Motion profile optimization

[Howard]

Let's say we have a ball bearing that is free to move in the x-y plane. Now, we strap a tiny rocket on it, which is free to pivot around the ball around the z-axis, to provide a motive force in any direction in x-y. From point a to point b, how do you describe a non-linear path which minimizes peak forces (not counting accelerations around point a and b) such that...

http://pics.bbzzdd.com/users/Howard/CCF06222010_00001.png

 

[Howard]

I wish monospace were all the new rage again.

 

[Swivelguy2]

Your problem needs more constraints, or it's trivial.

You minimize the peak force by accelerating very, very slowly as you move along whatever path you like from A -> A' -> B' -> B

 

[Howard]

Your problem needs more constraints, or it's trivial.

You minimize the peak force by accelerating very, very slowly as you move along whatever path you like from A -> A' -> B' -> B

Given any average velocity... the problem is not in adjusting the forces, but picking the path that allows you to use the least force.

Maybe the question should be finding the highest average velocity given a limited force by optimizing the path of motion?

 

[Howard]

Perhaps this is what I'm looking for:

"Hogan noted that, in general, if something you wanted to move something from location to in seconds, the minimum jerk trajectory would be:"

http://www.shadmehrlab.org/book/minimum_jerk/minimumjerk.htm

 

[schenley101]

Perhaps this is what I'm looking for:

"Hogan noted that, in general, if something you wanted to move something from location to in seconds, the minimum jerk trajectory would be:"

http://www.shadmehrlab.org/book/minimum_jerk/minimumjerk.htm

The third derivative?

 

[Howard]

The third derivative?

What?

 

[TuxDave]

What?

The first paragraph. Jerk is defined as the third derivative of location to time.

 

[Howard]

The first paragraph. Jerk is defined as the third derivative of location to time.

Yeah, but I'm not looking for jerk...?

 

[TuxDave]

"Maybe the question should be finding the highest average velocity given a limited force by optimizing the path of motion"

Technically that could be trivial too since you would ideally start the path with you accelerating in a straight line to increase your average velocity and then start apply a weak force perpendicular to your path such that you eventually turn to hit the other points.... (pic coming soon)

 

[Howard]

I failed to constrain the problem sufficiently.

This is basically an exercise to determine how best to program the motion of a robotic end effector. Points A and B, as previously defined, are either the start or end points, and points A' and B' exist because whatever the EE is carrying must not physically interfere with certain items. However, because of these points, the EE will have a vertical velocity on one side of the trajectory at points A' and B'... How to take into account this already-existing velocity?

So, to find the trajectory between points A' and B' given the trajectories between A and A', and B and B'...