Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements
For researchers in multi-agent systems and control theory, this work provides theoretical guarantees for formation control under realistic quantized sensing, though it is an incremental extension of known gradient-based methods.
This paper studies how quantization of distance measurements affects rigid formation control systems, showing that uniform quantization leads to bounded distance errors, logarithmic quantization enables convergence to zero, and binary signum quantization yields finite-time convergence to the target formation.
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.