Modeling and Simulation of Virtual Rigid Body Formations and Their Applications Using Multiple Air Vehicles
Suguru Sato, Kamesh Subbarao
TL;DR
This work addresses coordinating multi-vehicle formations to behave as virtual rigid bodies by enforcing constant inter-agent distances and coordinated rigid-body motions. It develops a $6$-DOF multiagent dynamics model and a constraint-force synthesis framework based on $d\'Alembert$'s principle, Lagrange multipliers, and Baumgarte stabilization, with quaternion-based attitude representation and input decoupling for distributed control. The contributions include deriving the constraint forces, formulating the translational and rotational EOM, and conducting extensive simulations (including $N=3$ and $N=8$) that demonstrate formation establishment, reconfiguration, and station-keeping under single and multiple waypoint missions using LQR feedback. The approach is scalable and applicable to UAV swarms, with future work focusing on collision avoidance and enhanced safety.
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.