Cooperative Coordination and Formation Control for Multi-agent Systems
Date
2016
Authors
Sun, Zhiyong
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Abstract
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.
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Multi-agent Systems, Cooperative Coordination, Formation Control, Networked Systems, Stability
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