Maths in 3D

[Music plays and the Maths inside, UTS, AAMT and CSIRO logos and text appears: Investigating the maths inside, Maths in 3D]

 

[Image appears of a hand, writing with a pencil and then the camera zooms out to show the formulas that are being written]

 

[Image changes to show Robert Zlot writing on a piece of paper and the camera zooms in on Robert’s hand as he writes]

 

Robert Zlot: When I was a child growing up in Canada, I was never really sure that this is what I wanted to do as a profession.

 

[Image changes to show Robert seated and working at a desk and then the image changes to show a close-up of Robert in a car]

 

I had a pretty ordinary childhood.

 

[Image shows views of Robert driving the car and then the image changes to show a view through the side window and then the front windscreen]

 

I liked to play outside, riding my bike, playing sports. I particularly enjoyed playing video games which back then in the ‘80s were a bit different than they are now.

 

[Images move through of Robert’s head as he drives and Robert’s face in the rear vision mirror and then the image changes to show Robert walking into a factory building as the roller door opens]

 

My parents really encouraged me in maths and science and by the time I got through high school and into university, that gave me a lot of opportunities and options.

 

[Image changes to show a close-up of Robert’s face and text appears Robert Zlot, Research Scientist, CSIRO]

 

Hi, I’m Robert Zlot and I’m a Robotics Research Scientist.

 

[Music plays and the image changes to show a 3D laser image of a boat and formulas in the background and text appears across the image: #MATHEMATICS]

 

[Images move through of a rear view of Robert walking through an office, sitting at a desk, working on a computer, a robotic vehicle and a sign which reads: Queensland Centre for Advanced Technologies]

 

I first came to Australia in 2007 and that was after completing a PhD programme in the US which is really where I learnt how to be a researcher and a lot of what I know about robotics, the CSIRO Field Robotics Group, they’re internationally known, and I was aware of the research that they were doing.

 

[Images move through of a hand picking up the Zebedee laser]

 

Zebedee is a 3D laser mapping system.

 

[Image changes to show a close-up of Robert’s face and then the camera zooms out to show Robert talking to the camera]

 

It’s a device that you can hold in your hand, walk through an environment and it will capture measurements of the environment as you go.

[Image changes to show a large robotic vehicle and then the camera zooms in on a “Danger” sign on the vehicle and then the image shows Robert moving the Zebedee scanner around while he walks]

 

Originally, we were looking at how we can take a laser scanner which was much larger than the one on Zebedee and have it continuously moving while on a vehicle that’s driving around and still build maps without the vehicle having to stop to take measurements.

 

[Image changes to show Robert talking to the camera]

 

The big issue was how can we downsize the technology from an autonomous vehicle to something that a person walking, or crawling, or climbing through a cave can carry with them.

 

[Camera zooms in on Robert talking and displaying a small laser scanner being waved around and then the image changes to show Robert walking along and scanning with the laser]

 

So, we started to look at these smaller laser scanners and we thought, “Well, you can kind of wave it around like a torch and paint the laser as effectively onto the cave surface”.

 

[Image changes to show a male walking through bushland waving a laser scanner around and then the image changes to show a male walking around a shipwreck on a beach and waving the laser scanner]

 

And obviously if you’re doing this for hours on end you get very tired and that’s when we though of this idea of putting a spring on it.

 

[Image changes to show Robert demonstrating with the Zebedee scanner and then the camera zooms in on Robert as he holds up the scanner]

 

The device up here at the top of Zebedee is a laser scanner and how it works is it fires an infra-red laser pulse inside it and that fires about 40,000 times every second.

 

[Image changes to show a 3-D laser image of the shipwreck and the image shows the laser moving around the ship]

 

And inside there’s a mirror that spins around, 100 times per second and that deflects the laser to various surfaces around the environment.

 

[Image changes to show Robert talking to the camera as he holds the Zebedee scanner]

 

And every single pulse that it makes is actually taking a measurement of how far away that surface is. It’s using a principle called Time of Flight.

 

[Camera zooms in on Robert as he talks]

 

Time of Flight means that if you measure how long that that pulse takes to come back to the laser you can use that time to work out how far away that surface is because you know what the speed of light is.

 

[Image changes to show Robert walking along inside a warehouse waving the Zebedee scanner around]

 

And you need to measure that time so precisely because if you’re off by even one millionth of a second, you’ll be off by 300 metres in your measurement.

 

[Image changes to show a Point Cloud Map and the image shows lines moving over the map as the camera pans over the map]

 

The type of maps that we produce are called Point Cloud Maps. Point Clouds just means it’s a collection of point measurements.

 

[Image changes to show Robert talking to the camera and then the image changes to show Robert sitting down in front of a computer at a desk]

 

So, if you consider a single surface in the environment, we’ll have a lot of dots that represent that surface. The processing software can process the data faster than it’s collected.

