Distributed stabilization control of rigid formations with prescribed orientation

Abstract

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. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.

Affine Formation Maneuver Control of Multiagent Systems

“…Note that control law (14) does not require additional measurements compared to (11). By defining a new state for the integral term, control law (14) can be rewritten aṡ…”

“…However, the scale or orientation of the formation is difficult to control using this approach because changing the scale or orientation requires changing the displacement constraints. As a comparison, distance-based control laws can be applied to track target formations with time-varying translations and orientations [13], [14], but it is difficult to track time-varying formation scales. Bearing-based control laws can track formations with time-varying translations and scales [9], [10], but it is difficult to track time-varying orientations.…”

Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems

“…Very often, such potential functions are defined by geometric quantities such as distances or areas related with agents' positions over an interaction graph in the configuration space. Typical scenarios involving gradientbased control in multi-agent coordination include distance-based formation control [5][6][7][8][9], multi-robotic maneuvering and manipulability control [10], motion coordination with constraints [11], among others. Comprehensive discussions and solutions to characterize distributed gradient control laws for multi-agent coordination control are provided in [3] and [12], which emphasize the notion of clique graph (i.e., complete subgraph) in designing potential functions and gradient-based controls.…”

Distance‐based control of formations with hybrid communication topology

“…Center manifold theory was employed to obtain local asymptotic stability in the work of Krick et al A general case of controlling rigid formations was then discussed in the work of Oh and Ahn by directly controlling the Euclidean distance matrix of the given formation. The control of rigid formations was also discussed in n ‐dimensional spaces, with mismatched measurements and prescribed orientation . On the other hand, if the distance between i and j is only maintained by one of the two agents, the formation is then depicted by a directed graph, and the term persistence is introduced to describe such kind of formations .…”

“…The control of rigid formations was also discussed in n-dimensional spaces, 10 with mismatched measurements 11 and prescribed orientation. 12 On the other hand, if the distance between i and j is only maintained by one of the two agents, the formation is then depicted by a directed graph, and the term persistence is introduced to describe such kind of formations. 13 In the works of Yu et al 14 and Summers et al, 15 the control of minimally persistent formation in a 2-dimensional (2D) space was discussed.…”