Physical AI Formula Extraction Skill

When to Use This Skill

• •User asks to "extract formulas" or "find equations" related to Physical AI or Humanoid Robotics
• •User provides textbooks, lecture notes, or research papers with formulas
• •User wants formulas explained with units, meaning, and practical applications

Procedure

1. •Read the text: Identify all mathematical formulas related to Physical AI, robotics, or control systems
2. •Format formulas: Convert formulas into clear LaTeX or plain-text notation
3. •Explain formulas: Provide a brief description, meaning of variables, and units
4. •Provide examples: Give small, practical examples when possible
5. •Optional context: Link formulas to applications in humanoid robotics, sensors, actuators, or control systems

Output Format

Formula: The extracted formula in LaTeX or plain-text
Description: Explanation of the formula and its purpose
Variables / Units: Meaning and units of each variable
Application / Example: How the formula is used in robotics

Quality Criteria

• •Formulas must be accurate and correctly formatted
• •Explanations should be clear and concise
• •Include observable outcomes or examples when possible
• •Maintain relevance to Physical AI and humanoid robotics

Example

Input: "The torque τ required for a robotic joint can be calculated using τ = I * α, where I is the moment of inertia and α is the angular acceleration."

Output:

• •Formula: τ = I * α
• •Description: Torque τ equals the moment of inertia I multiplied by angular acceleration α
• •Variables / Units: τ [Nm], I [kg·m²], α [rad/s²]
• •Application / Example: Used to calculate torque requirements for joint actuators in humanoid robots