I have a decoupled mechatronic system with two motors. I want for each motor to give a s-curve path as reference. You can see in the image below the position path, velocity and acceleration.
The way I have designed the system, the position is given as the reference. So I need the equations for it. From what I saw, this is what is referred to as a "s-curve" path. The way I understand it, the equation is broken down in to 4 different parts:
- $0\le t\le 0.05$
- $0.05<t\le 0.2$
- $0.2<t\le 0.25$
This seems like a fairly standard equation but I have not been able to find anything that works. I have tried to used the equations from Constant Jerk Equations For A Trajectory Generator1 but the results where not the same. I also found Mathematics of Motion Control Profiles, and maybe I don't understand it, but the equations found there do not seems to be enough for what I want.
Can anybody provide the correct equations (preferably in a generalized form, so I can apply them else where in the future) or some other help?