# Forced Variational Integrators for the Formation Control of Multiagent Systems

@article{Colombo2021ForcedVI, title={Forced Variational Integrators for the Formation Control of Multiagent Systems}, author={Leonardo Jesus Colombo and H{\'e}ctor Garc{\'i}a de Marina}, journal={IEEE Transactions on Control of Network Systems}, year={2021}, volume={8}, pages={1336-1347} }

Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this article, we construct and implement forced variational integrators for the formation control of autonomous agents modeled by double integrators. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. We find error estimations for the rate of…

## One Citation

Variational integrators for non-autonomous systems with applications to stabilization of multi-agent formations

- MathematicsArXiv
- 2022

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class…

## References

SHOWING 1-10 OF 32 REFERENCES

Optimal Control of Left-Invariant Multi-Agent Systems with Asymmetric Formation Constraints

- Mathematics2018 European Control Conference (ECC)
- 2018

In this work we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left invariant…

Exponential and practical exponential stability of second-order formation control systems

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This work proves local exponential stability with respect to the total energy by applying Chetaev’s trick to the Lyapunov candidate function and proposes a novel formation control law, which does not require measurements of relative positions but instead measurements of distances.

Rigid formation control of double-integrator systems

- Computer ScienceInt. J. Control
- 2017

Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results, and some new links between single-integrator formation systems and double-integration formation systems are established.

Motion Feasibility Conditions for Multiagent Control Systems on Lie Groups

- MathematicsIEEE Transactions on Control of Network Systems
- 2020

The problem of motion feasibility for multiagent control systems on Lie groups with collision-avoidance constraints for kinematic left-invariant control systems and next, for dynamical control systems given by a left-trivialized Lagrangian function is studied.

Conservation and decay laws in distributed coordination control systems

- Computer ScienceAutom.
- 2018

Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups

- MathematicsIEEE Transactions on Automatic Control
- 2020

We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the…

DISCRETE MECHANICS AND OPTIMAL CONTROL: AN ANALYSIS ∗

- Computer Science
- 2008

The DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and this fact is employed in order to give a proof of convergence.

Exponential stability for formation control systems with generalized controllers: A unified approach

- MathematicsSyst. Control. Lett.
- 2016

Discrete mechanics and optimal control for constrained systems

- Mathematics
- 2010

The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms of the states and controls by applying a constrained version of the…

Discrete Geometric Optimal Control on Lie Groups

- Mathematics, Computer ScienceIEEE Transactions on Robotics
- 2011

This work constructs necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develops numerical methods for their computation that exploit the structure of the state space and preserve the system motion invariants.