  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 this 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 a finite time. Lastly, we discuss the
effect of asymmetric uniform quantization on rigid formation control.

Systems and Control