Angle-Constrained Formation Control under Directed Non-Triangulated Sensing Graphs (Extended Version)

Angle-constrained formation control has attracted much attention from control community due to the advantage that inter-edge angles are invariant under uniform translations, rotations, and scalings of the whole formation. However, almost all the existing angle-constrained formation control methods are limited to undirected triangulated sensing graphs. In this paper, we propose an angle-constrained formation control approach under a Leader-First Follower sensing architecture, where the sensing graph is directed and non-triangulated. Both shape stabilization and maneuver control are achieved under arbitrary initial configurations of the formation. During the formation process, the control input of each agent is based on relative positions from its neighbors measured in the local reference frame and wireless communications among agents are not required. We show that the proposed distributed formation controller ensures global exponential stability of the desired formation for an nagent system. Furthermore, it is interesting to see that the convergence rate of the whole formation is solely determined by partial specific angles within the target formation. The effectiveness of the proposed control algorithms is illustrated by carrying out experiments both in simulation environments and on real robotic platforms.