Distributed estimation and control with applications to multi-robotic systems

The control of networked systems has emerged as a topic of significant interest due to applications in many fields, e.g., robotics, smart grids, wireless sensor networks. For the consideration of scalability, robustness, and spatial complexity, it is often required to design distributed control subject to topological constraints introduced by the network structure, which distinguishes it from conventional control and signal processing problems. The thesis contributes to the field of consensus-based distributed estimation and control, and is partitioned into two parts. In Part I, we study the fundamental problems on how to achieve distributed estimation using consensus based algorithms; and then in Part II, we apply the results to distributed multi-robotic systems. Throughout this thesis, graph theoretical tools and Lyapunov stability theory are utilized for the analysis of the system convergence and performances.;Average consensus is an efficient model protocol for distributed estimation. However, direct application of the average consensus protocol encounters problems in solving real-world problems. In Part I of this thesis, we focus our attention on two issues: one is the quantization problem of the consensus protocol, and the other is the extension to consensus filtering protocols for distributed tracking. On the problem of average consensus with quantized communication, we formulate the problem as an Hinfinity optimal control problem and minimize the upper bound of the L2 gain from the quantization error to the consensus deviation. A set of linear matrix inequalities, which has efficient solutions via semi-definite programming, are obtained to solve the problem. One limitation of average consensus is that it cannot directly track time-varying signals due to the absence of explicit inputs. Researchers extended the average consensus protocol to consensus filters to deal with this limitation. However, existing results limit to undirected non-switching topology, which does not fully capture the nature of networked systems. We investigate convergence properties of the PI consensus filter, and extend existing results to directed switching graphs with guaranteed convergence. Its discrete-time counterpart is also obtained.;In Part II of the thesis, the distributed estimation techniques are applied to the control of multi-robotic systems. Two application scenarios are considered. One is the distributed source seeking, and the other is the distributed plume front tracking by cooperative robots. For the first application, we aim to design a distributed control law to drive a group of robots to an unknown source by exploiting the local sampling of the concentration using neighboring communication only. For the second application, the control object is to drive a group of robots to track dynamic plume front that is modeled by the advection-diffusion equation. We first design a nonlinear observer for a single robot to estimate the dynamics of the plume front, and then design control laws to track the plume front. We then extend it to the multi-robot case allowing distributed cooperative tracking.;This thesis aims to provide a tractable framework to extend conventional estimation and control methodologies to the ones restricted by distributed communication on a network. Provable convergence results are obtained theoretically. Simulation results demonstrate the effectiveness of the proposed strategies.