Distributed leaderless formation maneuvers over directed graphs

Abstract

This paper investigates fully distributed leaderless formation control over a directed sensing topology. For formation maneuvering, generally, a leader-follower approach is adopted. Leaderless formation maneuvers have no designated leaders, unlike traditional approaches. Some of the leaderless approaches proposed recently in literature considered undirected sensing graphs, which means the agents need to sense in both directions. Also, in these approaches, although the control law implementation is distributed in nature, the design of the control laws requires a stabilizing diagonal matrix design, which makes the design of the control law centralized and knowledge of exact interaction among the agents is required for this design. When an agent's sensing capabilities are limited, directed sensing topology becomes crucial. First, we propose control laws for leaderless formation maneuvers in $2$-D by manipulating the weights of complex-laplacian for single integrators with directed sensing graphs, and GAS (Global Asymptotic Stability) is established for it. In this approach, only translational, scale, and rotational formation maneuvers are possible. Then, we propose control laws for leaderless affine formation maneuvering for single integrators with directed sensing graphs for $2$-D and $3$-D, where translational, rotational, scale, and sheer formation maneuvering is possible. Also, an extension for the higher-order integrators is provided using a back-stepping-based design. Constant disturbances are also considered in the system dynamics. Finally, simulations are provided to validate the results.