Control of Directed Formations Using Interconnected Systems Stability

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Pengpeng Zhang ◽  
Marcio de Queiroz ◽  
Milad Khaledyan ◽  
Tairan Liu
Keyword(s):  
Formation Control ◽  
Directed Graphs ◽  
Three Dimensional ◽  
Interconnected Systems ◽  
Control Analysis ◽  
Multi Agent ◽  
Error Dynamics ◽  
The Stability ◽  
Interconnected Nonlinear Systems ◽  
Systems Simulation

This paper deals with the problem of rigid formation control using directed graphs in both two-dimensional (2D) and three-dimensional (3D) spaces. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. We show that the directed version of the gradient descent control law asymptotically stabilizes the interagent distance error dynamics of minimally persistent formation graphs. The control analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems, which are recursively analyzed using the stability of interconnected systems. Simulation and experimental results are presented for the directed formation controller in comparison to the standard undirected controller.

Three-Dimensional Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Pengpeng Zhang ◽  
Marcio de Queiroz ◽  
Xiaoyu Cai
Keyword(s):  
Formation Control ◽  
Three Dimensional ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
3D Space ◽  
Multi Agent ◽  
Error Dynamics ◽  
Integrator Model ◽  
Double Integrator ◽  
Dynamic Formation

In this paper, we consider the problem of formation control of multi-agent systems in three-dimensional (3D) space, where the desired formation is dynamic. This is motivated by applications where the formation size and/or geometric shape needs to vary in time. Using a single-integrator model and rigid graph theory, we propose a new control law that exponentially stabilizes the origin of the nonlinear, interagent distance error dynamics and ensures tracking of the desired, 3D time-varying formation. Extensions to the formation maneuvering problem and double-integrator model are also discussed. The formation control is illustrated with a simulation of eight agents forming a dynamic cube.

scholarly journals Study on the Formation Control Methods for Multi-Agent Based on Geometric Characteristics

2013 ◽  
Vol 765-767 ◽  
pp. 1928-1931
Author(s):  
Li Li He ◽  
Xiao Chun Lou
Keyword(s):  
Formation Control ◽  
Three Dimensional ◽  
Target Point ◽  
Control Methods ◽  
Agent Based ◽  
Geometric Characteristics ◽  
Specific Direction ◽  
Multi Agent ◽  
Formation Method ◽  
Dimensional Simulation

Multi-agent formation control is the process in which the teams formed by multiple agents move to specific target or specific direction. The formation method of the linear formation and circular formation are given in this paper, based on the geometric characteristics of the formation formed by multi-agent. The process in which 5 agents arrived at the designated target point and formed a linear formation is achieved through simulation; and 4 agents formed a circular formation and cooperated to carry heavy weights. The result of the three-dimensional simulation shows the feasibility of the method to form multi-agent formations in different environments and different tasks.

Rigidity-Based Stabilization of Multi-Agent Formations

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Xiaoyu Cai ◽  
Marcio de Queiroz
Keyword(s):  
Formation Control ◽  
Potential Functions ◽  
Control Law ◽  
Multi Agent Systems ◽  
Rigidity Matrix ◽  
Agent Model ◽  
Multi Agent ◽  
Error Dynamics ◽  
Integrator Model ◽  
Double Integrator

This paper is concerned with the decentralized formation control of multi-agent systems moving in the plane using rigid graph theory. Using a double-integrator agent model (as opposed to the simpler, single-integrator model), we propose a new control law to asymptotically stabilize the interagent distance error dynamics. Our approach uses simple backstepping and Lyapunov arguments. The control, which is explicitly dependent on the rigidity matrix of the undirected graph that models the formation, is derived for a class of potential functions. Specific potential functions are then used as a demonstration inclusive of simulation results.

Swarm Motion as Particles of a Continuum With Communication Delays

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Hossein Rastgoftar ◽  
Suhada Jayasuriya
Keyword(s):  
Time Delay ◽  
Formation Control ◽  
Communication Delay ◽  
Multi Agent Systems ◽  
Local Communication ◽  
Agent Systems ◽  
Characteristic Roots ◽  
Multi Agent ◽  
Homogeneous Map ◽  
The Stability

In this paper, we give an upper bound for the communication delay in a multi-agent system (MAS) that evolves under a recently developed continuum paradigm for formation control. The MAS is treated as particles of a continuum that transforms under special homeomorphic mapping, called a homogeneous map. Evolution of an MAS in ℝn is achieved under a special communication topology proposed by Rastgoftar and Jayasuriya (2014, “Evolution of Multi Agent Systems as Continua,” ASME J. Dyn. Syst. Meas. Control, 136(4), p. 041014) and (2014, “An Alignment Strategy for Evolution of Multi Agent Systems,” ASME J. Dyn. Syst. Meas. Control, 137(2), p. 021009), employing a homogeneous map specified by the trajectories of n+1 leader agents at the vertices of a polytope in ℝn, called the leading polytope. The followers that are positioned in the convex hull of the leading polytope learn the prescribed homogeneous mapping through local communication with neighboring agents using a set of communication weights prescribed by the initial positions of the agents. However, due to inevitable time-delay in getting positions and velocities of the adjacent agents through local communication, the position of each follower may not converge to the desired state given by the homogeneous map leaving the possibility that MAS evolution may get destabilized. Therefore, ascertaining the stability under time-delay is important. Stability analysis of an MAS consisting of a large number of agents, leading to higher-order dynamics, using conventional methods such as cluster treatment of characteristic roots (CTCR) or Lyapunov–Krasovskii are difficult. Instead we estimate the maximum allowable communication delay for the followers using one of the eigenvalues of the communication matrix that places MAS evolution at the margin of instability. The proposed method is advantageous because the transcendental delay terms are directly used and the characteristic equation of MAS evolution is not approximated by a finite-order polynomial. Finally, the developed framework is used to validate the effect of time-delays in our previous work.

Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

2014 ◽  
Author(s):  
Xiaoyu Cai ◽  
Marcio de Queiroz
Keyword(s):  
Graph Theory ◽  
Formation Control ◽  
Control Law ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Simulation Results ◽  
Error Dynamics ◽  
Integrator Model ◽  
Dynamic Formation

In this paper, we consider the problem of formation control of multi-agent systems where the desired formation is dynamic. This is motivated by applications, such as obstacle avoidance, where the formation size and/or geometric shape needs to vary in time. Using a single-integrator model and rigid graph theory, we propose a new control law that exponentially stabilizes the origin of the nonlinear, inter-agent distance error dynamics and ensures tracking of the desired formation. The extension to the formation maneuvering problem is also discussed. Simulation results for a five-agent formation demonstrate the control in action.

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