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Cheat Sheet
Units & Conventions
SI units, quaternion convention, common conversions
Robotics uses SI units consistently across all data types and interfaces.
| Quantity | Unit | Notes |
|---|---|---|
| Length / Distance | meters (m) | Always meters, never mm or cm |
| Angle | radians (rad) | Never degrees in data; 2*pi = full rotation |
| Time | seconds (s) | float64 or nanosecond integers |
| Mass | kilograms (kg) | Used in URDF inertial properties |
| Force | Newtons (N) | kg * m/s^2 |
| Torque | Newton-meters (N*m) | Joint effort and wrench torque |
| Linear velocity | m/s | Twist linear component |
| Angular velocity | rad/s | Twist angular component |
| Linear acceleration | m/s^2 | IMU linear acceleration |
| Temperature | Celsius | Standard for robotics sensors |
| Frequency | Hertz (Hz) | Typically 10-1000 Hz for sensors |
Quaternion Convention
- Order:
(x, y, z, w)— Hamilton convention - Identity:
(0, 0, 0, 1)means no rotation - Normalization: Must satisfy
x^2 + y^2 + z^2 + w^2 = 1 - 90 deg yaw:
(0, 0, 0.7071, 0.7071) - 180 deg yaw:
(0, 0, 1, 0)
Common Conversions
| From | To | Formula |
|---|---|---|
| Degrees | Radians | rad = deg * pi / 180 |
| Radians | Degrees | deg = rad * 180 / pi |
| RPM | rad/s | rad/s = RPM * 2 * pi / 60 |
| km/h | m/s | m/s = km/h / 3.6 |
| mph | m/s | m/s = mph * 0.44704 |
| Euler (RPY) | Quaternion | Use a rotation library (e.g. scipy.spatial.transform) |