Forced variational integrator for distance-based shape control with flocking behavior of multi-agent systems

TL;DR

This paper develops a new forced variational integrator for multi-agent systems that enhances numerical accuracy and efficiency in distance-based shape control with flocking, while preserving system symmetries.

Contribution

It introduces a novel forced variational integrator tailored for multi-agent shape control, improving computational efficiency and accuracy over traditional methods.

Findings

Lower computational cost compared to traditional integrators

Preserves configuration space and symmetries

Effective in multi-agent flocking simulations

Abstract

A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are given by the discretization of Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. We derive forced variational integrators that can be employed in the context of control algorithms for distance-based shape with velocity consensus. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions, while preserving the configuration space and symmetries. We also provide an explicit expression for the integration scheme in the case of an arbitrary number of agents with double integrator dynamics. For a numerical comparison of the performances, we use a planar formation consisting of three autonomous agents.