What is a flexible manipulator£¿

It seems that I get to choose the subject.

Jerry

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This isn't helpful. I would look at

The input shaping algorithm works for moving swinging or vibrating masses into position. I am researching Galerkin's info. Funny, the Convolve site claims their algorithm is used on the space shuttle arm.

I am using a very crude form of the Convolve Input shaping in my realistic version of JCH's crane problem. I am doing a convolution of a simple velocity motion profile, with no accelerations or decelerations, with two impulses 180 degrees apart. These impulses

180 degrees apart cause the swing to cancel itself out. You can see that there is no problem getting a swinging or vibrating mass to move into position with excess vibration. I am using only a very simple form of PID.

If you do a search for Convolve you will that this algorithm is used for hard disk head position and Convolve has a law suit against the some hard disk manufacturers.

Mean while it is fun to torture JCH about his crane example but I am trying to be educational about it.

The alternative to input shaping is to have a higher order controller with position and acceleration feedback. It is possible to estimate the acceleration from a feedback from only a position feedback, but estimating the jerk is another matter. Acceleration feedback works but it is more expensive and accelerometers may not last in an industrial environment. Acceleration feedback works but I find few customers willing take advantage of it. Customers want simple or at least something they can understand.

Peter Nachtwey

It was a long shot. Workaholic didn't say what he wanted the tutorial to teach.

...

Your two impulses remind me of Hohenauer's cascaded integrator/comb filters.

A pendulum isn't the only system where ringing should sometimes be suppressed.

Jerry

I thought it was obvious. He wanted to know more about flexible manipulators. Galerkin had the right interpretation. All it takes is a web search for "flexible manipulator". I recommend the OP do a search for "flexible manipulator tutorial" . It looks like one must pay for papers or buy a book tied to some engineering package. This isn't an easy topic.

Peter Nachtwey

I guess I missed something. The first post of the thread I saw was (in toto; there was no context) "Can someone give me an example or a tutorial ? thx!" The subject was simply "Re ?". I posted sarcasm, for which I apologize.

Jerry

Great thanks to Galerkin and Nachtway! And it is also my fault of poorly expressing myself in the context of the message. However, I have one more question: What is the advantage of using a flexible robot rather a rigid one, since it is more difficult to cope with?

If possible it is best to have a rigid robot. Unfortunately this isn't always possible when moving large structures or heavy loads. The structure or load will tend to oscillate. It takes extra code, feedback devices or/and complexity to compensate for flexible loads. This should be avoided if possible.

Peter Nachtwey

Galerkin and Nachtway! And it is also my fault of

A little disappointing... I thought the flexible manipulator might be one of the current innovation in robotics... According to your explanation, it is just a circumstance where we have to take a lot of things into consideration. So what is the prerequisite for research on this topic? My major is automatic control.I've no idea about the mechanics of the beams or structures, how can I amend for it? What kind of books should I read ahead?

Galerkin and Nachtway! And it is also my fault of

Mechanical engineering courses cover this stuff. This would, I believe, come under the heading of "vibes" or "vibration", although you'd need to start out with a course in dynamics (everyone who controls mechanical systems should take one eventually, or undertake to study the subject independently) and proceed through a course in strengths of materials to get there.

wrote:> Great thanks to Galerkin and Nachtway! And it is also my fault of

I get involved with moving big things. Everything flexes a little. It would be nice if the mechanical engineers really designed their equipment and presented the control guys with a transfer function along with the machine. That would be too easy.

Since the mechanical engineers will not provide a transfer function it is up to you to be able to do system identification. You should have had some class on this already. You need to learn what systems can be controlled and what can be done to modify the machine to make it a little easier to control. You need to know the machine you are trying to control.

I would get Scilab and learn how to use the optimization functions like optim and lsqrsolve so you can find equations that will allow you to generate equations that will generate estimated positions that closely match actual positions given an control signal using an equation. That equation is your transfer function. You need the transfer function and a desired response to produce controller gains. Now you have designed an autotuning program.

