environmental boundary tracking using multiple autonomous vehicles mayra cisneros & denise lewis...
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Environmental Boundary Tracking Using Multiple Autonomous Vehicles
Mayra Cisneros & Denise Lewis
Mentor: Martin Short
July 16, 2008
Project Details
Goal: Using autonomous vehicles, track the boundary of some gas released in Los Angeles.Boundary tracking One autonomous vehicle Multiple autonomous vehicles Images with noise Moving boundary
Gas diffusion Evolve concentration equation Include obstacles like buildings in the simulation
Sensor networks
Boundary Tracking Algorithm – One Autonomous Vehicle
Input: angular velocity , tracking velocity v
User selects a point on the image
If the point is inside the boundary, d=1
Else, d=-1
Set =0
For a fixed number of iterations = +d* If a full circle is completed, v=2*v If the boundary is crossed
d=-d update using angle correction
x=x+v*cos y=y+v*sin
θ
θ θ θ θ
ω
ω
θ Gradient-Free Boundary Tracking Zhong Hu
(Kemp-Bertozzi-Marthaler 2004)
Boundary Tracking With One Autonomous Vehicle
Starting inside the boundary
Starting outside the boundary
CUSUM Filters
If the image has noise, the algorithm fails to track the boundary. In order to use the algorithm we have to use CUSUM filters:
U and are the accumulation threshold, is the image, is
the intensity at point , is the threshold for the image, and
and are the “dead-zone” parameters.
L A ),( yxA),( yx B uc
lcGradient-Free Boundary Tracking Zhong Hu
(Kemp-Bertozzi-Marthaler 2004)
CUSUM Filters
Without CUSUM With CUSUM
Boundary Tracking Algorithm – Multiple Autonomous Vehicle
Similar to the algorithm for one autonomous vehicle
Additional input: number of robots
The user can select a point on the image or a starting point can be randomly generated
Instead of using a for loop, the algorithm runs until all the robots have stopped
A robot stops when it intersects the boundary track of any other robot including itself
Boundary Tracking With Multiple Autonomous Vehicles
18 robots, without noise 18 robots, with noise
Boundary Tracking With Multiple Autonomous Vehicles
Gas Diffusion
Concentration equation:
D ~ 0.15 cm2/s
Evolving the concentration equation over time will produce a simulation of gas diffusing
0C
Dtr
– initial concentration
– diffusion coefficient
– time
– radius
Boundary Tracking Algorithm - Diffusion Simulation
Uses the boundary tracking algorithm for multiple robotsAdditional input: maximum time T, size of time step dtGiven an image, the user selects starting points for the robotsWhile t T and the robots aren’t done tracking the boundary Create an image of the diffusion simulation at the current
time step, t Plot the current position of all the robots along with all the
previous positions on the new image t=t+dt
Boundary Tracking on the Diffusion Simulation
Smart Sleeping Policies for Energy Efficient Tracking in Sensor Networks
Tracks a randomly moving object in a dense network of wireless sensors.
Sensor may be put in a sleep mode to conserve energy.
Therefore, energy saving can result in tracking errors.
Goal: Build a simulation of the algorithm where the trade off is optimized.
Assumptions
Sensor has a limited range for detecting the object.
The network is sufficiently dense.
Central controller assign sleep times.
A sensor that is asleep cannot be communicated with or woken up prematurely .
Once the object leaves the network, it will not return.
Markov chain is used to describe an object whose statistics are known a priori.
Sleeping Policies
To determine the best sleeping policy: Partially observable Markov decision process (POMDP).
There is two solutions: Optimal and suboptimal solutions.
Suboptimal solution perform better than a random
sleeping time.
Future Work
Including obstacles like buildings in the diffusion simulation.
Smart Sleeping Policies simulation Tracking a randomly moving object in a dense network of
wireless sensors.