Local Shape-Preserving Formation Maneuver Control of Multi-agent Systems: From 2D to 3D

Abstract

In this paper, we propose a formation maneuver control strategy to steer a triangulated formation from two dimensional (2D) space to three dimensional (3D) space, while maintaining the shape of each triangle during the transition. To describe the desired 3D formation shape, we adopt a weak rigidity function containing both distance and angle constraints, together with a sign function. The local shapes are preserved by restricting agents’ motions to the null-space of the distance rigidity function. Furthermore, we formulate this formation maneuver control as an optimal control problem to minimize the control efforts subject to system dynamics, local shape preserving constraints, initial and terminal boundary conditions, which can be solved via a nonlinear programming solver. In the end, two simulation examples are provided to show the effectiveness of our formation control strategy.