This paper discusses a formation control problem in which a target formation is defined with both distance and signed area constraints. The control objective is to drive spatially distributed agents to reach a unique target rigid formation shape (up to rotation and translation) with desired inter-agent distances. We define a new potential function by incorporating both distance terms and signed area terms and derive the formation system as a gradient system from the potential function. We start with a triangle formation system with detailed analysis on the equilibrium and convergence property with respect to a weighting gain parameter. For an equilateral triangle example, analytic solutions describing agents’ trajectories are also given. We then examine the four-agent double-triangle formation and provide conditions to guarantee that both triangles converge to the desired side distances and signed areas.Z. Sun was supported by the Australian Prime Minister’s Endeavour Postgraduate Award from Australian Government. Sugie is supported by JSPS
KAKENHI Grant Number JP16K14284. Azuma is supported by JSPS
KAKENHI Grant Number JP15H00814. Sakurama is supported by
JSPS KAKENHI Grant Number JP15K06143
