The RoBeetle runs for over an hour
weights 88 milligram. It runs on methanole as a
power source. Methanole is an alcohol which can be found in some solvents or antifreeze.
Sciencemag. The artificial muscle can contract and relax.
Nickel-titanium alloy wires covered in a platinum powder speed up the burning of methanol vapor
producing heat, which causes wires in the robot's legs to shorten.
Here is the article.
And here is a video:
From the calculus point of view the following graphics from the article is interesting.
It shows the position as a function of time.