Oral-History:Roger Brockett

About Roger Brockett

Roger W. Brockett founded the Harvard Robotics Laboratory in 1983 and is the the An Wang Professor of Computer Science and Electrical Engineering at Harvard University. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), and a recipient of the 1991 the IEEE Control Systems Award, and the 2009 IEEE Leon K. Kirchmayer Graduate Teaching Award.

About the Interview

ROGER BROCKETT: An Interview Conducted by John Baillieul, IEEE History Center, August 2021

Interview #865 for the IEEE History Center, The Institute of Electrical and Electronics Engineers, Inc.

Copyright Statement

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Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program, IEEE History Center, 445 Hoes Lane, Piscataway, NJ 08854 USA or ieee-history@ieee.org. It should include identification of the specific passages to be quoted, anticipated use of the passages, and identification of the user.

It is recommended that this oral history be cited as follows:

Roger Brockett, an oral history conducted in 2021 by John Baillieul, IEEE History Center, Piscataway, NJ, USA.

Interview

INTERVIEWEE: Roger Brockett

INTERVIEWER: John Baillieul

DATE: August 2021

PLACE: Cambridge, MA

Baillieul:

The purpose of our gathering here today is I'm conducting an oral history with Roger Brockett, who is to my left. Roger is known to many people for many different things. I brought along a recent republication of a classic text that many people still use to teach finite dimensional linear systems. But there's much to tell. And I think that the way that these oral histories like to start is by just some words about the very beginnings of one's life that you remember and how you grew up and where you went to school and maybe just tell us a little bit about yourself, Roger.

Brockett:

Sure. So I was the youngest of seven children, born in a hospital in Wadsworth, Ohio. My parents lived a couple of miles West of the very small town of Seville, Ohio. My childhood was remarkably uneventful in the sense that I had a very stable family, children preceding me had a whole range of skills and limitations. And so I saw some of everything. And mainly growing up on a farm, I saw plenty of opportunity to ask questions about how things worked. And I did find out, for example, even though I lived very closely with animals every day, I found machines more interesting than the animals. In fact one of my children told me that you don't know how lucky you are that you knew what you wanted to do from almost the time you were born. That's not typical, he assured me, and so stop asking me what I want to do. So I did. Anyway, my high school was small, average graduating class of probably something like 20 children. And I would say that I did have a plane geometry teacher who influenced me in a couple different ways. One of them, he believed in me enough to take time in the evening on one occasion when I was preparing for a big statewide test, to take time to coach me a bit. But he also let me know that he valued my opinion about which teachers were doing their job well and which were not, and things that were just between him and me. So that was fun; that was fun. I don't know. Athletics was a big part of my life all the way through undergraduate school, and I think I understand why athletics is taken into account to such extent in, both in college admissions and also in employers seeking to add to their expertise. There's something about competiting in sports, learning about the fact that you're going to lose some time and it's not the end of the earth, et cetera, et cetera. Anyway, let's say that takes me up to age 21.

Baillieul:

Okay. So just picking up on that, that transitions neatly to your alma mater, where you spent a significant fraction of your education. And this reminds me, you probably played football for the Mighty Case Western football team.

Brockett:

I did; I played football and basketball and got varsity letters in both. I was not great at either one of those by any means, but I deeply enjoyed it. And I think I kept myself healthy in the process. But about college, I majored in engineering science, which was appealing to me because it was all, it convinced me that it was all-encompassing. Now of course that's silly, but it did appear to be the most encompassing major that I was, would've been able to take. And my only goal in college really was to understand things. I didn't have any particular interest in grades. I didn't have any particular career path in mind either. But I did want to gain the understanding of as much stuff as I could because it was interesting, not because I was particularly interested in pleasing anyone, but just because it was interesting.

Baillieul:

And you liked it well enough that you kept doing it, because you—

Brockett:

Oh, I liked it, yeah.

Baillieul:

You have a number of degrees from Case.

Brockett:

Yes, three degrees in seven years.

Baillieul:

Three degrees, yeah.

