Distributed Adaptive Control for Networked Multi-Robot Systems

Synchronization behavior among agents is found in flocking of birds, schooling of fish, and other natural systems. Synchronization among coupled oscillators was studied by (Kuramoto 1975). Much work has extended consensus and synchronization techniques to manmade systems such as UAV to perform various tasks including surveillance, moving in formation, etc. We refer to consensus and synchronization in terms of control of manmade dynamical systems. Early work on cooperative decision and control for distributed systems includes (Tsitsiklis 1984). The reader is referred to the book and survey papers (Ren & Beard 2008; Ren, Beard et al., 2005; Olfati-Saber et al., 2007; Ren, Beard et al., 2007). Consensus has been studied for systems on communication graphs with fixed or varying topologies and communication delays. See (Olfati-Saber & Murray 2004; Fax & Murray 2004; Ren & Beard 2005; Jadbabaie et al., 2003), which proposed basic synchronizing protocols for various communication topologies. Early work on consensus studied leaderless consensus or the cooperative regulator problem, where the consensus value reached depends on the initial conditions of the node states and cannot be controlled. On the other hand, the cooperative tracker problem seeks consensus or synchronization to the state of a control or leader node. Convergence of consensus to a virtual leader or header node was studied in (Jadbabaie et al., 2003; Jiang & Baras 2009). Dynamic consensus for tracking of time-varying signals was presented in (Spanoset al., 2005). The pinning control has been introduced for synchronization tracking control of coupled complex dynamical systems et al., 2004; Z. Li et al., 2009). Pinning control allows controlled synchronization of interconnected dynamical systems by adding a control or leader node that is connected (pinned) into a small percentage of nodes in the network. Analysis has been done using Lyapunov and other techniques by assuming either a Jacobian linearization of the nonlinear node dynamics, or a Lipschitz condition, or contraction analysis. The agents are homogeneous in that they all have the same nonlinear dynamics. The study of second-order and higher-order consensus is required to implement synchronization in most real world applications such as formation control and coordination among UAVs, where both position and velocity must be controlled. Note that Lagrangian motion dynamics and robotic systems can be written in the form of second-order systems. Moreover, second-order integrator consensus design (as opposed to first-order integrator node dynamics) involves more details about the interaction between the system dynamics/ control design problem and the graph structure as reflected in the Laplacian matrix. As