Swarm Robot Theoretical Research - Revision history

Jonathan Lee at 21:20, 18 August 2009

2009-08-18T21:20:00Z

Sam Bobb at 19:28, 18 August 2009

2009-08-18T19:28:51Z

Sam Bobb: /* '''Theoretical Research''' */

2009-08-18T19:28:12Z

'''Theoretical Research'''

Sam Bobb: New page: == '''Theoretical Research''' == ==='''Introduction'''=== In this theoretical research part, we will introduce project related research papers and provide with a brief explanation for ma...

2009-08-18T19:27:36Z

New page: == '''Theoretical Research''' == ==='''Introduction'''=== In this theoretical research part, we will introduce project related research papers and provide with a brief explanation for ma...

New page

== '''Theoretical Research''' ==

==='''Introduction'''===

In this theoretical research part, we will introduce project related research papers and provide with a brief explanation for main ideas, algorithms, for papers. Major mathematical expressions, or equations, for each paper will be presented. Also, there will be link for original papers.

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==='''Bibliography Report'''===

===='''i. Distributed Kriged Kalman Filter for Spatial Estimation'''====

'''Author: Jorge Cort´es'''

This paper considers robotic sensor networks performing spatially-distributed estimation tasks. A robotic sensor network takes successive point measurements, in an environment of interest, of a dynamic physical process model as a spatio-temporal random field. The paper introduces Distributed Kriged Kalman Filter for predictive inference of the random field and its gradient.

Physical process as spatio-temporal Gaussian random field Z:
 
[[Image:Gaussian random field.gif]]
 
Mean: [[Image:Mean.gif]]

 
Robotic network of n agents {p1, … , pn} in Rd:
 
[[Image:Robotic Network.gif]]
 
Number of network agent n is a priori known to everybody

 
Spatial Prediction:
 
[[Image:Spatial Prediction.gif|650px]]
 
For spatial prediction, simple kriging and parameter estimation are combined. Similar procedure can be carried out for sequential estimation, when measurements are taken successively.

Link for this paper: [http://tintoretto.ucsd.edu/jorge/publications/data/2007_Co-tac.pdf http://tintoretto.ucsd.edu/jorge/publications/data/2007_Co-tac.pdf]

===='''ii. Data Assimilation via Error Subspace Statistical Estimation'''====

'''Author: P. F. J. LERMUSIAUX'''

This paper introduces an efficient scheme for data assimilation in nonlinear ocean atmosphere models via ESSE approach. The main goal of this paper is to develop the basis of a comprehensive DA scheme for the estimation and simulation of realistic geophysical fields. The main concept, or whole flow, of this paper is depicted as a figure below:
[[Image:ESSE_flow.gif|left|thumb|ESSE flow]]
Dynamical model: [[Image:Dynamical Model.gif]]

Mesurement model: [[Image:Mesurement Model.gif]]

Predictability and Model errors: [[Image: Predictability and Model Errors.gif]]

[[Image: f hat.gif]]: the expected value of f

 

Link for this paper: [http://web.mit.edu/pierrel/www/Papers/mwr2_99.pdf http://web.mit.edu/pierrel/www/Papers/mwr2_99.pdf]

===='''iii. Parameter Uncertainty in Estimation of Spatial Functions: Bayesian Analysis'''====

'''Author: Peter K. Kitanidis'''

This paper analyzes the problem of uncertain parameter and its effect on inference of spatial functions with Bayesian analysis. Parameters are treated as random variables with probability distributions reflecting the known facts. The analysis shows how prior information about the parameters may be combined in the analysis with information in the sample. The result provides insight into the applicability of maximum likelihood versus restricted maximum likelihood parameter estimation, and conventional linear versus kriging estimation.
 
