Understanding the dynamics of robots and living bodies
That’s Maths: Progress is being made in attempts to simulate such human functions as blood flow and movement
C-3PO: The Star Wars robot – described as a walking humanoid – was one of many robots discussed at a symposium in Izhevsk, east of Moscow, on mechanical and biological systems
The application of mathematics in biology is a flourishing research field. Most living organisms are far too complex to be modelled in their entirety, but great progress is under way in simulating individual organs and modelling specific functions such as blood flow and locomotion. Biologists and mathematicians each have their own distinct jargon and special efforts are needed to enable them to communicate. So, conferences are organised where experts from different areas try to overcome these barriers and collaborate effectively.
I recently attended such a conference in Izhevsk (about 1,000km east of Moscow), From Mechanical to Biological Systems: An Integrated Approach. It was an International Union of Theoretical and Applied Mechanics symposium. It brought together scientists in classical mechanics, biomechanics, control theory and robotics. The main goal was to promote an integrated approach to understanding the dynamics of mechanical systems such as robots on the one hand, and living bodies on the other.
The main force behind the symposium was Alexey Borisov, a brilliant applied mathematician and author of many books and papers. Alexey has built up the Institute of Computer Science at Udmurt State University in Izhevsk to be a world-class centre. He has also spearheaded a scientific translation and publishing programme. In my presentation, I mentioned John Jellett, one-time provost of Trinity College Dublin and president of the Royal Irish Academy.
Jellett worked on the mathematical theory of friction, and he derived an integral or a quantity that remains constant, relating to the angular momentum of the mechanical system that I was discussing.
Jellett’s book A Treatise on the Theory of Friction was published in Dublin in 1872. After the talk, I was greatly surprised and pleased to be presented with a Russian translation of this book, published in Izhevsk in 2009.
Borisov does not fit the shy, awkward stereotype of a mathematician – he is an accomplished accordion player. We were treated to a concert of accordion music and Russian dance, arranged by him.
A late-night party followed, where we had a chance to sample the local fare. Wine and brandy were in plentiful supply, but no Kalashnikov vodka, which was surprising – Izhevsk is the home of Mikhail Kalashnikov, who died late last year, and it is in this city that the infamous assault rifle the AK-47 is manufactured.
Several symposium talks discussed flagella and cilia – whiskers and tails, if you like – used by animals for many purposes, such as feeding, clearing the lungs and swimming. Robots have also been designed to use cilia for locomotion. The mechanism and modelling of robotic dynamics is a challenging area of interdisciplinary research that has thrown up several tough problems for applied mathematicians.
The robots described at the meeting were of many forms, from walking humanoids such as C-3PO in Star Wars to worm- like machines for cleaning pipe networks, from spherical vehicles that roll around driven by internal rotors to tiny, fish-like devices that may one day swim up your arm to mend your broken heart.