Safe formation control with obstacle avoidance

In this paper, we consider the general problem of guaranteeing safe interaction of humans and a group of mobile agents in an environment of interest. The way that we guarantee such a safe interaction is via proposing algorithms that prevent the agents from colliding with environmental obstacles with unknown sizes and locations, e.g. human operators. To do so, we first consider the problem of forcing a set of autonomous agents form a desired formation and follow a trajectory only known to one of them, namely the leader of the formation. Then we build upon the solution given to this problem and solve another problem of interest. This is to guarantee obstacle collision avoidance while the agents are following an unknown trajectory and keeping the desired shape of the formation. The stability of the control laws presented here is analytically established and some simulation results are presented to show the performance of the proposed control laws in different scenarios.