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