Brockett:

But I would like to say, if and when we're going to leave Case, I would like to say that I was extremely fortunate in terms of the timing of my coming of age, so to speak, and the people that I was able to interact with. And again, not necessarily because they were absolutely astoundingly brilliant people, but because they cared. For example, in 1957, Sputnik went up. Now that doesn't happen every year; it happens once in a lifetime, anybody's lifetime. It happens once. What was the effect of that? Well, the next year Congress passed the National Defense Education Act. As part of that, they made available a bunch of fellowships, three-year fellowships, to go to graduate school so we could catch up with the Russians. Now, that might or might not have been the right thing to do at the time. But I received one of those fellowships as soon as I graduated with my bachelor's degree. And between the time that my wife and I got married and I started graduate school and the time we finished our formal education we had saved enough money for the down payment of our first house. Graduate students nowadays are not so fortunate in that regard. They often graduate with huge debts. And it just is incomparable and amazing that such a disparity should be allowed to exist over such a short period of time. I can go on and tell you a bit more about how it happened that Case was able to garner eight of these National Defense Education scholarships. Donald P. Eckman, people probably know the name but little else about him, he started the Systems Research Center at Case about 1960. And he's now known because the, Donald P. Eckman Award is named after him. But he was a chemical engineer by trade and started the Systems Research Center as a bold initiative. Nothing like that existed, certainly not at Case, and I think perhaps not at that time anywhere else in the nation. That together with the scare that the Russians put into some people who mattered in the US, he was able to write a proposal and get some of these fellowships. And he also was able to hire some people who would not, would not necessarily be the first person you would think of. For example, my advisor Mike Mesarovic was a Serbian electrical engineer who was a bit of a renegade in the sense that he told me that he was assigned to go to a job in a mine doing something or other when he graduated with his Ph.D. And he said no, I'm not going to do that. And he eventually worked his way into a position as a researcher at MIT. And then he was hired by Case. But in any case, Mike was extremely supportive, very visionary, not very much on details, but very much a visionary. You ought to think big. Don't think small; think big. His thinking was instrumental in broadening my horizons. For example, Case brought in with his help, and with Eckman's help, researchers from the Soviet Union that were at the top of their field. They came with a person to keep them in tow so they didn't defect. But anyway, so you might be be sitting around the room with a few scientists and one enforcer. And this was, this was enlightening. It made you feel like this was important stuff. That's important.

Baillieul:

Did you, following up on this train of thought, did you go to Moscow in 1960?

Brockett:

Regrettably not. Mesarovic did and Eckman did, and they liked to tell the story that they came from the far corners of the earth and met at a statue in Stockholm and then went together to Moscow. But I heard about it. In the library we had the proceedings of that conference. But regrettably not, I was not in attendance.

Baillieul:

Just for people who are watching the video, we're sitting here at the beautiful new building at Harvard University, the School of Engineering, and it's August 2021. And what we're recalling is IFAC, the very first International Federation of Automatic Control, in Moscow. And this is another place where people from the Soviet Union and the US who were interested in the kinds of engineering questions that enabled Sputnik and enabled subsequent space programs, so it was a very heady time. And so this is pretty exciting to have lived through that.

Brockett:

Absolutely, absolutely true.

Baillieul:

One of the things that I noticed too about this is that Mike Mesarovic, your mentor at Case, is still with us. He's 92 years old?

Brockett:

Regrettably not. He—

Baillieul:

Oh, is that true?

Brockett:

He died about a year ago. He was a supportive person but more interested in big pictures like the Club of Rome and things like that. He had a charming wife, and she predeceased him and he was not quite the same after that.

Baillieul:

Well, that's too bad. I'm sorry that I have out-of-date information on that. Just to pick up on this a little bit before we leave Case, you've been a very loyal alumnus, and you've done a lot for the institution, I think. Anything you want to share?

Brockett:

Well I served on their visiting committee for a while, but I would say the following thing about Case. I think that they had a very dynamic president, T. Keith Glennan, in the years that I was there as a student. And I think they were not so fortunate in the intermediate years. But now I think they're back on track again. And I did spend some time on their visiting committee. I don't think I was terribly effective, sorry to say.

