Environmental Boundary Tracking Using Multiple Autonomous Vehicles

1. Environmental Boundary Tracking Using Multiple Autonomous Vehicles Mayra Cisneros & Denise Lewis Mentor: Martin Short July 16, 2008

2. 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

3. 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 Boundary Tracking Algorithm – One Autonomous Vehicle • x=x+v*cos • y=y+v*sin Gradient-Free Boundary Tracking Zhong Hu (Kemp-Bertozzi-Marthaler 2004)

4. Starting inside the boundary Starting outside the boundary Boundary Tracking With One Autonomous Vehicle

5. 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: 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. Gradient-Free Boundary Tracking Zhong Hu (Kemp-Bertozzi-Marthaler 2004)

6. Without CUSUM With CUSUM CUSUM Filters

7. 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

8. 18 robots, without noise 18 robots, with noise Boundary Tracking With Multiple Autonomous Vehicles

9. Boundary Tracking With Multiple Autonomous Vehicles

10. Gas Diffusion • Concentration equation: • D ~ 0.15 cm2/s • Evolving the concentration equation over time will produce a simulation of gas diffusing – initial concentration – time – diffusion coefficient – radius

11. Boundary Tracking Algorithm - Diffusion Simulation • Uses the boundary tracking algorithm for multiple robots • Additional input: maximum time T, size of time step dt • Given an image, the user selects starting points for the robots • While 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

12. Boundary Tracking on the Diffusion Simulation

13. 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.

14. 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.

15. 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.

16. 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.