defence presentation [autosaved] final
TRANSCRIPT
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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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)
35
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)
42
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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