      <ode>
        <!-- Coefficient of friction in primary direction -->
        <mu>1.0</mu>
        <!-- Coefficient of friction in secondary direction -->
        <mu2>1.0</mu2>
        <!-- Direction of the friction pyramide -->
        <fdir1>1 0 0</fdir1>
      </ode>
    </friction>
  </surface>
</collision>

Bounce and Restitution​

Model energy loss during impacts:

<collision name="ball_collision">
  <geometry>
    <sphere>
      <radius>0.1</radius>
    </sphere>
  </geometry>
  <surface>
    <bounce>
      <!-- Coefficient of restitution (0 = no bounce, 1 = perfect bounce) -->
      <restitution_coefficient>0.8</restitution_coefficient>
      <!-- Velocity threshold below which objects don't bounce -->
      <threshold>100000</threshold>
    </bounce>
  </surface>
</collision>

Physics Engine Configuration​

ODE (Open Dynamics Engine) Parameters​

ODE is the default physics engine in Gazebo:

<physics type="ode">
  <max_step_size>0.001</max_step_size>
  <real_time_factor>1.0</real_time_factor>
  <real_time_update_rate>1000.0</real_time_update_rate>
  <gravity>0 0 -9.8</gravity>
  
  <ode>
    <!-- Solver parameters -->
    <solver>
      <!-- Type of solver (quick, world, dantzig, pgs) -->
      <type>quick</type>
      <!-- Number of iterations for the solver -->
      <iters>50</iters>
      <!-- Successive over-relaxation parameter -->
      <sor>1.3</sor>
    </solver>
    
    <!-- Constraint parameters -->
    <constraints>
      <!-- Constraint Force Mixing parameter -->
      <cfm>0.0</cfm>
      <!-- Error Reduction Parameter -->
      <erp>0.2</erp>
      <!-- Maximum correcting velocity for contacts -->
      <contact_max_correcting_vel>100.0</contact_max_correcting_vel>
      <!-- Contact surface layer depth -->
      <contact_surface_layer>0.001</contact_surface_layer>
    </constraints>
  </ode>
</physics>

Understanding Key Parameters​

ERP (Error Reduction Parameter)​

  • Controls how quickly constraint errors are corrected
  • Range: 0.0 to 1.0
  • Higher values: Faster error correction but potential instability
  • Lower values: Slower error correction but more stable

CFM (Constraint Force Mixing)​

  • Adds softness to constraints
  • Range: 0.0 to infinity
  • Higher values: Softer constraints, more compliant behavior
  • Lower values: Stiffer constraints, more rigid behavior

Optimizing Physics for Humanoid Robots​

Balancing Accuracy and Performance​

For humanoid robots, consider these trade-offs:

<!-- Example: Physics configuration optimized for humanoid simulation -->
<physics type="ode">
  <max_step_size>0.001</max_step_size>  <!-- Small steps for stability -->
  <real_time_factor>1.0</real_time_factor>  <!-- Real-time simulation -->
  <real_time_update_rate>1000.0</real_time_update_rate>  <!-- 1kHz update rate -->
  
  <ode>
    <solver>
      <type>quick</type>
      <iters>100</iters>  <!-- More iterations for complex humanoid -->
      <sor>1.3</sor>
    </solver>
    
    <constraints>
      <cfm>1e-5</cfm>  <!-- Stiff constraints for stable joints -->
      <erp>0.9</erp>  <!-- Fast error correction for joint constraints -->
      <contact_max_correcting_vel>10.0</contact_max_correcting_vel>
      <contact_surface_layer>0.001</contact_surface_layer>
    </constraints>
  </ode>
</physics>

Humanoid-Specific Considerations​

Balance and Stability​

Humanoid robots require special attention to balance:

<!-- Enhanced foot collision for better balance -->
<collision name="left_foot_collision">
  <geometry>
    <!-- Use a box instead of complex mesh for better contact stability -->
    <box>
      <size>0.18 0.08 0.01</size>  <!-- Slightly larger than actual foot -->
    </box>
  </geometry>
  <surface>
    <friction>
      <ode>
        <mu>0.8</mu>  <!-- High friction for stable standing -->
        <mu2>0.8</mu2>
      </ode>
    </friction>
    <contact>
      <ode>
        <!-- Increase contact stiffness for better foot-ground interaction -->
        <soft_cfm>0.0001</soft_cfm>
        <soft_erp>0.8</soft_erp>
        <kp>1e5</kp>  <!-- High position constraint stiffness -->
        <kd>100</kd>  <!-- Damping coefficient -->
      </ode>
    </contact>
  </surface>
</collision>

Joint Configuration for Realistic Movement​

Configure joints to match human biomechanics:

<!-- Knee joint with realistic limits -->
<joint name="left_knee_joint" type="revolute">
  <parent link="left_upper_leg"/>
  <child link="left_lower_leg"/>
  <origin xyz="0 0 -0.4" rpy="0 0 0"/>
  <axis xyz="1 0 0"/>  <!-- Knee flexes in x-axis -->
  <!-- Human knee can't hyperextend significantly -->
  <limit lower="0.0" upper="2.356" effort="100" velocity="3"/>
  <!-- 2.356 radians = 135 degrees, realistic for human knee -->
</joint>

<!-- Ankle joint for balance -->
<joint name="left_ankle_joint" type="revolute">
  <parent link="left_lower_leg"/>
  <child link="left_foot"/>
  <origin xyz="0 0 -0.4" rpy="0 0 0"/>
  <axis xyz="0 1 0"/>  <!-- Ankle pitches in y-axis -->
  <limit lower="-0.5" upper="0.5" effort="50" velocity="2"/>
  <!-- Limited range for realistic ankle movement -->
</joint>

Advanced Physics Features​

Custom Contact Materials​

Define custom material properties for specific interactions:

<!-- Define a custom material -->
<material name="rubber">
  <script>
    <uri>file://media/materials/scripts/gazebo.material</uri>
    <name>Gazebo/Rubber</name>
  </script>
</material>

<!-- Apply custom physics properties -->
<gazebo reference="left_foot">
  <surface>
    <friction>
      <ode>
        <mu>1.2</mu>  <!-- High friction for rubber-like grip -->
        <mu2>1.2</mu2>
      </ode>
    </friction>
    <bounce>
      <restitution_coefficient>0.1</restitution_coefficient>  <!-- Low bounce -->
    </bounce>
  </surface>
</gazebo>

Different parts of the robot may need different physics treatment:

<!-- Head with low mass for safety -->
<gazebo reference="head">
  <self_collide>false</self_collide>  <!-- Prevent head from colliding with itself -->
  <gravity>true</gravity>
  <max_contacts>10</max_contacts>  <!-- Limit contact points -->
</gazebo>

<!-- Arms with appropriate mass and inertia -->
<gazebo reference="left_upper_arm">
  <implicit_spring_damper>true</implicit_spring_damper>
</gazebo>

Performance Optimization Techniques​

Simulation Quality vs. Speed Trade-offs​

For different simulation purposes, adjust parameters accordingly:

<!-- For fast testing and debugging -->
<physics type="ode">
  <max_step_size>0.01</max_step_size>  <!-- Larger steps for speed -->
  <real_time_update_rate>100.0</real_time_update_rate>  <!-- Lower update rate -->
  <ode>
    <solver>
      <iters>20</iters>  <!-- Fewer iterations -->
    </solver>
    <constraints>
      <contact_surface_layer>0.01</contact_surface_layer>  <!-- Larger surface layer -->
    </constraints>
  </ode>
</physics>

<!-- For accurate validation -->
<physics type="ode">
  <max_step_size>0.001</max_step_size>  <!-- Small steps for accuracy -->
  <real_time_update_rate>1000.0</real_time_update_rate>  <!-- High update rate -->
  <ode>
    <solver>
      <iters>100</iters>  <!-- More iterations -->
    </solver>
    <constraints>
      <contact_surface_layer>0.001</contact_surface_layer>  <!-- Smaller surface layer -->
    </constraints>
  </ode>
</physics>

Reducing Computational Load​

  1. Simplify collision geometry: Use simple shapes instead of complex meshes where possible
  2. Reduce update rate: Lower the physics update rate if your application allows
  3. Limit contact points: Use max_contacts to limit the number of contact points per collision
  4. Use appropriate solver iterations: Balance between stability and performance

Troubleshooting Physics Issues​

Common Problems and Solutions​

Robot Falling Through Ground​

<!-- Solution: Check collision geometry and surface parameters -->
<collision name="ground_collision">
  <geometry>
    <plane>
      <normal>0 0 1</normal>
    </plane>
  </geometry>
</collision>

<!-- Ensure the ground has appropriate physical properties -->
<gazebo reference="ground_plane">
  <static>true</static>  <!-- Make ground immovable -->
  <mu1>1.0</mu1>  <!-- High friction -->
  <mu2>1.0</mu2>
</gazebo>

Robot Jittering or Vibrating​

<!-- Solution: Adjust ERP and CFM values -->
<joint name="problematic_joint">
  <physics>
    <ode>
      <limit>
        <cfm>0.0001</cfm>  <!-- Increase constraint softness -->
        <erp>0.8</erp>     <!-- Reduce error correction speed -->
      </limit>
    </ode>
  </physics>
</joint>

Robot Not Standing Properly​

<!-- Solution: Check mass distribution and friction -->
<link name="torso">
  <inertial>
    <mass value="15.0"/>  <!-- Ensure realistic mass -->
    <inertia ixx="0.5" ixy="0" ixz="0" iyy="0.5" iyz="0" izz="0.5"/>
  </inertial>
</link>