Experience and study on my own has helped me. My company makes hydraulic motion controllers and we sell thousands of axes of control each year. I am an EE who has had to learn hydraulics out of self defense because the customers would often call up about not being able to go as fast as they wanted ( bad sizing ), could accelerate as fast as they want, the system is hard to tune ( hose between the valve and the cylinder ) etc. After awhile you have seen most of the mistakes. In my case I knew that hose between the valve and the cylinder is bad, but then I did research on how to quantify the problem so I can show proof it is the hose and not the controller that is giving the customer problems. Now I can tell customers how to chose components that will allow them to move a mass so fast and accelerate quickly enough to meet their production rate specifications. The mechanics are still out of my domain but I do know that one should make them as stiff as economically possible. I can also show the designers how the natural frequencies and damping factors will affect their system so they can better chose the trade offs. Nothing is perfect. One must find the optimal compromise.

Obtain and learn to use a math package such as Matlab, Scilab, Mathcad, Maple or Mathematica. I prefer the symbolic math packages because one can see symbolically how things interact. The equations just don't result in a simple number. Scilab is free. That is my second math package.

Every control system has feedback devices. Sometimes these feedback devices don't provide the quality of feedback you desired either in resolution or the order of feedback. For instance, how do you calculate the acceleration given a position feedback? It is hard enough to calculate a meaningful derivative. This is when you will want to study observers, Kalman filters and H infinity filters.

Search for system identification, optimization, pole placement, Kalman filters, observers, H infinity. Most of the info on the net about tuning is just junk but there are some gems. That is a lot to study. It takes a while.

It is all about controlling the flow of energy from one for to another.

Peter Nachtwey

Great thanks for sharing your work experience, I still have a lot to learn! Sometimes I think that my major is very embrassing because you can't tell which domain is your own specialty, for we have to know a lot of unfamiliar things in various kinds of disciplines!

That sounds more like Life In The Real World than any sort of university major I've ever heard of. Should be good training for when you get out... :-)

Cameron:-)

Well, it turns out I missed quite an existing discussion among us control folk...

"However, I have one more question: What is the advantage of using a flexible robot rather a rigid one, since it is more difficult to cope with?"

In my original post I gave some background on the most famous flexible manipulator, the Canada Arm. In the academic community there are still many persons looking at various way to control flexible structures. Flexible robots are the most frequently researched plant, but there has been significant investigation on other forms of vibration control such as active vibration suppression of bridges and machine tools (such as milling machines). Flexible robots are generally the most interesting because the control objective is not only to suppress vibration, but also to execute tracking and grasping tasks in the task space rather then the joint space (task space being the x y z coords of the end effector, and joint space bing the angular position of the joints i.e. theta_1, theta_2... theta_N). The equations of motion are highly nonlinear and they offer a significant challenge to engineers, as opposed to a stationary object that just vibrates (such as a bridge, where the vibration of the bridge is to be suppressed). Almost every kind of controls algorithm in existence has been executed on flexible robots. For example, PD, PI, PID, Lead-Lag, H2, H infinity, passivity based control, adaptive control and mu synthesis. You might be surprised to find out that on the famous Canada Arm is actuality controlled with a PD controller, which leads me nicely into your original question. Peter Nachtwey is absolutely right, if you can use a rigid robot then use one. A flexible system is a very complicated plant to observe and control. The only advantage to using a flexible robot is weight and actuator reduction. The reason the Canada Arm is flexible is because the payload of the Space Shuttle is fixed... that is to say there is a weight restriction on the Canada Arm because at the end of the day, it has to be blasted off into space! Thus, until there is a demand for significant weight reduction of robots here on earth, we are not going to see many flexible robots. As a side note, that day very well may come. Currently in North America (and the world) there are hundreds of thousands of large, bulky energy intensive 6 axis robots executing tasks such as robotic welding and other manufacturing tasks in the automotive sector. I think it is quite silly when I see a huge ABB, Motoman or Panasonic robot (with its large bulky energy intensive motors) moving around a light weight welding gun (GMAW, or "Mig" welding gun). Why? The tip mass of that robot is maybe 5 kg max! But, the reason that bulky robot is there is because there is not a demand for it to be smaller and more energy efficient. We as humanity are entering an energy crisis. In the (near) future I would not be surprised to see a demand for smaller, lighter weight (and thus flexible) robots that can still execute tasks such as robotic welding. These smaller robots will be more energy efficient and will eventually cost less (less material = lower cost, and less mass = smaller motors, and yes there will be a slight increase in cost based on the added sensing and control but that will be drowned out after a few years of engineering iteration). Once we have a few, accurate and robust flexible robotic systems then more will be created. The next thing you will see is large gantry cranes that are totally flexible, but totally safe! I should also mention that another reason (I believe) that flexible systems are only tackled in academia is "fear of the unknown". The vast majority of industry is afraid of new technology, or things they don't know. There are not flexible robotic systems in industry (I don't count space as industry), and which comnay has the guts to be the guinea pig and test out a flexible robotic system? Until a company is in a sink or swim position, and is forced to innovative I would not count on seeing complex systems such as flexible robots utilized. This point matches nicely with my previous point about "demand" based on energy efficiency.