General Model: [[Image:General model.gif]]
 
x: the vector of spatial coordinates of the point where y is sampled
 
β: (generally unknown) parameter
 
fi(x): known functions of the spatial coordinates
 
ε(x): zero-mean spatial random function; existed random measurement error would be incldued

 
Prediction model: [[Image:Prediction model.gif]]
 
Prediction model may be defined as finding the PDF
 
y0: a vector of unknown point or weighted-average values of given observation y
 
X0: the matrix of deterministic effects for y0

Download this paper:[[Media:parameter uncertainty in estimation of spatial functions, bayesian analysis.zip | parameter uncertainty in estimation of spatial functions, bayesian analysis]]

===='''iv. Adaptive Sampling Using Feedback Control of an Autonomous Underwater Glider Fleet'''====

'''Author: Edward Fiorelli, Pradeep Bhatta, Naomi Ehrich Leonard'''

This paper presents strategies for adaptive sampling using Autonomous Underwater Vehicle, simply AUV, fleets. The main idea is the use of feedback that integrates distributed measurements into a coordinated mission planner. The cooperative gradient climbing is intended to allow the glider fleet make use of observational data and therefore overcome errors in forecast data.

Link for this paper: [http://www.princeton.edu/~naomi/uust03FBLSp.pdf http://www.princeton.edu/~naomi/uust03FBLSp.pdf]

===='''v. Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment'''====

'''Author: Petter Ögren, Edward Fiorelli,and Naomi Ehrich Leonard'''

This paper presents a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed and distributed environment. It focuses on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb.

Link for this paper: [http://www.princeton.edu/~naomi/OgrFioLeoTAC04.pdf http://www.princeton.edu/~naomi/OgrFioLeoTAC04.pdf]

===='''vi. Adaptive Sampling for Estimating a Scalar Field using a Robotic Boat and a Sensor Network'''====

'''Author: Bin Zhang and Gaurav S. Sukhatme'''

This paper shows an adaptive sampling algorithm for a mobile sensor network to estimate a scalar field. The data from robots are used to estimate the scalar field. It also explains how the IMSE and the second derivatives of the phenomenon investigated are related to each other. In this paper, the estimation is based on local linear regression, the non-parametric regression where the predictor does not have the fixed form but the predictor is going to be constructed by the information gathered from the data. Of many non parametric estimators, this paper deals with the Kernel estimator.

Basic Model: [[Image:basic_model.jpg]]

Y = scalar response

m(x) = function to be estimated

LLR estimator:
 
[[Image:LLR_estimator.jpg]]
 

IMSE of LLR estimator: [[Image:IMSE_of_LLR.jpg]]

Link for this paper: [http://cres.usc.edu/pubdb_html/files_upload/524.pdf http://cres.usc.edu/pubdb_html/files_upload/524.pdf]

===='''vii. Consensus Filters for Sensor Networks and Distributed Sensor Fusion'''====

'''Author: Reza Olfati-Saber, Jeff S. Shamma'''

This paper introduces a distributed filter that allows the nodes of a sensor network to track the average of n sensor measurements using an average consensus based distributed filter called consensus filter. This consensus filter is very important in solving a data fusion problem. The objective of this algorithm mentioned in this paper is to design the dynamics of a distributed low-pass filter that takes u as an input and y = x as the output whose property is that asymptotically all nodes of the network reach an ε-consensus regarding the value of signal r(t) in all time t. This paper also introduces the various properties of this distributed filter.

Consensus Algorithm: [[Image:consensus_algorithm.jpg]]

Sensing Model: [[Image:sensing_model.jpg]]

Dynamic Consensus Algorithm: [[Image:dynamic_consensus_algorithm.jpg]]

Link for this paper: [http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc05/pdffiles/papers/1643.pdf http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc05/pdffiles/papers/1643.pdf]

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← Older revision		Revision as of 19:28, 18 August 2009
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			[[Category:SwarmRobotProject]]

← Older revision		Revision as of 19:28, 18 August 2009
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	== '''Theoretical Research''' ==

