Defence Presentation [Autosaved] Final

Examining Committee:

Dr. Ya-Jun Pan (Supervisor)Dr. Jason Gu (External)Dr. Robert Bauer (Internal)

Moderator: Dr. George Jarjoura

- Presented by Ajinkya Pawar (M.A.Sc Candidate)

Leader-following Consensus of Multi-agent System with Communication Constraints using Lyapunov-based Control

Presentation Outline

Introduction to Multi-agent Systems (MAS)

Leader-following Consensus of MAS

Consensus Control of MAS

Simulink Results

Experimental Setup and Results

Conclusion and Future Works

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Multi-agents Systems (MAS)

An Agent is defined as a computational entity

that can sense and act as well as decide on its

actions in accordance with some assigned

tasks or goals.

Multi-agent System (MAS) is a specific type of

system which composes of several agents that

interact with each other to achieve certain

objectives.

Agent

Environment

Sen

sory

Inp

ut

Act

ion

Ou

tpu

t

Source: http://www.dcsc.tudelft.nl/Research 3

Advantages of Multi-agents Systems (MAS)

Distributes computational resources and capabilities.

MAS models problems in terms of autonomous interacting agents.

MAS efficiently retrieves and filters the global information states.

Can work and also find solutions in conditions where it is difficult for human

to reach or even to work.

Comparing with independent working of agents, MAS seems more reliable

and more efficient.

Decentralized MAS eradicates the system failure chances.4

Applications of Multi-agents Systems (MAS)

Formation Control

Autonomous Formation Flight (AFF).

Unmanned Aerial Vehicles (UAVs)

significantly attracted military’s interest

because of low cost, easy maneuver, high

stability and zero casualty.

AFF control laws utilize a combination of local

and global information states.

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-886

NASA, in 2002,

implemented AFF by

using F/A-18 fighters. 5

Applications of Multi-agents Systems (MAS)

Rendezvous and Cooperative Surveillance

Rendezvous problem involves bringing a

collection of vehicles to a common location at a

common time.

Cooperative Surveillance involves using several

vehicles to maintain a centralized or

decentralized description of the state of a

geographical area.

http://users.cms.caltech.edu/~murray/preprints/mur07

Information states about

spatially fixed or

moving entities are part

of surveillance. 6

Applications of Multi-agents Systems (MAS)

Environmental Sampling

Autonomous Ocean Sampling Network (AOSN)

consists of robotic vehicles that are used for

“adaptive sampling”.

The vehicles traverse random paths to record

observations. This approach allows the sensors to

be positioned in areas where they are highly

efficient.

http://users.cms.caltech.edu/~murray/preprints/mur07

Cooperative control

strategy is used to

control motion of

vehicles. 7

Applications of Multi-agents Systems (MAS)

Intelligent Transport System

Make use of modern communication and

information technology to increase the efficiency

of transport management system in order to

optimize vehicle life, fuel efficiency, safety and

traffic.

California Partners for Advanced Transit and

Highways (PATH) demonstrated automatic

highway system.

http://www.horiba-mira.com/MIRA/

Also suitable for air

traffic control.

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Thesis Motivation

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Wireless networked communication control systems pose different

challenges to control engineers like time-delays, packet data loss,

switching topologies, noise, quantization error etc.

Very few literature on the leader-following consensus of MAS with

presence of both time delays as well as packet dropout.

Lyapunov-based control methodology to be adopted for consensus

Leader-follower Consensus of MAS

Leader

Follower 3Follower 1 Follower 2

Source: http://users.ece.gatech.edu/

Agents are differentiated as leaders and followers.

Leader agent follows pre-assigned trajectory or

generates it’s own trajectory.

Follower agent tracks the leader’s trajectory.

Follower agent tries to reduce its distance from the

leader agent.

Leader-following consensus can be easily

extended to leader-formation control.

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Multi-agent System Dynamics

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Multi-agent System Dynamics

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Multi-agent System Dynamics with Constant Time-Delay and Packet Loss

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14

Multi-agent System Dynamics with Constant Time-Delay and Packet Loss

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Multi-agent System Dynamics with Constant Time-Delay and Packet Loss

Multi-agent System Error Dynamics with Constant Time-Delay and Packet Loss

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Multi-agent System Error Dynamics with Constant Time-Delay and Packet Loss

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Multi-agent System Error Dynamics with Constant Time-Delay and Packet Loss

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Multi-agent System and Error Dynamics with Time-varying Delay and Packet Loss

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Consensus Control of MAS with Constant Time-Delay and Packet Loss

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Consensus Control of MAS with Constant Time-Delay and Packet Loss

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Consensus Control of MAS with Constant Time-Delay and Packet Loss

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Consensus Control of MAS with Constant Time-Delay and Packet Loss (Final LMI)

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Consensus Control of MAS with Time-varying Delay and Packet Loss

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Consensus Control of MAS with Time-varying Delay and Packet Loss

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Simulink Results

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There are five conditions for which Simulink results are plotted but categorized

in three cases.

Case 1: Effect of different data loss rate without time delays on consensus of

MAS.

Case 2: Effect of time delays on consensus of MAS, where one condition is

with constant time-delay and other condition with time-varying delay.

Case 3: Effect of increasing the number of agents on consensus of MAS,

where one condition is without time-delay and other condition with constant

time delay.

Simulink Results (Case 1)

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Case 1: Effect of different data loss rate without time delays on consensus

of MAS.

