Further results on the distance and area control of planar formations

Abstract

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, viz., the signed area of a triangle. In this paper, we seek to generalise this method to planar formations of n agents for both first- and second-order agent models while using unidirectional sensing and control. In addition to directed formation shape control, we also consider the problem of formation motions. We prove that, under certain conditions on the edge lengths of the triangulated desired formation and control gains, the distributed controller ensures the almost-global asymptotic stability of the correct formation and is coordinate frame invariant. Experimental evaluations are presented to support the theoretical results.

Keywords:

• Multi-agent system
• formation control
• signed area
• distance
• rigid graph

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The extension to the formation manoeuvring problem is discussed in Sections 4.2 and 5.3.

2 Translation and rotation of these vertices as a rigid body will not affect the following analysis since it is only dependent on their distances.

3 Since functions $\ln (V+1)$ and V are positively correlated, this variable change does not affect the function extrema.

Additional information

Funding

This work was supported by LSU Economic Development Assistantship Program.