Flexible Shape Formation Control for Quadrotor UAVs

Abstract

In this work, we address the problem of quadrotor flexible formation control. To this end, a control algorithm is proposed to achieve geometric platoon formations based exclusively on similarity transformations (rotation, translation, and scale) rather than rigid structures with fixed geometric references for the quadrotors. Firstly, the dynamic model of the quadrotor is established along with a nonlinear stabilizing control that uses saturated inputs. Then, we introduce the flexible formation behavior into the resulting quadrotor’s lateral and longitudinal subsystems using a control law that combines the transformation of a chain of integrators into a system described by a single integrator, and a shape optimization cost function. The optimization criterion consists of a geometric deformation measure term inspired by the Procrustes problem, which is a shape-alignment problem. Results are validated using the nonlinear quadrotor model in a simulated environment based on platforms such as ROS 2 and Gazebo, providing a realistic approximation to experiments with physical hardware.