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

Colombo, Leonardo; Moreno, Patricio; Ye, Mengbin; Marina, Héctor García de; Cao, Ming

doi:10.1016/j.ifacol.2020.12.1499

Cited by 7 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, F ij can describe consensus in the velocities between two agents. Lagranged'Alembert principle [30] implies that the natural motions of the system are those paths q…”

Section: B Agents Dynamics: Forced Euler-lagrange Equationsmentioning

confidence: 99%

Distributed Event-Triggered Flocking Control of Lagrangian Systems

Aranda-Escolástico

Colombo

Guinaldo

2022

IEEE Control Syst. Lett.

View full text Add to dashboard Cite

In this paper, an event-triggered control protocol is developed to investigate flocking control of Lagrangian systems, where event-triggering conditions are proposed to determine when the velocities of the agents are transmitted to their neighbours. In particular, the proposed controller is distributed, since it only depends on the available information of each agent on their own reference frame. In addition, we derive sufficient conditions to avoid Zeno behaviour. Numerical simulations are provided to show the effectiveness of the proposed control law.

show abstract

“…For instance, F ij can describe consensus in the velocities between two agents. Lagranged'Alembert principle [30] implies that the natural motions of the system are those paths q…”

Section: B Agents Dynamics: Forced Euler-lagrange Equationsmentioning

confidence: 99%

Distributed Event-Triggered Flocking Control of Lagrangian Systems

Aranda-Escolástico

Colombo

Guinaldo

2022

IEEE Control Syst. Lett.

View full text Add to dashboard Cite

show abstract

“…In a typical optimal control problem, one whishes to find a trajectory and a control minimizing a cost function of the form J (q, u) = T 0 C(q(t), q(t), u(t)) dt verifying a control equation such as (17) and, in addition, some boundary conditions giving information about the initial and terminal states of the system.…”

Section: Discrete Mechanics and Optimal Control Formentioning

confidence: 99%

“…These integrators retain some of the main geometric properties of continuous systems, such as symplecticity and momentum conservation (as long as the symmetry survives the discretization procedure), and good (bounded) behavior of the energy associated to the system. This class of numerical methods has been applied to a wide range of problems including optimal control [9], [10], constrained systems [11], [12], power systems [13], nonholonomic systems [14], [15], [16], multi-agent systems [17], [18], [19], and systems on Lie groups [20], [21]. Variational integrators for hybrid mechanical systems were used in [22] and [23].…”

Section: Introductionmentioning

confidence: 99%

Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage

Simoes¹,

Asier²,

Bloch³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. In this paper we model a passive walker with foot slip by using techniques of geometric mechanics, and we construct forced variational integrators for the system. Moreover, we present a methodology for generating (locally) optimal control policies for simple hybrid holonomically constrained forced Lagrangian systems, based on discrete mechanics, applied to a controlled walker with foot slip in a trajectory tracking problem.

show abstract

“…These integrators retain some of the main geometric properties of the continuous systems, such as preservation of the manifold structure at each step of the algorithm, symplecticity, momentum conservation (as long as the symmetry survives the discretization procedure), and a good behavior of the energy function associated to the system for long time simulation steps. This class of numerical methods has been applied to a wide range of problems in optimal control [25,12,11], constrained systems [21], formation control of multi-agent systems [8], nonholonomic systems [14], accelerated optimization [7], flocking control [10] and motion planning for underactuated robots [20], among many others.…”

Section: Introductionmentioning

confidence: 99%

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

Colombo¹,

Fernández²,

Diego³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 of geometric integrators. The general idea for those variational integrators is to discretize Hamilton's principle rather than the equations of motion in a way that preserves some of the invariants of the original system. In this paper we construct variational integrators with fixed time step for time-dependent Lagrangian systems modelling an important class of autonomous dissipative systems. These integrators are derived via a family of discrete Lagrangian functions each one for a fixed time-step. This allows to recover at each step on the set of discrete sequences the preservation properties of variational integrators for autonomous Lagrangian systems, such as symplecticity or backward error analysis for these systems. We also present a discrete Noether theorem for this class of systems. Applications of the results are shown for the problem of formation stabilization of multi-agent systems.

show abstract

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

Cited by 7 publications

References 11 publications

Distributed Event-Triggered Flocking Control of Lagrangian Systems

Distributed Event-Triggered Flocking Control of Lagrangian Systems

Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage

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

Contact Info

Product

Resources

About