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Relatively Prime Recap: Season 2, Episode 6: Principia Metropolica

Principia Metropolica

I’ve been looking forward to this one: cities in the mathematical domain. This is the kind of applied maths I can really get behind.

Samuel starts with Mike Batty of University College, London’s Centre for Advanced Spatial Analysis discussing how cities grow and organise themselves. The structure is frequently fractal; how does one calculate the dimension of a city?

From a top-level view of cities, he moves on to a low-level description of one of the biggest problem in cities: traffic (another thing that fascinates me). We get a glimpse of traffic waves, and the unfairness that the person responsible for the average jam doesn’t suffer from the effects. And we learn that Gábor Orosz (University of Michigan) tests his hypotheses using robots as well as simulations.

‘RightingBot’ simulates the way lizards right themselves when falling


RightingBot. Credit: Tom Libby

Lizards, just like cats, have a knack for landing on their feet when they fall. But unlike cats, which twist and bend their torsos to turn in the air, lizards swing their large tails one way to rotate their body the other, according to a recent study. And the longer the tail, the smaller the movement needed. The study used high-speed video, developed a mathematical model and finally used this to develop a lizard-inspired robot, called ‘RightingBot’, which replicates the feat.

Robot choreography and coupled oscillators

Nao robots are a programmable standard model of small scale humanoid robot by French firm Aldebaran Robotics, and they are used for, among other things, the RoboCup soccer tournament to provide a standard platform to compare programming skills. Anyone paying attention to robot/dancing-related news on the internet will be aware that Nao robots have been trained to do synchronised dance routines, although such routines are usually pre-programmed.

Patrick Bechon and Jean-Jacques Slotine, from MIT, have developed a means to link a group of robots, using coupled oscillators, so that a dance routine can be followed and synchronised – so a robot which gets disturbed during the piece can rejoin at the right point, as demonstrated beautifully in the video below. The robots use Network Time Protocol to synchronise their clocks, and while other co-operative programs have been seen before (not least, in the RoboCup where the team works together), this new work involves strong synchronisation, which means even if there’s a delay in loading the programme or transmitting between robots, or if a new robot is added during the choreography, they are still all in time with each other. Plus, they’re pretty cute.

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Source: Robot Choreography on MetaSD

Paper: Synchronization and quorum sensing in a swarm of humanoid robots