The directed graph topology for this case is,

The adjacency and Laplacian matrix are:

Simulink Results (Case 1)

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Example 1: Data Loss Rate, r = 0%

i.e. no data loss rate (ideal condition)

Example 2: Data Loss Rate, r = 10%

Simulink Results (Case 1)

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Example 3: Data Loss Rate, r = 20% Example 4: Data Loss Rate, r = 30%

Simulink Results (Case 1)

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Example 5: Data Loss Rate, r = 80% Example 6: Data Loss Rate, r = 98%

Simulink Results (Case 1)

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Summary of the effect of increase in data loss rate on consensus time

ExampleData Loss Rate in

%Consensus Time

(seconds)

1 0 19

2 10 27

3 20 36

4 30 102

5 80 300

6 98 1200 or inf

Simulink Results (Case 2)

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Case 2: Effect of time delays on consensus of MAS

The directed graph topology for this case is,

The adjacency and Laplacian matrix are:

Simulink Results (Case 2 – Condition 1)

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Condition 1: Effect of constant time delay and fixed data loss rate at 10%

Example 1: Data Loss Rate, r = 10% and Constant time-delay = 0.001 seconds or 1 millisecond

Example 2: Data Loss Rate, r = 10% and Constant time-delay = 0.005 seconds or 5 milliseconds

Simulink Results (Case 2 – Condition 1)

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Condition 1: Effect of constant time delay and fixed data loss rate at 10%

Example 3: Data Loss Rate, r = 10%

and Constant time-delay = 0.01

seconds or 10 milliseconds

Example 4: Data Loss Rate, r = 10% and Constant time-delay = 0.1 seconds or 100 milliseconds

Simulink Results (Case 2 – Condition 1)

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Summary of the effect of increase in constant time-delay at fixed data

loss rate of 10% on consensus time

ExampleTime Delay

(milliseconds)Consensus Time

(seconds)

1 1 33

2 5 34.5

3 10 37

4 100 41

Simulink Results (Case 2 – Condition 2)

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Condition 2: Effect of time-varying delay and fixed data loss rate at 10%

Example 1: Data Loss Rate, r = 10% and Time-varying delay= 0.001 seconds to 0.01 second

Example 2: Data Loss Rate, r = 10% and Constant time-delay = 0.01 seconds to 0.1 second

Simulink Results (Case 2 – Condition 2)

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Condition 2: Effect of time-varying delay and fixed data loss rate at 10%

Example 3: Data Loss Rate, r = 10% and Time-varying delay= 0.001 seconds to 0.1 second

Example 4: Data Loss Rate, r = 10% and Constant time-delay = 0.001 second to 0.5 second

Simulink Results (Case 2 – Condition 2)

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Summary of the effect of increase in range of time-varying delay at

fixed data loss rate of 10% on consensus time.

ExampleTime-Varying Delay Range

(milliseconds)

Consensus Time (seconds)

1 1-10 34

2 10-100 36

3 1-100 46

4 1-500 103

Simulink Results (Case 3)

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Case 3: Effect of increase in number of agents on consensus of MAS

The directed graph topology for this case is,

The adjacency and Laplacian matrix are:

Simulink Results (Case 3 – Condition 1)

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Condition 1: Effect of increase in number of agents with no time delay and 10 % Data Loss Rate

Simulink Results (Case 3 – Condition 2)

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Condition 2: Effect of increase in number of agents with constant time delay of 1 millisecond and 10 % Data Loss Rate

Simulink Results (Case 3)

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Summary of the effect of increase in number of agents with a no time

delay case and a constant time delay case.

Experimental Setup

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Omron-Adept Pioneer P3-DX Mobile Robot

16 Ultrasonic Sensors (8 Front and 8 Rear)

Max Speed: 1.6 m/s

Max Payload: 23 kg

Motor with 500 tick encoder

Three hot swappable 9Ah sealed batteries

Source: http://www.cyberbotics.com/

Experimental Setup

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Communication Channels

Experimental Setup

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ARIA- Advanced Robot Interface for Applications

Experimental Result

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Pioneer Robot Modeling

Converted Single-Integrator system:

In Discrete Time System:

Control Gain: 0.5638 0

0 0.8571

Experimental Result

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Experimental Result for 10% Data Loss Rate and 0.5 second Constant Time-

delay for one virtual leader and two follower agents

Video Of Experiment performed

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Conclusions

• A novel consensus algorithm for the MAS in the event of communication link failure over the network was developed and tested.

• The permissible value of data loss rate that can be permissible is 20% though it can be observed that the consensus is still possible for higher percentages of data loss rates.

• The consensus time for higher data loss rates are not feasible, for which there needs to be threshold range of consensus time within which the consensus if achieved should be treated as feasible.

• For, constant time-delay, the consensus time is permissible till 30 to 40 seconds.

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Conclusions

• Increasing the data loss rate increases the consensus time, but the feasible result was observed till 10% data loss rate.

• The experimental setup was also carried out at data loss rate of 10%.

• For constant time-delay, the increase in value of time delay increases the consensus time. For the considered system, the permissible value of time delay is limited to the sampling time i.e. 0.1 second or 100 milliseconds.

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Future Works

• Can be applied to higher order dynamics.

• Time delays higher than the sampling period should be considered as condition for controller design.

• Switching topology case can be considered.

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Author Publication List

Conference Paper:

A. Pawar and Y.J. Pan, "Leader-following Consensus Control of Multi-Agent Systems with Communication Delays and Random Packet Loss", In Proceedings of the IEEE American Control Conference, June 2016, Boston, USA, pp.4464-4469.

Journal Paper:

X. Gong, Y.J. Pan and A. Pawar, "A Novel Leader Following Consensus Approach for Multi-Agent Systems with Data Loss", International Journal of Control, Automation and Systems, Accepted, April 2016.

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