Lego Car

A. Fehnker, Miaomiao Zhang and F.W. Vaandrager. Modeling and Verifying a Lego Car Using Hybrid I/O Automata. In Third International Conference on Quality Software (QSIC 2003), Dallas, Texas, USA, November 6 - 7, IEEE Computer Society Press, 2003. To appear. Full version in M. Broy and M. Pizka, editors. Models, Algebras, and Logic of Engineering Software, Nato ASI Series III: Computer and Systems Sciences, Volume 191, pages 385-402, IOS Press, 2003. Also available as Technical Report NIII-R0308, University of Nijmegen, March 2003.


We illustrate the application of the hybrid I/O automata framework of Lynch, Segala & Vaandrager by using it to model and analyze the behavior of a simple Lego car with caterpillar treads. We derive constraints on the values of the parameters that occur in our hybrid model that guarantee that the car will always move forward along a black tape, and will never get off the tape or move backward. In order to simplify the correctness proof, we introduce a transition systems that abstracts from the hybrid automaton in a rather drastic manner, but still preserves validity of the correctness properties in which we are interested. Even though our original model does not involve any disturbances, the general parametric analysis of the system allows us to exend our results in a trivial manner to a hybrid model in which several disturbances are allowed (mistakes in measurements of lengths, drift and jitter of the hardware clock, velocity, and distance between the two caterpillar treads).

Postscript version technical report (This is the latest version, a minor mistake and some typos in the version that appears the Marktoberdorf proceedings have been corrected.)