Distance-based Control of Kn Formations in General Space with Almost Global Convergence

In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The undamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.This work was supported in part by the Australian Research Council under Grants DP130103610 and DP160104500, and in part by the National Research Foundation of Korea under Grant NRF-2017R1A2B3007034. The work of Z. Sun was supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award

Formation Control Algorithms With Limited or No Communication

Formation control refers to a collective behaviour of multi-agent systems where individual agents come together to form a pattern, often geometric. These formations can enable multi-agent systems to function more effectively in a broad range of applications. Many formation control algorithms require centralized decision making, communication between agents or a centralized decision maker and other factors that increase per-agent cost and reduce the robustness and scalability of multi-agent systems. To this end, we introduce two algorithms that operate using local decision making and limited or no communication. The first algorithm is a communication-free and index-free algorithm based on polar indicator distributions. The second is a progressive assignment algorithm using limited, situated communication that deterministically assigns agents a position in the objective formation along a convex spiral directed path graph. We also present an extension of the second algorithm for 3-dimensional formation definitions. The first algorithm is demonstrated in a physical experiment using ground-based agents while the second one is simulated using micro air vehicles (MAVs) in a physics-based simulator