Sampled-data formation control under dynamic directed interaction

This paper studies two discrete-time formation control algorithms for multi-vehicle systems with double-integrator dynamics in a sampled-data setting under dynamic directed interaction. With an absolute damping term, the first algorithm guarantees relative position keeping with a zero final velocity. With a relative damping term, the second algorithm guarantees relative position keeping with a constant final velocity. For the first algorithm, it is shown that formation control can be achieved if the interaction graph has a directed spanning tree jointly and the damping gain and the sampling period satisfy certain conditions. For the second algorithm, it is shown that formation control can be achieved if the interaction graph has a directed spanning tree at each time interval and the damping gain and the sampling period satisfy certain conditions.