The coordinate systems in mobile robotics
- world coordinate system
- ego-vehicle coordinate system
Rigid Body Assumption
Rigid Body is a solid body in which deformation is zero or so small it can be neglected.
rigid body assumption implied that movement of a sensor mounted on the robot should be the same as other co-located sensors and the whole platform.
Motion in general
Motion that can be described by a rotation and translation. There are 6 degree of freedom (DoF) in 3D space for rigid body.
Coordinate transformation
Rotation
rotation matrix
Direct Cosine Matrix
Direct Cosine Matrix (DCM), unit vectors, 3 assumptions
Eular Angles
Euler Angles, single axis rotation, in an intrinsic sequence (X, Y, Z).
Gimbal lock, loss of one DoF, cause singularity.
Quaternions
Quaternions and 3d rotation, explained interactively
Small summary
Order of rotation, rotation in 3D are non-commutative.
Reference Frame
Earth Centered Earth Fixed Frame
North East Down Frame
North East Down (NED) frame
Sensors’ frame
GNSS
Global Positioning System
Position in ECEF coordinate via accurate ephemeris information. Time of signal transmission via onboard atomic clock.
Reducing uncertainty every time we add a new circle.
In this case we have sphere.
Ephemeris & clock errors, Multipath effect affecting precision
ionosphere delay
Future Reading
- Understanding Direct Cosine Matrices, Euler Angles and Quaternions.
- Representing Robot Pose: The good, the bad, and the ugly.
- Rethinking GPS: Engineering Next-Gen Location at Uber
