Need help developing a movement function for motor motion

[assafMOCAP]

Hi,
I have a motor that i would like to rotate to a certain angle, in a controlled manner.
During the movement, i want to update the final position I want to reach.
The new updated function has to start with the same speed the initial function ended with
I wan to find a function that does this.

In green, the initial function.
In blue at t=t1, I update the endpoint.
I would also like to control the pivot points of the function (in red)
How do I do that ?
Thank you !

 

[etotheipi]

You could try playing around with the sigmoid function:

 

[pbuk]

For a mathematical solution you could look at spline function. Specifically (because presumably you cannot achieve an instantaneous change in velocity) I would suggest a clamped cubic spline.

However I'm not sure how you would use this function in practice to control a motor; this would normally be done by a more simple calculation using the SUVAT equations to answer the question "do I need to speed up or slow down", because that is all you can control.

 

[mfb]

What is the goal? Reach the position in the fastest possible way with limits on acceleration and speed? Reach it with the lowest peak acceleration? Something else? The best acceleration/velocity profile will depend on that.

When you update your target you can forget what happened before. Only the current position, velocity and maybe acceleration matter. Maybe other current parameters as well, but not their history. The ideal profile will depend on what you consider "ideal".