Control of one-dimensional guided formations using coarsely quantized information

Motivated by applications of platoon formations, the paper studies the problem of guiding mobile agents in a one-dimensional formation to their desired relative positions. Only coarsely quantized information is used which is communicated from a guidance system that monitors in real time the agents´ motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is firstly shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.