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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.

QuantityUnitNotes
Length / Distancemeters (m)Always meters, never mm or cm
Angleradians (rad)Never degrees in data; 2*pi = full rotation
Timeseconds (s)float64 or nanosecond integers
Masskilograms (kg)Used in URDF inertial properties
ForceNewtons (N)kg * m/s^2
TorqueNewton-meters (N*m)Joint effort and wrench torque
Linear velocitym/sTwist linear component
Angular velocityrad/sTwist angular component
Linear accelerationm/s^2IMU linear acceleration
TemperatureCelsiusStandard for robotics sensors
FrequencyHertz (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

FromToFormula
DegreesRadiansrad = deg * pi / 180
RadiansDegreesdeg = rad * 180 / pi
RPMrad/srad/s = RPM * 2 * pi / 60
km/hm/sm/s = km/h / 3.6
mphm/sm/s = mph * 0.44704
Euler (RPY)QuaternionUse a rotation library (e.g. scipy.spatial.transform)