MOB LEC9 Reference Frames and GPS

The coordinate systems in mobile robotics

1. world coordinate system
2. 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

1. Understanding Direct Cosine Matrices, Euler Angles and Quaternions.
2. Representing Robot Pose: The good, the bad, and the ugly.
3. Rethinking GPS: Engineering Next-Gen Location at Uber