	==='''Introduction'''===		==='''Introduction'''===

@@ Line 1: / Line 1: @@
-==='''Introduction'''===
+=='''Introduction'''==
-In this theoretical research part, we will introduce project related research papers and provide with a brief explanation for main ideas, algorithms, for papers. Major mathematical expressions, or equations, for each paper will be presented. Also, there will be link for original papers.
+In this theoretical research part, we will introduce project related research papers and provide with a brief explanation for main ideas, algorithms, for papers. Major mathematical expressions, or equations, for each paper will be presented. Also, there will be link for original papers. For more information regarding swarm robots and related projects, please refer to the [[:category:SwarmRobotProject|'''SwarmRobotProject''']] category link at the bottom of every related page.
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-==='''Bibliography Report'''===
+=='''Bibliography Report'''==
-===='''i. Distributed Kriged Kalman Filter for Spatial Estimation'''====
+==='''i. Distributed Kriged Kalman Filter for Spatial Estimation'''===
 '''Author: Jorge Cort´es'''
@@ Line 35: / Line 34: @@
 Link for this paper: [http://tintoretto.ucsd.edu/jorge/publications/data/2007_Co-tac.pdf http://tintoretto.ucsd.edu/jorge/publications/data/2007_Co-tac.pdf]
-===='''ii. Data Assimilation via Error Subspace Statistical Estimation'''====
+==='''ii. Data Assimilation via Error Subspace Statistical Estimation'''===
 '''Author: P. F. J. LERMUSIAUX'''
@@ Line 53: / Line 52: @@
 Link for this paper: [http://web.mit.edu/pierrel/www/Papers/mwr2_99.pdf http://web.mit.edu/pierrel/www/Papers/mwr2_99.pdf]
-===='''iii. Parameter Uncertainty in Estimation of Spatial Functions: Bayesian Analysis'''====
+==='''iii. Parameter Uncertainty in Estimation of Spatial Functions: Bayesian Analysis'''===
 '''Author: Peter K. Kitanidis'''
@@ Line 80: / Line 79: @@
 Download this paper:[[Media:parameter uncertainty in estimation of spatial functions, bayesian analysis.zip | parameter uncertainty in estimation of spatial functions, bayesian analysis]]
-===='''iv. Adaptive Sampling Using Feedback Control of an Autonomous Underwater Glider Fleet'''====
+==='''iv. Adaptive Sampling Using Feedback Control of an Autonomous Underwater Glider Fleet'''===
 '''Author: Edward Fiorelli, Pradeep Bhatta, Naomi Ehrich Leonard'''
@@ Line 88: / Line 87: @@
 Link for this paper: [http://www.princeton.edu/~naomi/uust03FBLSp.pdf http://www.princeton.edu/~naomi/uust03FBLSp.pdf]
-===='''v. Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment'''====
+==='''v. Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment'''===
 '''Author: Petter Ögren, Edward Fiorelli,and Naomi Ehrich Leonard'''
@@ Line 96: / Line 95: @@
 Link for this paper: [http://www.princeton.edu/~naomi/OgrFioLeoTAC04.pdf http://www.princeton.edu/~naomi/OgrFioLeoTAC04.pdf]
-===='''vi. Adaptive Sampling for Estimating a Scalar Field using a Robotic Boat and a Sensor Network'''====
+==='''vi. Adaptive Sampling for Estimating a Scalar Field using a Robotic Boat and a Sensor Network'''===
 '''Author: Bin Zhang and Gaurav S. Sukhatme'''
@@ Line 117: / Line 116: @@
 Link for this paper: [http://cres.usc.edu/pubdb_html/files_upload/524.pdf http://cres.usc.edu/pubdb_html/files_upload/524.pdf]
-===='''vii. Consensus Filters for Sensor Networks and Distributed Sensor Fusion'''====
+==='''vii. Consensus Filters for Sensor Networks and Distributed Sensor Fusion'''===
 '''Author: Reza Olfati-Saber, Jeff S. Shamma'''
@@ Line 131: / Line 130: @@
 Link for this paper: [http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc05/pdffiles/papers/1643.pdf http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc05/pdffiles/papers/1643.pdf]
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+=='''Conclusion'''==
+For the theoretical research part of the project, we found a few algorithms to process the data collected by the color sensor and estimate the environment, as listed above. Some algorithms uses a similar and related method, and some algorithms uses unique method. By comparing those algorithms, we will find the best method which can be applied to the Swarm Robot Project to process the data collected by the color sensor.
 [[Category:SwarmRobotProject]]