Can a robot be a better waiter than a human being? To answer this question, Dr. Luis Figueredo, senior scientist in the team of Prof. Sami Haddadin, sets up a robotic arm from the specialized robot maker Franka Emika on a table and hooks up a computer.
The robot’s hand grips a glass filled to the brim with water, raises it and rocks it back and forth without spilling a drop. “And it does it faster and more safely than a person,” says the scientist from the Munich Institute of Robotics and Machine Intelligence (MIRMI) of TUM.
Copying the motion of the Moroccan tea tray
How does it work? The team simply fed the robot with algebraic formulas dating back several centuries. They based their mathematics on a Moroccan tea tray that applies the principle of a spherical pendulum. With doctoral candidate Riddhiman Laha and masters student Rafael I. Cabral Muchacho, Figueredo embeds the dynamics of a spherical pendulum into the robot’s control software. That also means that the robot’s movements are limited by the basic principles of geometry. With his team, he also integrates the correct angles, speeds and accelerations into the model. “When you understand how a pendulum moves and know how it works, it is suddenly quite simple,” says Figueredo.
The mathematics of a pendulum: a simple solution to a complex problem
The science of “slosh-free movement” is a complex field. “Most approaches have focused mainly on limiting acceleration to keep the sloshing of liquids under control. Or they have worked with fluid dynamics to calculate how these substances behave in order to predict the trajectories,” explains Figueredo: “That takes at least a few minutes, if not hours, and the result is still uncertain.”
Image: Dr. Luis Figueredo of the robotics institute MIRMI at Technical University Munich (TUM) teaches a robot to carry a full glas of water without spilling. Photo: Wolfgang Maria Weber / TUM