Advanced Control: Clansman's and RWatson's robotics and mathemagic

This topic deserved to be a separate thread with and Advanced Control header.

The first video was made from videos a couple of years back.
You don't see it do much but there is an explanation of what the cylinders do.
Bruce Coons, our regional sales manager at the time is narrating. Bruce has retired now. He will be missed.

https://deltamotion.com/peter/Videos/Clansman App - Light Bkgd.mp4
This second video shows the grinder robot in action. The operator touches the surface at 3 points. Three points define a plane however the mathemagic that is required to do that is significant. Usually we must hand hold our customers but Richard worked all of this out himself. The purpose of defining the plane is that the grinding wheel must not grind beyond the plane. Also, the grinding wheel wears so the diameter is smaller. The touching the three points compensates for the grinding wheel wear. The area where the grind wheel is a nasty environment.
The amount of math required to compute where the grind wheel is at the end of several linkages and rotations is significant.


This next video shows the Clansman robot grinder in action. There is no sound.

https://deltamotion.com/peter/Videos/Grinding Arm.mp4
This may not look as neat as a Kuka robot playing ping pong but this grinder robot must move a lot of mass at the end effector and still apply force to grind.



I believe the Clansman robot can define planes that are not horizontal.



Richard can fill in any details that I may have missed or got wrong. Brag a bit Richard. Most people can not do the math or the programming on anying this complicated.

The most difficult thing for me about these machines is the fact that they are manually driven, but with semi-automatic assists, which means you are trying to tune a lot of things that are completely subjective. The machine in the video is driven from a control arm in the cabin which is effectively a small electrically actuated scale model of the main hydraulic arm with the motors being used to provide force feedback and give the driver a 'feel' of what the large hydraulic arm is experiencing.

To give a simplified explanation of what is going on in the video, after selecting 3 points, the equation of a plane is calculated. A kinematic calculation is done on the control arm to find the (x,y,z) coordinates of the raw target. If the raw target is on the forbidden side of the plane, it is modified to be the closest point on the plane. The desired hydraulic boom angles are calculated from the inverse kinematics of this point. To complicate things, the pressure exerted on the casting has to be limited to prevent the stone from gauging the surface. At the same time the control arm provides force feedback to the driver which depends on how hard the stone is pushing down or how far past the plane the control arm has gone. The whole idea is that it has to feel natural for the driver. He points the joystick at what he wants to grind and the feel of the joystick tells him if it's good or not - he is oblivious to the complicated things going on under the hood.

The program should be able to handle any plane, but there are limitations. Due to the design of the wrist and the fact that the axes aren't servo controlled you lose accuracy the further you stray from a horizontal plane. We have a new larger model with chain of 5 servo hydraulic axes that can handle any plane properly. If you mount a cutting stone instead of a grinding wheel you can cut on any angle without risking side loading the stone which would be nearly impossible to do for any large cut if you were trying to do it manually.

These machines are still almost a proof of concept but they seem to be working really well for our customers. I am looking at changing my role to be more R&D focussed next year to work full time on developing features for these machines as opposed to trying to squeeze new features in the week between the machine being built and shipping or at a customer site in the middle of the night. I would like to re-build it from the ground up to refactor everything and program it using more established robot control techniques as opposed to doing everything from first principles which can get really messy when you try to do more complex tasks.

What symbolic math software are you using or going to use?

I still use Mathcad but sometimes I use wxMaxima because it is free so I can share programs. Python's sympy works but it is an afterthought.

I usually use sympy within a jupyter workbook to do my calculations. I like the way that you can break everything down and execute it by section easily. I also like that I can lambdify any complicated expressions or matrices so that I can execute them over and over again much more quickly if I need to do a simulation or something. I think we have a Mathcad license, but I have never actually used it.