MOB LEC9 Reference Frames and GPS

The coordinate systems in mobile robotics

1. world coordinate system
2. ego-vehicle coordinate system

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Rigid Body Assumption

Rigid Body is a solid body in which deformation is zero or so small it can be neglected.

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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.

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Coordinate transformation

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Rotation

rotation matrix

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Direct Cosine Matrix

Direct Cosine Matrix (DCM), unit vectors, 3 assumptions

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Eular Angles

Euler Angles, single axis rotation, in an intrinsic sequence (X, Y, Z).

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Gimbal lock, loss of one DoF, cause singularity.

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Quaternions

Quaternions and 3d rotation, explained interactively

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Small summary

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Order of rotation, rotation in 3D are non-commutative.

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Reference Frame

Earth Centered Earth Fixed Frame

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North East Down Frame

North East Down (NED) frame

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Sensors’ frame

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GNSS

Global Positioning System

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Position in ECEF coordinate via accurate ephemeris information. Time of signal transmission via onboard atomic clock.

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Reducing uncertainty every time we add a new circle.

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In this case we have sphere.

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Ephemeris & clock errors, Multipath effect affecting precision

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ionosphere delay

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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