复杂系统chapter 4 multi-agent systems

Consensus tracking algorithms
Consensus tracking algorithms
When the consensus reference state is constant
i ui
Consensus tracking algorithms
Consensus tracking algorithms
Multi-agent formation control
Some space transformation 1.Translation transformation
Multi-agent formation control
Some space transformation 2.Scale transformation
Multi-agent formation control
Some space transformation 3.Rotation transformation
(1) Axis z y
x x cos y sin y x sin y cos z z
y y cos z sin z y sin z cos x x
Consensus tracking algorithms
When the consensus reference state is time-varying
i ui
Can the control is still valid?
Consensus tracking algorithms
the associated directed graph has a directed spanning tree
Multi-agent consensus control
Multi-agent consensus control
then the consensus equilibrium is the average of the initial information states, a condition called average consensus. Algorithm achieves average consensus asymptotically if and only if directed graph is strongly connected and balanced or undirected graph is connected.
Example: Vicsek model
Consensus tracking algorithms
Example: Vicsek model
Outline
Multi-agent consensus control
Multi-agent formation control
Multi-agent formation control
Consensus is achieved or reached by the team of agents if, for all xi(0),
Example
Multi-agent consensus control
What are the conditions under which the information states of consensus algorithm converge when the communication topology is time invariant and the gains aij are constant?
Optimization and performance evaluation for complex systems
Hu Jiangping School of Automation Engineering
Multi-agent systems
Introduction
Multi-agent consensus control
0 0 0 1
Multi-agent formation control
3.Rotation transformation
R(, , ) R z ( )R y ()R z ( ) cos sin 0 cos 0 sin cos sin 0 sin cos 0 0 1 0 sin cos 0 0 0 1 sin 0 cos 0 0 1
Consider a team of n = 4 vehicles together with the virtual team leader, vehicle 5. The virtual team leader has a constant consensus reference state ξr ≡ 1
Statistical Physics and emergence of collective behavior
Outline
Multi-agent consensus control
Multi-agent formation control
Multi-agent setting: Vicsek model
The main objective is to propose and analyze consensus algorithms to ensure that each agent in the team reaches consensus on a constant or time-varying consensus reference state that evolves with time or according to nonlinear dynamics when the consensus reference state is available only to a subgroup of the followers
Example (dynamical interconnection)
r
Connectivity condition
Matrix theory
ergodic
Example (dynamical interconnection)
Example (dynamical interconnection)
Consensus tracking algorithms
Consensus tracking algorithms
Consensus tracking algorithms
(a)
Consensus tracking algorithms
(b)
Consensus tracking algorithms
Multi-agent formation control
Introduction The problem of coordination of multiple agents arises in numerous applications, both in natural and in man-made systems. Examples from nature include:
How can a group of moving agents collectively decide on direction, based on nearest neighbor interaction?
r neighbors of agent i agent i
How does global behavior emerge from local interactions?
0 0 0 1
0 1 0 cos x y z 1 x y z 1 0 sin 0 0
0 sin cos 0
cos 0 x y z 1 x y z 1 sin 0
0 sin 1 0 0 cos 0 0
Example (dynamical interconnection)
Example (dynamical interconnection)
Example (dynamical interconnection)
Consensus tracking algorithms
Suppose that the team consists of the same n agents together with an additional (virtual) vehicle We call agent n +1 the team leader and agents 1,...,n the followers.
Multi-agent consensus control
Illustrative Example
Multi-agent consensus control
Multi-agent consensus control
Discrete-time consensus algorithm
Multi-agent consensus control
Crowd Dynamics and Building Egress
Introduction
Example from robotic cooperation
Multi-Robot Manipulation
Fundamental Questions In order to analyze such systems and design coordination strategies, several questions must be addressed: What are the dynamics of the individual agents? How do the agents exchange information? How do we couple the available outputs to achieve collective behaviors?