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This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the formation scaling control problem for multi-agent systems by utilizing the stress matrix associated with a universally rigid framework. Compared with the existing results on formation scaling control, we consider a more challenging scenario where only one agent has the knowledge of the desired formation size. To cope with this constraint, we first propose a distributed estimator for the remaining agents to estimate the scaling parameter. Then by employing the outputs of the estimator, we design a new class of formation scaling control algorithms for universally rigid frameworks such that the overall formation converges to the prescribed shape with the desired scaling. Numerical simulations are carried out to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we discuss and discover several conservation and associated decay laws in distributed coordination control systems, in particular in formation shape control systems. Specifically, we reveal conservations of linear momentum and angular momentum for gradient-based multi-agent formation systems modelled by single integrators, and show several corresponding conservation/decay laws for double-integrator formation stabilization systems and double-integrator flocking systems, respectively. By exploiting translation and rotation symmetry properties and insights from Noether’s theorem, we further establish a multi-agent version of the relation between symmetry and conservation laws for gradient-based coordination systems derived from general potential functions, from which we generalize the conservation/decay laws to more general networked coordination control systems. The results hold in ambient spaces of any dimensions, and we focus on the 2-D and 3-D cases due to their natural interpretation as positions of agents. [ABSTRACT FROM AUTHOR]

This paper proposes an elevation angle rigidity theory in both 2D and 3D spaces, and applies it to solve multi-agent formation control with only inter-agent bearing/direction measurements in agents' local coordinate frames. Motivated by the sensor technology in measuring elevation angle and angular diameter, we develop elevation angle rigidity by attaching each agent in a multi-agent framework with a rod in 2D and a ball in 3D, respectively. By defining the elevation angle rigidity matrix, conditions for infinitesimal elevation angle rigidity are derived. Compared to previously developed angle rigidity-based and bearing rigidity-based formation control laws, the proposed elevation angle rigidity-based control law can maintain the gradient-based control property. Compared to distance-based formation control laws, less sensor measurements are required. The formation maneuvering with desired translation and rotation is also realized by using only local bearing measurements. Simulation examples illustrate the advantages and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper develops a sign rigidity theory to characterize and examine multi-agent rigid formations consistent with a formation specification including distance- and signed area-constraints, and to control an arbitrarily positioned set of agents to take up the specifications. The sign rigidity theory can be viewed as an extended version of the standard distance rigidity theory with the addition of signed area constraints. This property enables elimination of possible formation specification ambiguities arising when a formation specification includes distance constraints only. As an application of the sign rigidity theory, this paper explores formation specification control in 2-D space. Under the proposed gradient-based formation control law, almost global convergence (from arbitrary initial positions) can be achieved when a target formation consists of triangulated sub-formations defined by distance- and signed area-constraints; the formation control law is applied for either single-integrator models or unicycle models. [ABSTRACT FROM AUTHOR]

This paper concentrates on multi-agent formation control problems under mixed measurements of distance and bearing. Towards this objective, a distributed event-triggered estimation-based control framework is developed such that only at necessary time instants, the event for estimation (namely, cooperative localization among a subgroup of agents) is triggered to recover relative position information by utilizing a mixed distance and bearing measurements from different agents. Firstly, it is shown by using the stiffness theory that a subgroup of agents are capable of recovering relative position information if a sufficient number of independent distance and range measurements are available. Secondly, a distributed event-triggered mechanism is presented for achieving an affine formation control, which can be implemented in an asynchronous manner and also ensures Zeno-free behavior. Simulation studies are provided to demonstrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]