Consensus algorithm of multi-agents in a non-rectangular bounded space

In this paper, we consider coordinated motion and cooperative control of multi-agents in a non-rectangular bounded space, and present a consensus algorithm for the agents with double-integrator dynamics. The traditional consensus algorithm for bounded space is only applied into rectangular bouncing boundaries, not suitable for non-rectangular space. Therefore, we introduce the concept of the mirror velocity and position matrix that not only can convert the discontinuous real velocity into the continuous mirror velocity, but also can expand a bounded space into an infinite space, and introduce the saturation control in order to limit the input signals. The velocity and position of multi-agents asymptotically converge to the same values, respectively. Finally, the effectiveness of the proposed consensus algorithm is examined by numerical simulations.