Abstract: This talk will highlight our work over the past decade on controlling robots by giving them simple rules to reflect off of obstacles in their environment. This line of work pushes the extreme limits of minimalism and is suitable for scenarios where there are limited sensing and actuation capabilities, such as consumer security robots and nanorobotics. We take heavy inspiration from dynamical billiards, a branch of mathematics pioneered by Hadamard, Artin, Sinai, and others, but adapt the bouncing laws to models that are easily achievable by robots and are amenable to algorithmic analysis. Our results include basic conditions for attractors and limit cycles, simple achievement of linear-temporal logic specifications, visibility-based algorithmic analysis, and demonstrations on embarrassingly cheap robot systems. An abundance of simple, open problems remain in this area.

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