Angle-constrained formation control under directed non-triangulated sensing graphs

Angle-constrained formation control has attracted much attention due to the advantage that inter-edge angles are invariant under uniform translations, rotations, and scalings of the whole formation. However, 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. During the formation process, the control input of each agent is communication-free and based on relative positions from neighbors measured in the local reference frame. We show that the proposed distributed formation controller ensures global exponential stability of the desired formation. Furthermore, it is interesting to observe that the convergence rate of the whole formation is only determined by partial specific angles within the target formation. The effectiveness of the proposed control algorithm is illustrated by carrying out experiments both in simulation environments and on real robotic platforms.