Baillieul:

You're probably being too modest.

Brockett:

I'll repeat that. But I think they're on a good path, a much better path now and that they will rise again.

Baillieul:

So you mentioned that you were drawn very much to engineering to understand how things work. But a lot of people who've known you professionally throughout the years think of you as somebody who kind of moved into mathematics. And in some ways, you've seen to have similar characteristics to the late great Raoul Bott, who was trained as an electrical engineer but became a very well-known mathematician. Do you want to talk anything about that transition?

Brockett:

Well any comparison of that nature is welcome. I have enormous respect for Raoul Bott. Let me say a bit about that sort of thing. When I took my first job at MIT, and that was 1963, anyway, again by contrast with today's job market, I want to tell people that I never wrote an application. What happened was is that my advisor invited the chairman of the electrical engineering department of MIT to give a talk at Case. Peter Elias and I sat down for about an hour talking about things. And very soon thereafter I got a letter in the mail appointing me assistant professor at MIT. It's not going to happen again, I don't think. And if you wanted to make the argument that I was just lucky, not going to argue with you. I have been extremely lucky in that respect. Anyway, I went to MIT, and that was really exciting. Big names, lots of them around every corner. Lots of ambitious people, and that was good, and I enjoyed that a lot. New beginnings are always ripe with possibilities, and it's hard to say no to anything when it's new, and that was great. I appreciated my time at MIT very much. And you might ask, as I have been often why did you, you're an engineer, why did you leave MIT to go to Harvard? Harvard's not so much known for engineering. That was dumb. Why did you do that? I can tell you the reason. I thought that I would have fewer committees to go to and I would have more time to think, and I would have to write fewer proposals. Now, that last part was only true for a short time, but the other parts were more or less sound thinking on my part. And so after six very exciting years at MIT, and I should say something about that period as far as automatic control is concerned, and that is that at the same time or very nearly the same time that I went to MIT, the famous group at RIAS, the Research Institute for Advanced Study, organized by the Martin Marietta company, their people moved to Brown University. And Brown is only 50 miles away or something like that. And so we used to have joint seminars. And so I got to know Solomon Lefschetz that way, who is Raoul Bott's equal perhaps in terms of mathematical chops, and Harold Kushner, Murray Wonham, and I'm sure I'm forgetting important people. Oh, Joe LaSalle and so forth. So anyway, we had joint seminars and also included Larry Ho and Art Bryson from Harvard. And that was, that was enlightening and broadening of horizons and so forth and so on. So there was a little nexus there which was important in terms of broadening people's view as to what research ought to be. All that was before I came to Harvard. So why did I come to Harvard? I told you that. Did I have buyer's remorse? No. I think one thing that people need to understand is that if you put too many like-minded expertise in a small space, you encourage people to become narrow. And if you have room to expand like a nice gas in an open container, then they can explore various parts of the universe that they might otherwise not. And I think I lived that.

Baillieul:

So one of the things that certainly you did and as far as I recall from just being around you in those days a little bit after you came to Harvard, is that you became very focused, and you became a focal point for thinking about nonlinear control in a way that was different from what most people thought of as nonlinear control in years prior to that. And there was quite a little group that grew up around that, of people that visited and that you interacted with. Do you want to reflect on any of that?

Brockett:

I do. I do; I do. And let me start just a few years earlier. While I was at MIT, I had directed some ten or so Ph.D. students. Among them was Jan Willems, his twin brother Jacques had earlier done a master's thesis with me earlier. Jan went on to have an absolutely pivotal career in European Control and was a joy to work with and to have as a student. He was, and his brother also, very imaginative, very inventive. And we wrote some papers together I'm very happy about. I was working at that point in stability theory, where the only interesting problems are nonlinear. Aspects of that theory were made famous by a Russian by the name of Aizerman. He made a conjecture that was easily shown to be wrong. But nonetheless, in trying to make it right, there was a lot of imaginative stuff, especially by the group at Brown that I mentioned earlier. I had a taste of success there, and I wanted to do something equally, dare I say flamboyant, I don't know what the right word is when you're talking about science. But I didn't want to do a small thing; I wanted to do a big thing. And so I felt that it was necessary really to do something quite, quite novel. And at that time, due to the electrical engineering department at MIT having such close relationship with Lincoln Laboratory, I had some consulting arrangement with them, and the area where I was consulting was on satellites. And there were a couple aspects of satellite control that were of interest to them. The first was how to keep a satellite fixed at a certain point over the earth, given that you could only make observations accurately a few times a day or maybe even once a day. And given the fact that contrary to what Physics 101 says, the earth is not perfectly round. It has concentrations of mass here and there, and so it looks more like an oblate spheroid. A geocentric satellite would, left to its own desire, drift backwards to a place over Mexico, or if were on the other side, back to Mexico. But they didn't want Mexico; they wanted middle Atlantic. So how do you keep a satellite in place, using gas thrusters to keep it over the middle of the Atlantic? That was a problem I worked on a bit. And the problem was good in the sense that it was almost linear, and I worked out those equations in such a simplified form that it was, that I actually used that problem in my textbook that you mentioned earlier. Anyway, that was one.

But the other part of the problem was is it, satellites have antennas on them, and you want the antenna to be pointed at the earth, not somewhere else. And so you're trying to control rigid body dynamics. And this set me on the path of how do you control something whose intrinsic geometry is the space of all orientations rather than some nice, neat vector space? And that played a huge role in the next 15 years my life. But I didn't answer your question yet. Graduate students, graduate students have been the lifeblood of my existence, you mentioned 62, but who's counting? Anyway, there were students that contributed in very different ways to the way I thought about the world. But let me say that I found them energizing and fun to work with. And to the extent that I helped put them on career paths that they could then sustain, I feel proud. I mentioned Jan and Jacques and failed to mention many others. But once I moved to Harvard, one of the things that was good is that we had some money for students. And, accidentally, we had some money that would allow us to bring post-docs. And so when I first came to Harvard, we had, I'll mention a few names here, Sussman and Jurjevic and Krenner and Paul Fuhrmann and oh, the list could go on, but an important part of the mix was the graduate students many who have gone on to have extremely successful careers by the measures I understand. People like Alan Willsky, who was a full professor at MIT. David Dobkin who was the dean of the Faculty of Arts and Sciences at Princeton for eight years or so. And I mentioned Jacques before. He was the director of the University of Ghent for a couple of terms, lasting about a decade. And then on the more scientific side, John Baras, who started the Engineering Research Center sponsored by the National Science Foundation in the first batch of these. John, was generous enough to include Harvard's program with that, and we benefited by that funding for a long time. I might mention Krishnaprasad, Tony Bloch, and John Baillieul, all of whom worked on a variety of problems. I tried not to have people do the same thing. And that again is a way that you can keep yourself alive by not falling into the trap of becoming too narrow.

Baillieul:

Yeah, I think back on your careers, in the cohort would turn over a bit, and the sociology of the place would change a little bit. But I do remember being there with Krishna and John Baras and David Dobkin. That was a pretty rich experience, actually. So we're coming somewhat toward the, I think the end of the hour.

Brockett:

No, you're not. No, you're not.

Baillieul:

And there are other things to talk about.

Brockett:

I want to talk about more things.

Baillieul:

All right, all right. So I can feed you another question, but I think maybe you can improvise.

Brockett:

Well, what I want to address is the fact that around the early '80s I decided that I had done what I thought was interesting enough to do in the area of differential geometry. And I decided to start a robotics lab. Now this was an abrupt change, and the opportunity for failure was certainly there if you looked at it from the outside. I didn't entertain that possibility myself. But you could say why would you do something where other people already have a head start on you and the people at Carnegie Mellon and so forth were well ahead? Why did you do this? I think there are three reasons. I want to mention three important reasons, one of them is that I thought that nonlinear control had entered a sort of a Baroque stage, and I didn't want to do that anymore. Another one was, is that our two older children were approaching college; they had been early adopters in the personal computer world and had filled our house with such things for some time. I saw how exciting they found it, and I didn't think they shared that same excitement for different geometry. So I said well gee, if I'm going to interact with the, the now generation, maybe it would be better to do something that's more now-like. It's also true that about the same time the Engineering Research Center was beginning to get funded. Part of the plan for that was that there was supposed to be joint industry-university collaboration. Now, I didn't believe this could work and I was, I was paying lip service to it to some extent, not flattering but anyway. I thought that if I were going to make the case that we were on board with this, I had to do something that industry cared about. So I broadened my view of robotics to include computer vision. This was more or less response to NSF, personal considerations, and boredom. So the big challenges were how do you set up a laboratory? You need space, you need equipment, you need a certain size of operation. You cannot have a one-man robotics laboratory. The cost of the equipment is simply too big. You need to amortize that, and you need space. So as people often say about university, space is the last frontier. You have to struggle for it oftentimes, but not in my case because I was lucky. The Dean provided space without any struggle. My previous sponsors, particularly people in the Army Research Office, were forthcoming with the kind of help that was needed. And amazingly enough, there was a heretofore hidden, but present nonetheless, group of people at Harvard who were interested and felt like they wanted to be part of this. And of course, as you know, you played a role in that also by starting the laboratory and spent, I don't know, one year working on it?

Baillieul:

It was a year, yeah.

Brockett:

You, spent a year here helping make that get off the ground. If people want to know why, a former student of mine said one time when I was starting the robotics laboratory why don't you leave that stuff to other people and just concentrate on research? I can say now, 20, 30, 40 years later, is that out of that research came two things that, have been kindly received by the research community. One of them is, relates to the kinematic chain idea. In robotics for years and years and years, people had thought about kinematic chains in a sort of idiosyncratic way. What I noticed early on was is that you could describe these things as a product of elements of a Lie group. And then it was quite easy to say what the problems were. The notation instead of being a page long became a line long. And that was good, and I loved it. And it still has found its way into textbooks, more than one, and that makes me happy.

Second thing is, is that so far as computer vision is concerned, one of the problems is that if two, two pictures are taken of the same thing but the camera is a little bit one way or another, you might want to put those in alignment. And one thing that you could ask is if I make a distance-preserving transformation, that is an orthogonal transformation, to try to line up the pictures, what is that transformation that would do it with ending up with the least error after you registered them? There's going to be some error because life is like that. But how can you minimize that through an orthogonal transformation? And that simple question led me to think and think and think. And I was sitting in the women's faculty club in Berkeley, California, and I realized that I could write the steepest descent equation in such a simple way. And that turned out, again luckily no forethought on my part, but luckily the equation turned out to be related to integral systems, related to algorithms for finding eigenvalues of matrices, et cetera, et cetera. And it lives today, among other ways, in a textbook written by Uwe Helmke and John Moore and other places as well. So message, change fields with confidence, and don't get in a rut. Interesting stuff is everywhere.

Baillieul:

Okay, so we're coming to the end of the hour, and the question is what does the future hold?

Brockett:

Well, there are certainly no shortage of possibilities. Medicine, quantum mechanics, nano, automobile control, driverless cars, you name it. Problem is how to take these questions and put them into a form that is mathematically amenable. So as an example, the 2012 Nobel Prize in molecular biology or some such, was given to a Japanese person by the name of Yamanaka. The clever thing that he did was to change a a skin cell, which is a totally differentiated cell back into a stem cell, which is pluripotent cell. He did this in a way that required patience. He tried a large number of possible transcription factors to effect the change and he found a combination of four that would do this job. I've worked on possibilities for formulating this problem mathematically as a control problem and finding out which sequence of transcription factors in which order would make this transition as efficient as possible. Now, whatever model one uses, and this was joint work with people at the medical school at the University of Michigan, whatever methods we were using were highly approximate. It's a very complicated stuff if you want to model it in detail. So maybe the mathematics will work, and if it does, it'll be a substantial contribution. If not, we'll have to build a better model.

Baillieul:

Okay, thanks very much.

Brockett:

You're welcome.

Baillieul:

And I think it's a very positive note that if you define systems and control broadly enough, all of these things are part of the mix.

Brockett:

Thank you, John. Thank you very much.

Baillieul:

Okay.