<!-- Increase foot friction -->
<gazebo reference="left_foot">
  <surface>
    <friction>
      <ode>
        <mu>1.0</mu>  <!-- High friction -->
        <mu2>1.0</mu2>
      </ode>
    </friction>
  </surface>
</gazebo>

Best Practices for Humanoid Physics Simulation​

1. Realistic Mass Distribution​

Ensure the robot's mass is distributed realistically:

<!-- Example: Realistic humanoid mass distribution -->
<link name="torso">
  <inertial>
    <mass value="15.0"/>  <!-- Torso contains most mass -->
    <origin xyz="0 0 0" rpy="0 0 0"/>
    <inertia ixx="0.8" ixy="0" ixz="0" iyy="0.6" iyz="0" izz="0.4"/>
  </inertial>
</link>

<link name="head">
  <inertial>
    <mass value="3.0"/>  <!-- Head is lighter -->
    <origin xyz="0 0 0" rpy="0 0 0"/>
    <inertia ixx="0.02" ixy="0" ixz="0" iyy="0.02" iyz="0" izz="0.02"/>
  </inertial>
</link>

2. Appropriate Joint Limits​

Set joint limits that match human capabilities:

<!-- Shoulder joint with human-like limits -->
<joint name="left_shoulder_pitch" type="revolute">
  <parent link="torso"/>
  <child link="left_upper_arm"/>
  <axis xyz="1 0 0"/>
  <!-- Human shoulder can move about 90 degrees in each direction -->
  <limit lower="-1.57" upper="1.57" effort="100" velocity="2"/>
</joint>

3. Tuned Contact Parameters​

Fine-tune contact parameters for realistic interactions:

<!-- Foot-ground contact tuned for walking -->
<gazebo reference="left_foot">
  <surface>
    <friction>
      <ode>
        <mu>0.8</mu>   <!-- Good grip for walking -->
        <mu2>0.8</mu2>
        <fdir1>1 0 0</fdir1>  <!-- Primary friction direction -->
      </ode>
    </friction>
    <contact>
      <ode>
        <soft_cfm>0.001</soft_cfm>
        <soft_erp>0.9</soft_erp>
        <kp>1e6</kp>    <!-- High stiffness for stable contact -->
        <kd>100</kd>    <!-- Adequate damping -->
      </ode>
    </contact>
  </surface>
</gazebo>

Hands-On Exercise: Physics Tuning​

Objective​

Tune physics parameters for stable humanoid standing and walking.

Prerequisites​

  • Completed previous chapters
  • Working humanoid robot model
  • Gazebo simulation environment

Steps​

  1. Create a simulation world with a flat ground
  2. Spawn your humanoid robot in a standing pose
  3. Adjust physics parameters to achieve:
    • Stable standing without jittering
    • Realistic response to small disturbances
    • Good performance (maintain real-time factor)
  4. Test with different contact parameters
  5. Document the best configuration for your robot

Expected Result​

Students will have a humanoid robot that stands stably in simulation with properly tuned physics parameters.

Assessment Questions​

Multiple Choice​

Q1: What does ERP (Error Reduction Parameter) control in physics simulation?

  • a) The stiffness of joints
  • b) How quickly constraint errors are corrected
  • c) The friction between surfaces
  • d) The maximum velocity of objects
Details

Click to reveal answer Answer: b
Explanation: ERP (Error Reduction Parameter) controls how quickly constraint errors are corrected in the physics simulation.

Short Answer​

Q2: Explain why it's important to use appropriate friction coefficients for humanoid robot feet in simulation.

Practical Exercise​

Q3: Create a physics configuration for a humanoid robot that can stand stably without jittering. Include appropriate mass distribution, contact parameters, and solver settings. Test the configuration by applying small forces to the robot and verifying it remains stable.

Further Reading​

  1. "Open Dynamics Engine Manual" - Detailed physics engine documentation
  2. "Robot Dynamics and Control" - Theoretical background on robot physics
  3. "Simulation Optimization Techniques" - Performance optimization for physics simulation

Summary​

In this chapter, we've explored the physics simulation capabilities of Gazebo, focusing on configuring and optimizing physics parameters for realistic humanoid robot simulation. We've covered collision detection, contact modeling, and techniques for achieving both realistic behavior and computational efficiency.

Physics simulation is critical for humanoid robotics as it determines how the robot interacts with its environment. Properly configured physics parameters enable realistic movement, stable balance, and accurate sensor simulation, making the transition from simulation to reality more successful.

In the next chapter, we'll explore sensor simulation in detail, learning how to configure and use various sensors in Gazebo for humanoid robotics applications.