Quantization effects on synchronized motion of teams of mobile agents with second-order dynamics

For a team of mobile agents governed by second-order dynamics, this paper studies how different quantizers affect the performances of consensus-type schemes to achieve synchronized collective motion. It is shown that when different types of quantizers are used for the exchange of relative position and velocity information between neighboring agents, different collective behaviors appear. Under the chosen logarithmic quantizers and with symmetric neighbor relationships, we prove that the agents’ velocities and positions get synchronized asymptotically. We show that under the chosen symmetric uniform quantizers and with symmetric neighbor relationships, the agents’ velocities converge to the same value asymptotically while the differences of their positions converge to a bounded set. We also show that when the uniform quantizers are not symmetric, the agents’ velocities may grow unboundedly. Through simulations we present richer undesirable system behaviors when different logarithmic and uniform quantizers are used. Such different quantization effects underscore the necessity for a careful selection of quantization strategies, especially for multi-agent systems with higher-order agent dynamics.