Keeping robots in perfect formation

PhD candidate Ewoud Vos has created a very useful spring and damper system. It controls the movement of robots or satellites and consists entirely of mathematical algorithms. It could also provide the brainpower for the next generation of Google Cars. PhD candidate Ewoud Vos has created a very useful spring and damper system. It controls the movement of robots or satellites and consists entirely of mathematical algorithms. It could also provide the brainpower for the next generation of Google Cars.

Have you ever considered how much mathematics is involved in your car? It’s not just the dimensions or the amount of horsepower produced by the engine that need maths to express them. Cruise control, for example, is much more than a button: it’s a complex algorithm that keeps your speed constant. The control of such dynamical systems is a field of study in which mathematicians take the lead, but it also has close links with technology.

Vos’s PhD research is at the intersection of maths and technology, and was conducted at the Engineering and Technology Institute Groningen (ENTEG) and the Johann Bernoulli Institute for Mathematics and Computer Science (JBI). His project is part of the programme ‘Autonomous Sensor Systems’, which is funded by technology foundation STW.

‘The project we took on was the design of a group of autonomous robots that could inspect dikes’, says Vos. ‘There are some 17,000 kilometres of dikes in the Netherlands, and some of them are centuries old, so we don’t really know what they are made of.’ Human inspectors can’t look into the dikes, and it takes them a lot of time to walk the total distance. So a ‘multi-agent system’ of autonomous robots fitted with sensors seemed like a good alternative.

The requirements for these dike-inspecting droids are complex. They need to travel along the dikes in a formation that allows them to make a complete scan of the interior. ‘But we didn’t want a central control system that would make it vulnerable, so each robot only communicates with its direct neighbours.’

Now a robot moving along a dike is no simple system, especially when a lot of them work together as a multi-agent system. That is why these systems are often simplified in control theory. ‘They are represented as linear systems or mere points, while in reality they are non-linear’, explains Vos.

Simplifying systems makes it easier to handle the maths, but harder to implement such systems in the real world. ‘For example, a basic four-wheel robot cannot move sideways. If your control system isn’t aware of this, it could leave your robot in deadlock.’ Vos therefore chose another method to control his robot team, a method pioneered by one of his supervisors, University of Groningen mathematician Arjan van der Schaft.

Vos designed a virtual spring and damper, which exerts a force to keep the robots at the pre-programmed distance. ‘If they are too far apart, the spring will pull them together, and if they are too close, it will push them away from each other.’ Vos used what is known as a port- Hamiltonian framework to design and analyze the system.

This framework uses a physical structure to control the system. This approach, in which control is expressed as a force exerted on the system, also allowed Vos to prove mathematically that his control system is stable. ‘We can prove that the added energy plus the internal energy of the system are always equal to or greater than the final energy, which means it is stable.’ When using the simplified approaches, it is very difficult to provide mathematical proof of a system’s stability. ‘And that means you need to do much more testing.’

Under the supervision of Jacquelien Scherpen, Professor of Discrete Technology and Production Automation and Director of the Engineering and Technology Institute Groningen (ENTEG), Vos used the virtual springs to design a control system for a team of robotic dike inspectors. His algorithms will be the brains for a robot designed by a colleague at the University of Twente, who is also on the STW project.

The virtual spring isn’t limited to moving robots. ‘Other partners in the project are SRON Space Research Institute. They envisage sending a group of telescopes into space that will work together to form one huge telescope. But to do that, they have to fly in a tightly controlled formation.’ Another off-world application is a control system for a future Mars Rover, which has the interest of the European Space Agency (ESA).

The system would also be ideal to control a ‘swarm’ of cars on the motorway. ‘Once you were on the motorway, the system would place a spring at the front and back of your car, so you wouldn’t have to worry about your speed.’ It would allow more cars to use the same stretch of motorway at a higher speed, an approach that is already being tested , albeit not with Vos’s algorithms. ‘But I think our system would prove safer and more robust than the current algorithms.’

Ewoud Vos will defend his thesis Formation Control in the Port-Hamiltonian Framework on 20 February.

Partners are Stichting IJkdijk, TNO, the European Space Agency (ESA), SRON Space Research, Controllab bv and DEMCON.