Distributed Adaptive Control for Networked Multi-Robot Systems

Abstract

Synchronization behavior among agents is found in flocking of birds, schooling of fish, and other natural systems. Synchronization among coupled oscillators was studied by 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 The reader is referred to the book and survey papers Consensus has been studied for systems on communication graphs with fixed or varying topologies and communication delays. See 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 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; 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 www.intechopen.com Multi-Robot Systems, Trends and Development 34 such, second-order consensus is interesting because there one must confront more directly the interface between control systems and communication graph structure. See the book The article (Ren et al., 2007) studied the case of higher-order consensus for linear chained integrator systems. The detailed analysis there is performed for 3 rd order systems but it extends to the higher order case. The paper Ref. Papers The article Few papers study second-order consensus for unknown nonlinear systems. Few papers study consensus for heterogeneous agents with different unknown nonlinear dynamics. Leaderless or uncontrolled synchronization with nonlinear non-identical passive systems is reported in By contrast, this Chapter concerns controlled consensus or the multi-agent tracker problem on general directed graphs. Neural networks (NN) have a universal approximation property Neural networks have been used since the 1990s to extend the abilities of adaptive controllers to handle larger classes of unknown nonlinear dynamical systems. Novel NN weight tuning algorithms have been developed to make NN suitable for online control of dynamical systems with real-time learning along the system trajectories. Rigorous proofs of convergence, performance, and stability have been offered. The reader is referred to (