Mathematics of Robotics Inspire Hutchinson

Robots seem inherently fascinating to humans, but Beckman Institute robotics researcher Seth Hutchinson is much more interested in the science behind the mechanical creations.

Robotics researcher Seth Hutchinson describes the action at his group's Beckman Institute Open House exhibit this way: "We have the little mobile robot chasing a red ball and kids play soccer with it. It's great fun until a kid with a red shirt gets in the arena. Then all bets are off as to who the robot is going to chase."

That image could serve as a snapshot for the current state of robotics since difficulties like distinguishing a ball from a child aren't limited to Hutchinson's Open House performer. In fact, the scene illustrates a broader problem that has dogged the field since researchers began making predictions in the 1960s about the potential robots had to improve our lives.

Hutchinson, a full-time faculty member in Beckman's Artificial Intelligence group and professor of Electrical and Computer Engineering, said that issues such as limited processing power and the challenge of mathematically accounting for every possible scenario a robot might face in navigating the world have proven far more difficult than any of the early robotics researchers expected.

"I never want to build a robot from scratch. I like to take them out of the box and use them."
- Seth Hutchinson.

"That's the reason you don't have robots out in the world doing interesting things, unless you consider vacuuming your floor while you're at work an interesting thing," he said.

If people get the impression that Hutchinson isn't all that excited about today's robots they would be correct, but it's a perspective grounded in nearly 20 years of doing high-level research in the field. He sits on the editorial boards of two robotics journals and is editor-in-chief of the IEEE Robotics and Automation Society journal. He has been at the Beckman Institute since 1990 focusing on robotics, an area that intrigues him because of the science underlying robots rather than the end products themselves.

"I never want to build a robot from scratch," he said. "I like to take them out of the box and use them."

And, Hutchinson says, most robotics researchers he knows would not ride shotgun on a robot-controlled road trip to Vegas: "I think most of us would not want to be in the passenger seat of a car driving in the desert, say for the extended trip to Vegas from L.A. A few of us would like to do that but I'm not on the list."

Hutchinson's comments about the general state of robots are reflective of a shift in attitude toward the mechanical critters over the past two decades. Except for that little vacuuming robot that stars in infomercials, robot development on a mass scale could be described as disappointing.

Some scientists and many science fiction writers going at least as far back as the 1940s had exciting visions of a future society bustling with multi-tasking robots. A seven-foot giant named Elektro captured the imagination of visitors to the 1939 New York World's Fair, while science fiction depictions from 1950s B films to TV shows like Lost in Space to more recent movies like the Star Wars series continued to paint robots as essential players in the future.

Academic papers on robotics were just as optimistic 40 to 50 years ago, drawing a fairly straight line from conceptualization to future machines that would approximate human beings in their cognitive capabilities and ability to perform tasks. While robotics have become an important component of modern industry, especially for repetitive tasks like those found on assembly lines, robots as an integral part of people's everyday lives have yet to materialize.

"Part of that is the fault of the robotics community that oversold expectations, starting in the 60s," Hutchinson said. "If you go back to the 1960s and read some Ph.D. dissertations from the major university Artificial Intelligence labs, you will find that they have titles like sensor-based robotics, or sensor-based manipulation of random parts using computer vision, and it sounds exactly like the end goal of what we are after."

Hutchinson said the early theories were too simple and the practical applications much more difficult than anyone realized.

"And yet they staked out this enormous turf with these big titles and buzzwords," he said. "At the same time, artificial intelligence was talking about how pretty soon computers will be playing chess with chess masters and who knows what all, automatic translation of French into Japanese. They just promised a lot and all those problems turned out to be much harder than anybody expected them to be."

As an example, Hutchinson said doing something as simple as going from his office to the Beckman Café for coffee would be a major undertaking for a robot and its computerized planning system.

"I probably have got 40 different joints my body I have to coordinate in order to do that," he said. "In the worst-case scenario the time it takes for a computer to figure out that plan, the best algorithm that we know to do it, takes an amount of time that grows exponentially with the number of joints in my body. So anything with a 40 in the exponent is too big."

Not that those types of difficulties were a bad thing, at least from Hutchinson's point of view.

"If robots are out doing all the stuff you want them to do, then why do you need robotics researchers?" Hutchinson said. "I like the fact that there are these really hard problems that we don't know how to solve that are fertile ground for generating new ideas and new kinds of mathematics."

