Roll-Pitch-Yaw (RPY)

Orientation described by three rotation angles about the x, y, and z axes: roll, pitch, and yaw.

This naming comes from aviation and maritime navigation: roll is tilting about the front-to-back axis, pitch is tipping the nose up or down about the side-to-side axis, and yaw is turning about the vertical axis. ROS's REP 103 convention points a body's x-axis forward, y-axis left, and z-axis up; RPY means rotating in sequence about the fixed frame's x, y, and z axes by angles γ, β, and α, giving the rotation matrix R = Rz(α)·Ry(β)·Rx(γ) — where Rz(α) is a rotation of α about z — which comes out identical to Z-Y-X Euler angles. RPY is intuitive and easy to tune by hand, and it's exactly what URDF's rpy attribute uses. The downside is that roll and yaw become coupled when pitch nears ±90° (gimbal lock), and the angles jump discontinuously near ±180°, which is why code usually stores orientation as a quaternion internally instead.

ExampleA humanoid robot's IMU (inertial measurement unit) commonly reports roll, pitch, and yaw directly: a sudden jump in roll or pitch means the body is tipping sideways or pitching forward, and yaw tells you which way the body is facing.

Also called

RPY, RPY Angles

Related

Euler Angles · Gimbal Lock · Intrinsic vs. Extrinsic Rotations · Rotation Matrix · Quaternion · Inertial Measurement Unit

Sources

Modern Robotics (Lynch & Park, 2017), Appendix B.2 Roll–Pitch–Yaw Angles
ROS REP 103: Standard Units of Measure and Coordinate Conventions
Wikipedia: Aircraft principal axes