Adaptive Neural Network Consensus Based Control of Robot Formations H. M. Guzey, and S. Jagannathan Dept. of Electrical and Computer Engineering Missouri University of Science and Technology 301 W. 16-Th St. Rolla MO 65409-0040 ABSTRACT In this paper, adaptive consensus based formation control scheme is derived for mobile robots in a pre-defined formation when full dynamics of the robots which include inertia, Corolis, and friction vector are considered. It is shown that dynamic uncertainties of robots can make overall formation unstable when traditional consensus scheme is utilized. In order to estimate the affine nonlinear robot dynamics, a NN based adaptive scheme is utilized. In addition to this adaptive feedback control input, an additional control input is introduced based on the consensus approach to make the robots keep their desired formation. Subsequently, the outer consensus loop is redesigned for reduced communication. Lyapunov theory is used to show the stability of overall system. Simulation results are included at the end. Keywords: consensus; mobile robots; uncertain dynamics; adaptive control; feedback linearization; neural network 1. INTRODUCTION Formation control of multi agent systems is widely studied in last couple of decades. There are different strategies to keep the agents in a specific formation. These are, leader follower approach, behavioral approach, and virtual structure approach. Each method has its own benefits and limitations. In this paper, the consensus based formation control, which can be categorized in virtual structure approach, is utilized. Consensus is known in the literature [9] as converging to a common value or agreement of multiple agents. Even though, consensus based approaches for multi agent systems is widely studied [1][2][3][4][5][6], it is mainly considered as a theoretical approach. However, the consensus approach is utilized in wide engineering areas such as network of robots[8], and evolutionary computing [7] for instance. Consensus protocols has recently been utilized to keep the multi agent systems in a desired formation [9][10][11][12]. Only local interactions of robots are needed to calculate a desired path of each robot while the robot dynamics are ignored. In order to utilize consensus protocol to keep the mobile robots in a predefined formation, one has to consider highly nonlinear robot dynamics. However, the existing consensus based formation control schemes are applied to non- holonomic mobile robots in [16][18][19] by using kinematic equations. It will be shown in this paper that ignoring dynamics may result in instability with consensus control. In real word applications, dynamics of mobile robots can change due to friction or objects being picked or dropped off. In this paper, it is mathematically shown that uncertainties on Coriolis and friction forces of robots can make the overall formation bounded which if not careful can lead to instability. Subsequently, by using approximated robot dynamics, feedback linearization based inner loop control [13] is derived to convert nonlinear robot dynamics into linear dynamics. A high level consensus based outer-loop is utilized to control the closed loop dynamics in order to ensure stability of the formation since consensus approach is more scalable and robust compared to other methods. However, in the consensus based scheme, all robots are assumed to know their neighbors position and velocity errors as well as their own current position and velocity errors. Next, the consensus-based approach is derived when the communication among the robots is reduced. The net result is a combination of a NN feedback linearization inner loop for compensating the dynamics with outer consensus control loop for formation control. Unmanned Systems Technology XV, edited by Robert E. Karlsen, Douglas W. Gage, Charles M. Shoemaker, Grant R. Gerhart, Proc. of SPIE Vol. 8741, 87410M © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2015166 Proc. of SPIE Vol. 8741 87410M-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/16/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx