Cooperative Coordination and Formation Control for Multi-agent Systems

The primary aim of this thesis is to study cooperative coordination control and formation control for multi-agent systems, with a focus on distributed stabilization control of rigid formation shapes. We consider several problems in the field, ranging from the equilibrium and stability of formation control systems, some practical considerations in formation control, and cooperative coordination control when agents have general dynamical models. In the first part of the thesis, we study in detail the equilibrium property of rigid formation control systems. A rank-preserving property is established for this coordination control system, and with this property we further prove the instability of a special equilibrium set (termed degenerate equilibria) at which agents' positions only span an affine space with dimension less than that of the full space. The exponential stability of rigid formation control systems for a large family of formation controllers is also proved, with the property applying for both minimally rigid formations and non-minimally rigid formations. This approach provides a general and unified way for stability analysis of formation control systems. In the second part, we investigate several practical issues on formation control, including robustness issues, rigid shape stabilization with a prescribed orientation, and formation control with quantized measurements. From the exponential stability proved in the first part, we discuss the convergence and robustness property for 3-D rigid formation control systems with distance mismatches, and identify a helical rigid motion induced by mismatched distances. In addition, we propose a feasible formation controller to achieve a desired rigid shape and a prescribed formation orientation in ambient 2-D and 3-D spaces, with minimal knowledge of the global coordinate frame orientation. Furthermore, quantization effects on rigid formation shape stabilization are discussed in detail in the case that the cooperative formation control only uses quantized distance measurements. In the third part, we extend some main results considered in previous chapters on formation control systems modelled by single integrators to systems modelled by more general dynamics, including double integrator models and nonlinear control systems. First, two types of double-integrator cooperative control systems (i.e. formation stabilization systems and flocking control systems with a target rigid shape) are thoroughly investigated. By using a family of parameterized Hamiltonian-like systems, we further establish certain invariance principles concerning the equilibrium set and local stability, which build the link between the stability analysis for formation systems modelled by single integrators and those modelled by double integrators. In addition, we consider a fundamental problem termed formation feasibility in multi-agent cooperative control. The problem concerns general forms of both formation constraints and individual agent's kinematics constraints. In this cooperative control framework, we assume each agent is modelled by an affine system with possible drift terms, and the network consists of multiple heterogeneous agents which could have totally different dynamics. Via tools from nonlinear control and differential geometry, an algebraic condition is provided to determine the existence of feasible formations for such heterogeneous networked systems, and a systematic procedure is proposed to generate feasible formations if they exist