Frenet Coordinate System

The Frenet–Serret coordinate system is constantly rotating as an observer moves along the curve. Hence, this coordinate system is always non-inertial. The angular momentum of the observer’s coordinate system is proportional to the Darboux vector of the frame.

Example:

The Frenet system is representing an object and its trajectory with respect to a reference path, which in the autonomous driving domain is the road or lane that your vehicle is on. This dramatically simplifies the problem of calculating where things really are, and what implications they may have.

For instance if you are travelling around a sharp bend, the stationary vehicle in front of you will not be on the longitudinal axis of your vehicle until the last moment. It is however on the path that your vehicle is following and will mean that your vehicle must take some action other than persisting rigidly with that path.

The Frenet system will tell you in simple terms where this vehicle is with respect to you and the road you are on i.e the distance along the road you are on and it’s lateral position with respect to the centreline (if you use the centreline as your reference path).

Papers:

Optimal Trajectory Generation for Dynamic Street Scenarios in a
Frenet Frame

Video:

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Trajectory Generation

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