Doctor of Philosophy (PhD)
A multi-agent system is a network of interacting "agents" that collectively perform a complex task. This dissertation is concerned with the decentralized formation control of multi-agent systems moving in the plane. The formation problem is defined as designing control inputs for the agents so that they form and maintain a pre-defined, planar geometric shape. The focus is on three related problems with increasing level of complexity: formation acquisition, formation maneuvering, and target interception. Three different "dynamic" models, also with increasing level of complexity, are considered for the motion of the agents: the single-integrator model, the double-integrator model, and the full mechanical dynamic model. Rigid graph theory and Lyapunov theory are the primary tools utilized in this work for solving the aforementioned formation problems for the three models. The backstepping control technique also plays a key role in the cases of the double-integrator and full dynamic models. Starting with the single-integrator model, a basic formation acquisition controller is proposed that is only a function of the relative position of agents in an infinitesimally and minimally rigid graph. A Lyapunov analysis shows that the origin of the inter-agent distance error system is exponentially stable. It is then shown how an extra term can be added to the controller to enable formation maneuvering or target interception. The three controllers for the single-integrator model are used as a stepping stone and extended to the double-integrator model with the aid of backstepping. Finally, an actuator-level, formation acquisition control law is developed for multiple robotic vehicles that accounts for the vehicle dynamics. Specifically, a class of underactuated vehicles modeled by Euler-Lagrange-like equations is considered. The backstepping technique is again employed while exploiting the structural properties of the system dynamics. Computer simulations are provided throughout the dissertation to show the proposed control laws in action.
Document Availability at the Time of Submission
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Cai, Xiaoyu, "Graph rigidity-based formation control of planar multi-agent systems" (2013). LSU Doctoral Dissertations. 1666.
de Queiroz, Marcio