Stability Analysis of Swarm Based on Double Integrator Model

2006 ◽  
pp. 201-210 ◽  
Author(s):  
Dan Jin ◽  
Lixin Gao
Keyword(s):  
Stability Analysis ◽  
Integrator Model ◽  
Double Integrator

A Lyapunov Treatment of Swarm Coordination Under Conflict

2009 ◽  
Author(s):  
Paul McCullough ◽  
Mark Bacon ◽  
Nejat Olgac ◽  
Daniel A. Sierra
Keyword(s):  
Stability Analysis ◽  
Control Strategy ◽  
Interaction Force ◽  
Equal Mass ◽  
Local Vectors ◽  
Two Phases ◽  
Integrator Model ◽  
Force Profiles ◽  
Double Integrator ◽  
Approach Phase

This document considers hostile conflicts between two swarms, called pursuers and evaders, based on a double integrator model. In order to convert the marginally stable dynamics into stable-capture behavior, we introduce a control strategy based on the relative positions and velocities of opposing swarm members. To evaluate its effectiveness, a Lyapunov-based stability analysis is performed. For simplicity, this document considers swarms with equal membership strengths and equal mass only. The modeling is based on a set of suggested interaction force profiles, which are functions of local vectors. The group pursuit is conceived in two phases: the approach phase during which the two swarms act like two individuals; and the assigned pursuit phase where each pursuer is assigned to an evader.

Consensus problems in multi-agent systems with double integrator model

2010 ◽  
Vol 19 (5) ◽  
pp. 050520 ◽  
Author(s):  
Gao Li-Xin ◽  
Yan Hui-Juan ◽  
Jin Dan
Keyword(s):  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Integrator Model ◽  
Double Integrator

scholarly journals Second-Order Consensus for Multiagent Systems under Directed and Switching Topologies

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Lixin Gao ◽  
Jingjing Zhang ◽  
Wenhai Chen
Keyword(s):  
Function Method ◽  
Sufficient Conditions ◽  
Common Lyapunov Function ◽  
Special Cases ◽  
Lyapunov Function Method ◽  
Leader Following ◽  
The Common ◽  
Feedback Laws ◽  
Integrator Model ◽  
Double Integrator

We consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double-integrator model. Two different cases are considered: one is the leader-following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor-based feedback laws in both leader-following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.

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.

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.

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