It's the development of new kinds of mathematics for robotics that inspire Hutchinson. He says different people have different images of robots, so he summarizes his work for laymen this way: "I try to make robots do interesting tricks. When you say the word robot to somebody, you just don't know what image comes into their mind. It could be the mechanical system up at Ford Motor Company that's hammering bolts into cars, or it could be an android from Star Trek.

"After we get past that, what I normally tell people is that I work at the middle of sensing and planning and control. Planning is a very long term perspective for what a robot wants to figure out over the course of the next minutes or even days - what do I need to be doing; control is the short-term coordinating of motions, and then sensing is kind of the bridge between those things. What I like to do is coordinate those three levels of interaction with the environment."

Hutchinson earned a Ph.D. at Purdue in electrical engineering in 1988 and joined Illinois and Beckman in 1990 with a desire to concentrate on robotics. Like other robotics researchers around that time, he came to realize that limited processing power and the challenge of finding mathematical solutions for every possible uncertainty a robot could face were problems they weren't yet equipped to deal with on a practical level.

Hutchinson said approaches to robotics research began to change in the 1980s and 90s, and for him that change was instigated by former Beckman faculty member Jean Ponce. He said Ponce gave him a draft of a book by a Stanford professor shortly after he arrived at Beckman which described, among other things, a thesis from the 1980s that forced robotics researchers to take a hard look at the difficulties they were facing in trying to realize the potential that had been envisioned for robots.

"That was really good for us as a community because it said 'stop trying. You are not going to find the optimal and exact solution. Stop and look for practical and fast solutions' and that really revolutionized robotics," Hutchinson said. "I don't know if it happened instantaneously but it did sort of give a back slap of the hand to the community about how you are spending your efforts. Since then I think there has been enormous progress in what robots are able to do."

Hutchinson said that robotics research began changing when researchers "quit looking for exact and optimal solutions and we quit looking for guaranteed answers, the idea of a complete algorithm, an algorithm that gets you an answer every time an answer exists, and if there is no answer, it tells you so in finite time. Instead we started working on algorithms that give you an answer as good as they can find as quickly as they can find it. So now there is no guarantee."

With increased computing power beginning in the mid 1990s and a different approach to problems, Hutchinson said changes started to take place.

"That's when things really started to get interesting in robotics," he said. "In that period of time you started to see for the first time things like hand-eye coordination, robots that would put computer vision into the feedback loop so that they actually move and many times per second update their motion based on what they see."

Hutchinson said those developments are what have allowed robot advancements and research competitions like the DARPA Urban Grand Challenge that features autonomous vehicles making that trip from L.A. to Vegas.

"When you start taking advantage of the fact that the environment constrains what you can do and the computers are so fast, then you don't have to solve these worst-case problems where there is some kind of maze that you have to navigate through; then you can start to get practical solutions that really can work," Hutchinson said. "But we're not yet at the point where the practical solutions are very robust."

So Hutchinson works on interesting robotics challenges involving mathematics, geometry, and topics like vision-based motion trajectories and evasion and pursuit with visibility constraints. He gives an example of the latter from a robot's perspective: "Under what circumstance, for example, could I follow you around the Beckman Institute and never lose sight of you."

Those topics are of interest to Hutchinson because of the mathematics involved.

"They're pretty interesting problems that combine the mathematics of dynamical systems with geometry," he said. "You have these geometric constraints on whether or not I can see you or whether or not I can go through a doorway as opposed to encounter a wall. But then you also have the dynamical systems constraints (issues like the force and torque involved during acceleration.)

"That combination of dynamics and geometry makes it an interesting problem. It's not geared toward a specific application outcome. It's more geared toward can you write an interesting mathematics to describe it and can you solve the equations that come out of it."

Hutchinson said the work could result in creating algorithms for a robotic pursuer or for an evader, with a whole host of applications in industry and elsewhere. A pursuer could be used for safety purposes, such as following and monitoring a worker performing a hazardous job, or they could be used for surveillance purposes or in tandem with an evader robot for various missions.

"So they are useful for antagonistic as well as cooperative contexts," he said. "(Our work) doesn't always arrive to the physical robot but it does always arrive to some mathematical simulation that lets you show pretty movies on a computer."

And if someday solutions do lead to a physical robot that can live up to the models portrayed in countless science fiction tales, Hutchinson hopes he is not around.

"I do think ultimately the capabilities of robots will get to a place where I hope I'm dead before we get there," he said with a laugh. "They kill their masters first. If you watch any of these movies when things go bad, it's the robotic scientists who are the first to go."