Quantization effects in rigid formation control

In this paper we discuss quantization effects in rigid formation control systems when target formations are described by inter-agent distances. Because of practical sensing and measurement constraints, we consider in the paper distance measurements in their quantized forms. We show that under gradient-based formation control, in the case of uniform quantization, the distance errors converge locally to a bounded set whose size depends on the quantization error, while in the case of logarithmic quantization, all distance errors converge locally to zero. A special quantizer involving the signum function is then considered with which all agents can only measure coarse distances in terms of binary information. In this case the formation converges locally to a target formation within finite time.