"So what is the prerequisite for research on this topic? My major is automatic control.I've no idea about the mechanics of the beams or structures, how can I amend for it? What kind of books should I read ahead?"

I am a mechanical engineer, now partaking in a aerospace graduate program. My thesis topic is "optimization of controllers for flexible structures". Currently I do more electrical/controls engineering, but I would never be able to tackle what I am doing without my mechanical engineering background in dynamics AND control. Tim Wescott is absolutely right in that I had to first understand the dynamics and vibrations theory associated with flexible robotic systems before I could even touch the control aspect. I can tell that Peter Nachtwey knows his stuff, but I wouldn't agree with the statement "mechanical engineers will not provide a transfer function, it is up to you to be able to do system identification". In my opinion you must be a master of both the dynamics and the control. You cant effectively control a system without a full understanding of the dynamics, because the dynamics ARE the transfer function to control (for a LTI system anyway). This is why I chose an aerospace graduate program rather then jumping to electrical engineering. I find the research in EE is to disjointed from the physical world that I have an interest in (I am not so interested in designing feedback controllers for RLC circuits and the like). Thus far I have taken a few graduate engineering classes in the EE department at my university and I found them very unrealistic. In fact, I even had the professor of one of my classes ask me to do some system modeling for a mechanical system, so that she could look at designing a controller! Don't get me wrong, I am essentially doing full on EE research now, but I find that if you want to look at physical systems (rather then very EE type stuff like signal processing control) you need to have a very solid background in dynamics and strength of materials. If you are in an electrical engineering program and want to get into mechanical and aerospace control, you should defiantly take some dynamics and vibrations classes. To date I think I have taken 8 in the dynamics/solids field (UG and Grad school combined) but within those there is a lot of overlap. Doing an advance dynamics class at the undergrad level (a 4th year class) is probably a better place to start then just jumping into advanced dynamics at the grad level. Also my machine theory course in undergrad was basically a elementary vibrations class, so you might want to start with an undergrad vibrations class before doing one at the grad level. If you don't have time to take undergrad classes then basically what you need is some kind of advance dynamics class, and some kind of vibrations class. If you don't have time to take any more classes period, I suggest a book by Rao called "Mechanical Vibrations" (ISBN: 0-130-48987-5) to learn the vibrations stuff. I have yet to find a good advanced dynamics text, so I will refrain from suggesting one. One book that I have had a great amount of success with as far as fundamental theory of dynamics and vibration is "Methods of Applied Mathematics" by Hilderbrand. Is published by Dover , ISBN: 0-486-67002-3. Traditionally this is an applied mathematics book, but it is one of the best books I have ever used for learning some complicated dynamics and vibrations stuff. The book has a chapter devoted to a topic known as "the calculus of variations" which is the basis for a lot of dynamics and vibrations theory. For example, and energy based approach for developing the equations of motion for a system (which will give you the system transfer function if it is a linear system) is known as "Lagrange's Method", using "Lagrange's Equation" and something called the "Hamiltonian". This book goes through it all form start to finish. Next the book covers how to do basic vibrations problems using something called the "Raleigh Ritz Method", which is very similar to the Finite Element Method found in structural mechanics.

