Stability Analysis of Distance-Angle Leader-Follower Formation Control*

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.