Search

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]

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with certain chosen agents. In this control framework, we show the minimal number of agents which should have knowledge of a global coordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-D rigid formation), while all other agents do not require any global coordinate knowledge or any coordinate frame alignment to implement the proposed control. The exponential convergence to the desired rigid shape and formation orientation is also proved. [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 shows that the modified gradient control law proposed in Tian and Wang (2013) does not globally stabilize rigid formation shapes. Also, further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided. [ABSTRACT FROM AUTHOR]