# Is there any need to guarantee the duration of one planned trajectory is an integer times rather than a decimal times of interpolation period Ti

Take double S of velocity profile for example where the seven segments exist. Given the desired displacement s, the constraints jmax,amax, and vmax, after the computation I found that each duration which it takes respectively to reach amax,vmax,s are not the integer times of the period e.g. Ti=2 ms .

This picture is from Trajectory Planning for Automatic Machines and Robots.

I expect this would result in some problem when processed in CPU discretely. This would exceed the amax when round up the Tj1 to integer times of period or not reach the amax when round down. The similar problem also apply to vmax and s. This would not satisfy the accuracy of displacement.

Is there some solution or relevant investigation about this quesiton?

I thought up a solution by assigning the duration which equals the rounded up time as new constraints to resolve for the new jmax after the original computation.