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When both the speed profile and the path are given, they can be combined to form the trajectory. This is done in two places in the implementation, here for the planning, and here and here for the execution of the plan. The traveled distance (arc length) is calculated by integrating (i.e. summing) the speed profile.

The trajectory must contain the vehicle velocity vector (see Vehicle Commands for details). The velocity vector is calculated from the direction vector and the speed, with the equation:

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