Smoothing of Segment Transitions
Overview
Segment transitions with no continuous second differential cause instability in the dynamics unless the path velocity is reduced to 0 at those points. For dynamically stable segment transition at a finite speed it is possible to smooth segment transitions with Bezier splines which alter the local geometry and ensure that the complete path has a continuous second differential.
Tolerance spheres
A tolerance sphere is laid around every segment transition within which the path may deviate from its pre-set geometry for smoothing purposes. The radius of the tolerance sphere (parameterization) is predetermined by the user and applied modally for all segment transitions that imply no exact positioning or stop in the segment transitions. The radii of the tolerance spheres are automatically reset adaptively, thus preventing tolerance spheres from overlapping in the case of small segments.
Dynamic parameters
The smoothing enables faster dynamics. The system-determined maximum segment transition velocity VeloLink can be influenced by the user insofar as the system parameter C2 velocity reduction C2 (parameterization) sets the segment transition velocity to C2x VeloLink. The factor can be changed online.
General characteristics at segment transitions
When entering the tolerance sphere, the path acceleration is 0 and the path velocity equals the segment transition velocity. This is maintained within the tolerance sphere. The override is inactive within the tolerance sphere, i.e. the change of the velocity level caused by the override is interrupted within the tolerance sphere and continues after the exit from the tolerance sphere.