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.