Interaction between a robot and Bunimovich stadium billiards

The robot–environment–task triad provides many opportunities to revisit physical problems with fresh eyes. Hence, we develop a simple experiment to observe chaos in classical billiards with a macroscopic 3.38-m long setup. Using a digital video camera, one records the dynamic time evolution of the interaction between a robot and Bunimovich stadium billiards with specular reflection. From the experimental time series, we calculate the Lyapunov exponent λ as a function of a geometric parameter. The results are in concordance with theoretical predictions. In addition, we determine the Poincaré surface of section from the experimental data and check its sensitivity to the initial conditions as a function of time.