Distance-Based Formation Tracking with Unknown Bounded Reference Velocities

This paper studies a leader-follower formation tracking problem where the leaders are moving at the same unknown bounded velocity. A distance-based control law is proposed for follower agents to maintain the desired distances in the formation and move at the leaders' velocity. The control law consists of a component to handle the uncertainty of the leaders' velocity and a component to achieve the desired distances in finite time. Numerical simulations are also provided to support the theoretical results.Comment: accepted to ICCAS 202

Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems

Multi-agent coordination control usually involves a potential function that encodes information of a global control task, while the control input for individual agents is often designed by a gradient-based control law. The property of Hessian matrix associated with a potential function plays an important role in the stability analysis of equilibrium points in gradient-based coordination control systems. Therefore, the identification of Hessian matrix in gradient-based multi-agent coordination systems becomes a key step in multi-agent equilibrium analysis. However, very often the identification of Hessian matrix via the entry-wise calculation is a very tedious task and can easily introduce calculation errors. In this paper we present some general and fast approaches for the identification of Hessian matrix based on matrix differentials and calculus rules, which can easily derive a compact form of Hessian matrix for multi-agent coordination systems. We also present several examples on Hessian identification for certain typical potential functions involving edge-tension distance functions and triangular-area functions, and illustrate their applications in the context of distributed coordination and formation control

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

Comments on Global stabilization of rigid formations in the plane [Automatica 49 (2013) 1436-1441]

This paper shows that the modified gradient control law proposed in Tian and Wang (2013) does not globally stabilize rigid formation shapes. Also, further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided.The work of B.D.O. Anderson and Z. Sun was supported by NICTA, which is funded by the Australian Government through the ICT Centre of Excellence program, and by the Australian Research Council under grant DP130103610 and DP160104500. Z. Sun is also supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award from Australian Government. The work of M.H. Trinh and H.-S. Ahn was supported in part by Ministry of Culture, Sports and Tourism (MCST) and Korea Creative Content Agency (KOCCA) in the Culture Technology (CT) Research & Development Program 2014