 

[Image changes to show a rear and then profile view of Robert working on a computer]

 

So, if we collect the data, say that takes 15 minutes, we can process it even faster than that.

 

[Camera zooms in on Robert’s hands typing on the keyboard]

 

And that also means if we wanted to we could actually build the map as we are walking with the device.

 

[Image changes to show Robert talking to the camera and holding up the Zebedee scanner]

 

It just doesn’t work that way right now.

 

[Image changes to show a 3-D laser scan image map of bushland and then the image changes to show formulas written on a whiteboard]

 

Mathematics is fundamental to so much of research in computer science and robotics.

 

[Camera pans to the right over the whiteboard showing formulas, line graphs and formulas again]

 

You might think that computers can do all of this for you but we’re trying to develop new things, the next generation of what computers can do for you.

 

[Image changes to show a close-up of the Zebedee scanner and then the image changes to show a hand, writing formulas on paper]

 

If you think about all of the, the software and the programming that goes into it, a lot of that is mathematically based.

 

[Images move through of different 3-D laser scan images and the image shows the images moving around and rotating]

 

Generally programming itself has a lot of math behind it. In, specifically we’re doing a lot of modelling of geometry and spatial math including trigonometry, calculus. There are things called transformations and rotations.

 

[The image changes to show a Point Cloud Map and the image shows lines moving over the map as the camera pans over the map]

 

The laser scanner on Zebedee is measuring ranges around the environment and ranges in themselves they don’t tell you sort of where things are, relative to each other.

 

[Image changes to show Robert holding up a Zebedee scanner and talking to the camera]

 

In order to do that we need to know the angles that each measurement is taken at and also the position where it’s taken.

 

 

[Image changes to show a 3-D laser scan map and then the image shows different views of the laser map]

 

Calculus is a very important subject that is integral to how the software works for processing the data.

 

[Images move through of Robert talking to the camera, a rear view of a male walking through bushland and the laser scan map of the bushland]

 

What we really want to know is exactly where the scanner was at what time and what orientation it was facing and in order to do that, the analysis for that looks at how infinitesimal motions of the scanner would affect where the measurements are in the world.

 

[Image changes to show a close-up of Robert talking to the camera and then the image changes to show a 3-D laser scan map of a building]

 

So, if you think about it, it’s how small changes in x affect y which is your map. So, a lot of the software is using calculus at the core to try do that analysis and minimise sort of the errors in the measurements that we’re taking.

 

[Images move through of a rear view of Robert walking, Robert and a colleague working on a computer and a close-up of Robert and the colleague]

 

One user locally here in Australia is the Queensland Police Service and they’ve been using it for crime scene forensics.

 

[Image changes to show Robert talking to the camera]

 

So, after a crime occurs, they can actually take a Zebedee scanner into the scene, collect the data and they can use that for further analysis and measurements of the crime scene.

 

[Images move through of a rear view of a male walking down some stairs and waving the laser around as he walks and a facing view of the male walking along through a building]

 

A firm understanding of mathematics is becoming more and more important in today’s workplace.

 

[Images move through to show a side view of Robert talking to the camera, text which reads, “Zebedee Handheld 3D Scanning”, a laptop being packed into a bag and Robert moving the scanner]

 

Computers can do a lot of autonomous processing, crunching numbers together, but it’s really the creative aspect of developing the next generation technology that requires an understanding of the mathematical principles and a way to do new things that computers can’t do yet.

 

[Images move through of Robert working on a computer, Robert talking to the camera and Robert working at the computer again]

 

You might be looking at part of your math curriculum and wondering how is this particular thing useful.

 

[Images move through of Robert talking to the camera]

 

And you may not know the answer to that, and your friends may not know the answer, and your teacher may not know the answer but in ten or 15 years from now you might be working in a job and a new problem comes along that you haven’t seen before and then suddenly you remember back that you have the tools for this.

 

[Camera zooms in on Robert talking to the camera]

 

There is something that you’ve learned that you haven’t used in a few years that’s completely relevant to solve this.

 

[Music plays and the Maths Inside logo and text appears: Investigating the maths inside, Maths Inside is a project led by University of Technology Sydney, and funded by the Commonwealth Department of Education and Training under the Australian Maths and Sciences Partnership Program, The aim of Maths Inside is to increase engagement of secondary school students in mathematics, by using rich tasks that show the ways it is used in real world applications, To find out more about this project and other AMSPP resources, please go to http://dimensions.aamt.edu.au, Maths Inside 2016 except where otherwise indicated, the Maths Inside materials may be used, reproduced, communicated and adapted free of charge for non-commercial educational purposes provided all acknowledgements associated with the material are retained, Maths Inside is a UTS project in collaboration with CSIRO and AAMT]