Modeling and Simulation of Virtual Rigid Body Formations and Their Applications Using Multiple Air Vehicles

TL;DR

This paper develops a comprehensive mathematical framework for modeling and controlling virtual rigid body formations of multiple air vehicles, enabling formation stability and maneuverability similar to a single rigid body.

Contribution

It introduces a novel control and simulation approach for virtual formations using constraint forces and stabilization techniques, inspired by rigid body dynamics.

Findings

Framework successfully simulates stable formations under various scenarios

Formation control performs well with different numbers of agents

Simulation results demonstrate effective waypoint following

Abstract

This paper presents thorough mathematical modeling, control law development, and simulation of virtual structure formations which are inspired by the characteristics of rigid bodies. The stable constraint forces that establish the rigidity in the formation are synthesized by utilizing d'Alembert's principle of virtual work, constraint sensitivities (Lagrange multipliers) and constraint stabilization using Baumgarte stabilization. The governing equations of motion of a multiagent system are derived via Newton's and Euler's equations to include these constraint forces and to enable inputs regarding the formation as if it were an independent rigid body. The performance of this framework is evaluated under multiple cases including waypoint following missions, and using different number of agents.