  This paper presents a novel control protocol for robust distance-based
formation control with prescribed performance in which agents are subjected to
unknown external disturbances. Connectivity maintenance and collision avoidance
among neighboring agents are also handled by the appropriate design of certain
performance bounds that constrain the inter-agent distance errors. As an
extension to the proposed scheme, distance-based formation centroid maneuvering
is also studied for disturbance-free agents, in which the formation centroid
tracks a desired time-varying velocity. The proposed control laws are
decentralized, in the sense that each agent employs local relative information
regarding its neighbors to calculate its control signal. Therefore, the control
scheme is implementable on the agents' local coordinate frames. Using rigid
graph theory, input-to-state stability, and Lyapunov based analysis, the
results are established for minimally and infinitesimally rigid formations in
2-D or 3-D space. Furthermore, it is argued that the proposed approach
increases formation robustness against shape distortions and can prevent
formation convergence to incorrect shapes, which is likely to happen in
conventional distance-based formation control methods. Finally, extensive
simulation studies clarify and verify the proposed approach.
