Necessary and sufficient conditions are described for stable distance-angle leader-follower formation control of first- and second-order holonomic and non-holonomic mobile robots. The distance-angle leader-follower formation is a problem of maintaining the desired relative distance and orientation of robots in a group. Our analysis shows that the input constraints on the leader are necessary for stable formation control. These constraints are summarized as follows: 1) In a team of first (second) order holonomic mobile robots, the leader has to be controlled as a first (second) order non-holonomic mobile robot; 2) In a team of first (second) order non-holonomic mobile robots, the control input of the leader must be limited so that the curvature is first (second) order differentiable. We further show that these constraints are sufficient for the followers to maintain formation. Moreover, we present globally asymptotically stable controllers and describe simulation experiments that demonstrate the effectiveness of these controllers.

In swarm control, many robots coordinate their actions in a distributed and decentralized way. We propose a consensus-based control barrier function (CCBF) for a swarm. CCBF restricts the states of the whole distributed system, not just those of the individual robots. The barrier function is approximated by a consensus filter. We prove that CCBF constrains the control inputs for holding the forward invariance of the safety set. Moreover, we applied CCBF to a practical problem and conducted an experiment with actual robots. The results showed that CCBF restricted the states of multiple robots to the safety set. To the best of our knowledge, this is the first CBF that can restrict the state of the whole distributed system with only local communication. CCBF has various applications such as monitoring with a swarm and maintaining the network between a swarm and a base station.