Prescribed performance distance-based formation control of Multi-Agent Systems

This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances. Connectivity maintenance and collision avoidance among neighboring agents are also handled by the appropriate design of certain performance bounds that constrain the inter-agent distance errors. As an extension to the proposed scheme, distance-based formation centroid maneuvering is also studied for disturbance-free agents, in which the formation centroid tracks a desired time-varying velocity. The proposed control laws are decentralized, in the sense that each agent employs local relative information regarding its neighbors to calculate its control signal. Therefore, the control scheme is implementable on the agents' local coordinate frames. Using rigid graph theory, input-to-state stability, and Lyapunov based analysis, the results are established for minimally and infinitesimally rigid formations in 2-D or 3-D space. Furthermore, it is argued that the proposed approach increases formation robustness against shape distortions and can prevent formation convergence to incorrect shapes, which is likely to happen in conventional distance-based formation control methods. Finally, extensive simulation studies clarify and verify the proposed approach.

Prescribed Performance Distance-Based Formation Control of Multi-Agent Systems (Extended Version).

In this chapter, we move our focus from formation control systems modelled by single integrators (e.g. those considered in previous chapters) to formation systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely, formation stabilization systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results. We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterized Hamiltonian system, which in addition provide novel stability criteria for different equilibria in double-integrator formation systems by using available results from single-integrator formation systems.

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Rigid formation control of double-integrator systems

An Elementary Theory of Equations.

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 multiagent cooperative control. The problem concerns general forms of both formation constraints and individual agent’s kinematics constraints. In this cooperative control

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Cooperative Coordination and Formation Control for Multi-agent Systems

Three-Dimensional Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

A method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers was recently proposed by introducing an additional controlled variable, ...

Further results on the distance and area control of planar formations

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance and area-based scheme for the formation control of n-agent systems in two dimensions using directed graphs and the single-integrator model. We show that under certain conditions on the edge lengths of the triangulated desired formation, the control ensures almost-global convergence to the correct formation.

Directed Formation Control of n Planar Agents with Distance and Area Constraints

This paper deals with the problem of rigid formation control using directed graphs in both two-dimensional (2D) and three-dimensional (3D) spaces. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. We show that the directed version of the gradient descent control law asymptotically stabilizes the interagent distance error dynamics of minimally persistent formation graphs. The control analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems, which are recursively analyzed using the stability of interconnected systems. Simulation and experimental results are presented for the directed formation controller in comparison to the standard undirected controller.

Pengpeng Zhang

Papers

Three-Dimensional Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

Further results on the distance and area control of planar formations

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

Directed Formation Control of n Planar Agents with Distance and Area Constraints

Control of Directed Formations Using Interconnected Systems Stability