Peter Nachtwey also hit the nail on the head when stating "That is a lot to study. It takes a while."; I had the advantage of knowing a lot of dynamics and some control before coming to grad school. The most daunting task for me was acquiring the mathematical background required to understand what the controls guys in the EE department where talking about. For example when I finished my undergrad in ME (focusing on more dynamics and control in 4th year) I had no idea that the poles of a transfer function where the eigenvalues of the system! In my advanced dynamics class we talked about stability based on the eigenvalues of a system, and in my controls classes we talked about pole placement, but I had yet to connect the two. It sounds like your are going to be doing the reverse, staring at the EE end and moving to the ME end. It is doable though.

Peter Nachtwey also said "It is all about controlling the flow of energy from one for to another."; also true. In control we design systems to control how energy moves in a system. Sometime we add energy to the system (move a robot/crane from A to B), sometime we take energy away (suppress vibration due to external excitation such as wind blowing on a crane), sometimes we do both (move a crane from A to B while suppressing the vibration induced due to the wind). At the end of the day we are playing around with differential equations and changing the position of the closed loop eigenvalues. If we have a linear system (thus the natural eigenvalues or poles of the plant are fixed) then when we add a controller with its own dynamics (a controller with R L and C components, or the digital equivalent has its own associated eigenvalues), we can then "place" the over all closed loop system eigenvalues wherever we want. This is essentially shaping how the energy flows in a system, and the power required to do so is the rate of change of such energy shaping.

Well, an hour later I am done writing this... it was pretty fun for me though! I don't really get to "geek it out" with anyone these days, other then my supervisor! If anyone has any comments, please respond!

James Forbes

On Jul 10, 8:33 am, Galerkin wrote: I can tell that Peter Nachtwey

I am still waiting for the mechanical engineers to provide a transfer function. I have never seen one unless I generated it. Most have a hard time telling me enough information so I can make a rough estimate. Obviously this had better be different in aerospace but in industrial applications the controls guy is on his own.

Peter Nachtwey

Learn to live with it. I have yet to work with a ME who could cough up a transfer functions -- I expect to be on my one on this. The ones that I know of who can do it are all control engineers.

On Jul 10, 1:19 pm, Tim Wescott wrote:

Tim and Peter,

The intent of my comment was not to put down anyone (regardless of their background in ME or EE) but rather to make the point that to really be a master of the physical world you wish to control, you need to understand both the system dynamics and control design. Peter, I believe you are correct in saying that most mechanical engineers working as aerospace engineers doing dynamics and control are well versed in LTI transfer function creation (the ones I know sure are!). Tim, I can assure you that I have many colleagues who have ME degrees who are also very capable and able to develop an ordinary differential equation of a system. They may not hand you a transfer function directly (i.e they may hand you m*x_dot_dot + c*x_dot + k*x = u rather then x/u = 1/(s^2 + 2*zeta*omega_n*s + omega_n^2) ), but I am sure they know their dynamics and system modeling. With that being said Tim, I believe you said (on your website) "Within a year of starting (at FLIR Systems) I learned two things: how to be a real embedded software engineer, and how little the average software engineer knew about control theory"; persons such as Peter, yourself and myself live and breath dynamics and control. The "average" mechanical engineer has maybe had one control class during his undergraduate education. I would expect any "average" mechanical engineer could figure out how to give you a transfer function if they spend a day or a week and reviewed some books. If you don't do this stuff every day, then of course you wont know it. Even you didn't know it all at first... or so your quote eludes. And don't get me wrong, I still don't "know it all". I learn something new every day!

You know, I wrote another big long response to a post Peter made, and my post didn't show up! I spent about an hour on it! I will have to write it again at some point I suppose! Doh!

Cheers,

James Forbes

Control isn't the only subject that requires knowledge of a mechanical system's characteristic equations. Often, vibration and response to shock needs to be considered. Mostly, that's done empirically.

When I was implementing controllers for systems that came from the ME guys, they were aghast that I drilled and tapped holes to mount limit switches and other sensors, and to run wires in their newly anodized frames. Some were offended that sensors and actuators actually needed unsightly wires. One complained, "Why didn't you tell me?" I told one ME that an arm he designed to carry a microscope wasn't rigid enough. He didn't know enough to undertake the vibration analysis on his own. He went nuts when I turned out to be right and ended in a sanitarium. Whew!

Dig it out of your "sent" folder and repost.

Jerry

On Tue, 10 Jul 2007 23:58:34 -0400, Jerry Avins proclaimed to the world:

Not when he is posting via Google.