20 th Annual International Conference on Mechanical Engineering-ISME2012 16-18 May, 2012, School of Mechanical Eng., Shiraz University, Shiraz, Iran 1 ISME2012, 16-18 May, 2012 ISME2012-1509 Arbitrarily Shaped Formation Control of Multiple Electrically Driven Mobile Robots Using Backstepping Control A. Mohagheghi 1 , A. Khayatian 2 , M. Dehghani 3 1 School of Electrical and Computer Engineering, Shiraz University; a.mohagheghi@ieee.org 2 School of Electrical and Computer Engineering, Shiraz University; khayatia@shirazu.ac.ir 3 School of Electrical and Computer Engineering, Shiraz University; mdehghani@shirazu.ac.ir Abstract This paper presents a decentralized control scheme for the formation control of multiple electrically driven mobile robots based on artificial potential functions and backstepping control method. Backstepping control is used to extend the theoretical potential fields based formation control methods designed for mass-less kinematic agents to the case of fully actuated electrically driven mobile robots. The proposed method maintains the decentralized nature of the control method as well as its convergence and stability properties and improves the trajectories agents follow to the desired formation (transient system behavior). Asymptotic stability of the system is proved using Lyapunov stability analysis. Simulation results are presented to illustrate the effectiveness of this method. Keywords: multi-agent systems, formation control, backstepping control, electrically driven WMRs Introduction During recent years, the control problem of multi-agent robotic systems has been the subject of considerable attention and extensive research [1]-[5]. The formation control problem of multi-agent systems is defined as the organization of a swarm of agents into a particular shape in a 2D or 3D space [1]. Formation control is useful in satellite configurations in the space or search and rescue robots propagation. Many approaches have been developed to confront this problem, each with their own advantages and disadvantages. All these methods can be categorized in three different groups of centralized, decentralized and hybrid control. Compared to the conventional centralized control, distributed control of multi agent systems provides increased performance, efficiency and robustness. Some of the recently used control approaches in this area are potential fields [1], behavior-based [2], leader-following [3], graph-theoretic [4] and virtual structure [5] methods. Most of the formation control methods cited before consider a group of mass-less agents with kinematic models. Although the results of these researches can serve as a basis for designing the desired behavior in multi-agent systems, the mass-less kinematic model does not represent the dynamics of realistic agents and falls short of achieving the desired behavior in engineering applications with real agent dynamics. In this paper, we extend an artificial potential function based method of realizing the desired formation for mass- less kinematic agents, to the case of fully actuated electrically driven holonomic wheeled mobile robots using a backstepping control method. The main advantage of this novel control strategy is that it maintains the decentralized nature of the control method as well as its convergence and stability properties. It also introduces additional nonlinear terms to improve the transient performance [7]. The potential field based formation control method this work is based on [8], has the advantage of not being affected by the problem of local minima as opposed to the previous work where the existence of local minima in potential functions lead to guaranteeing only local convergence to the desired formation [9]. The rest of the paper is organized as follows: In section 2, the choice of potential function and the transformation strategy for obtaining arbitrarily shaped formations is explained briefly. In section 3, we consider the agents to be mobile robots with general vehicle dynamics and design a controller at the torque level using backstepping control method. Section 4 continues the backstepping design to obtain actual control inputs at actuator dynamics level. In section 5, simulation results concerning all the proposed controllers are presented to verify the theoretical results. Finally, conclusions are given in section 6. The Potential Fields Method In this section, the choice of potential function and the arbitrarily shaped formation control strategy for the kinematic model are explained briefly. As it was mentioned before, this potential field control method is based on the work in [8]. First, an artificial potential field is designed to obtain a formation with the shape of a regular polygon, then a bijective coordinate transformation is used to deform the polygonal formation into a completely arbitrarily shaped formation. Let denote the position vector of agent , where are the agents Cartesian coordinates. The polygonal formation potential function is considered of the form: (1) Where is the state vector of the system and is the potential between each agent and the center of the polygonal formation and of an attracting nature, while is the potential between agents in the group and of a repulsing nature and is the orientation potential. The first term is defined as: (2)