Interpolation

hi techies...i am currently working on a project that requires me to program a 2-axis linear actuator to perform both linear (in x and y directions) and circular patterns. A professor told me that what im doing involves interpolation...Can anybody help me with this...I will be using one of Allen Bradley PLCs. Thanks

Which AB PLC are you using and what control components do you have available? Are you using one of the AB motiuon controllers, someone elses motion controller or no motion controller at all. Linear and circular interpolation may not look all that conceptually complicated but the details can be a killer.

Generally, linear and circular interpolation involve the use of two or more coordinated axes to perform a vector or circular move. The trick is in keeping the two axes tied tightly enough together to perform the move as accurately as required. Usually this is something done with a dedicated motion controller unless the speed, accuracy and bandwidth requirements are VERY loose.

Keith

thanks...do you think i still need a motion controller? i will be driving two RCP2 robo cylinders from IAI with PIO...

If you have to do interpolation with w RCP2 actuators, then you will most likely need the new PSEL controller (2-axis version).

I will interpolate lines and arcs.

Check here for the latest catalog which includes information on it
http://www.intelligentactuator.com/product_catalogs.php#roboc2

Is this for a school project?

Are you interested in the final results or must you interoplate?

Here is a question for betamax6, Norm and Keith.
Linear interpolation is necessary because a point to point move involves only two points and there isn't a defined function between the two points, but why do circular interpolation when you can calculate the x and y positions directly without interpolating between points? What points are you interpolating between when one is doing circular interpolation?

When should you interpolate?

Betamax6, if you want to know about interpolation then look up cubic splines in chapter 3 of Numerical Recipes in C. This is standard in most motion controllers.

betamax6, how do you start the circle? One axis must start at a non zero velocity and the other a non-zero acceleration? This is impossible with physical devices.

I'm back with more mind games.

Peter, you're confusing me again.

Its probably because I tend to use a very specific case of interpolation, that being a linear interpolation between two points. The concept of circular interpolation has always seemed odd to me.

Given a multi-axis linear vector move, the position path for each axis between the two points can still be a known function. If you define the move in terms of the vector path the motion of the orthogonal components is a known relationship to the resultant vector in terms of position and all it's derivatives. If you are trying to optimize the move you may need to back-calculate the available peak velocity, acceleration and jerk of each axis. If you simply use the peak values from the vector move and don't allow a single axis vector move (on one of the planes) to violate the peak capability of an axis you have a simple, constant limit.

Similarly, with a circular move you only have non-zero initial velocity and acceleration if you start with a non-zero omega for the vector. If you accelerate the vector rotation the component axes will also accelerate and never at a greater value than the tangential acceleration at the end of the vector.

It all comes down to profiling.

Keith

Maybe the term interpolation is being used in the wrong way here. I think this is a hold over from CNC machines where any multi axis moves were/are called interpolated moves.

However, from scanning the chapter in Numerical Recipes that Peter cited, I don't believe betamax6 is doing this "interpolation".

To do lines and circular arcs, all the points and functions are known. From Numerical Recipes, interpolation involves inferring intermediate points from known points. There is no inference needed here.

I need to correct a point I made in my earlier post. You can't directly infer a maximum acceleration rate for an orthogonal axis used for a coordinated circular move based simply on the vector peak rotational velocity, although this will most likely be the case. It is possible to accelerate the vector quickly enough that the peak vector acceleration and the peak axis acceleration due to the location in the circle could be higher than the peak acceleration required by an axis to profile the circle at max velocity. Granted, this probably will not be the case, but it can be.

I guess I could make a case for linear interpolation in that you need to define accel, jerk or higher order break points at various locations in the move in order to correctly profile the move. But this isn't peculiar to coordinated moves. The same thing needs to happen if you are doing a single axis point-to-point move.

I love definitions.

Keith