Pursuer Evader Control Policies for RoboMotes & Robots

1. PEG Breakout Mike, Sarah, Thomas, Rob S., Joe, Paul, Luca, Bruno, Alec

2. What’s the goal? • Develop groundbreaking control Policies that bound the time to capture the evader • Pursuer(s) to catch dumb and smart evader(s) in bounded time • Proving it in the real world • Short Term (1yr): RC Car RoboMotes • Long Term (2-3yrs): Macro Robots and UAVs • ASAP

3. Pursuer Evader Game Overview • N pursuer chasing M Evader on a 2D grid • Pursuer: • Minimize the expected capture time • Evader: • Not captured by some time bound • Real time dynamic programming of this problem is intractable • Unreliable feedback with inherent errors on sensory data

4. Narrowing down the problem • 1 pursuer and 1 evader • Scale speed of the cars to compensate for network delay • Retain history and prediction to cope with delay • Given jitter/delay model and maximum error bound on estimation, bound the time to capture the evader • 1 hop communication to the pursuer and evader

5. Interface of different components • Position Estimation • X,Y for Pursuer and Evader with delay and error bound • Cars Control • Series of speed, angle commands

6. Action 1: Sense and Estimate • On line position calibration to give error bound • Make time of flight estimation work • Modeling delay and error • need to run and characterize the sensor network

7. Action 2: Close the loop • Computation of pursuer’s movement on MATLAB • Run with MATLAB simulation with traces • Send out commands to pursuer • Easy way to test out different algorithm in MATLAB • Control Evader • Same problem of pursuer’s algorithm but completely opposite • Have algorithms compete on both side at the same time and compare

8. Pursuer / Evader Development Kit • Sensor Network Provides P&E Location Estimates at > 1 Hz • These estimates can be modulated with different precision and delay • Magnetometer on the car • Acoustic / Sounder on the car • Centralized car control scheme • Position Estimates go to the base station • Mica RoboMotes accept commands to move • MATLAB UI • Test out 5 different strategies per day

9. Ideas to Pursue • Speed Up Position Estimates to 5-10Hz OR Reengineer Cars to go Slow • Car control with magnetometer giving car’s heading • Compass heading • Explore using sound and magnetic field to estimate position of pursuer/evader • Pursuer generates AC magnetic field • Needs a localization that supports multiple agents (3+3 MAX)

11. Specification • Pursuer/Evader Overview • N number of pursuer • 2D mobile robot • Same capabilities • Minimize the expected capture time • Pursuer is within some range of the evader • Pursuer can go at different speed

12. Game: dynamic programming • Not possible to compute in real time • Use heuristics • 8 cells around you • Creates a map • Simplest: cells that are on with probability one • Cells that are far away have some probability < 1 • Do a local finding by pursuer • Sensor networks augment it • Color detection on the evader • Laser pointing • Helicopter has a camera

13. Design a policy • Map one or more pursuer to the evader • Narrow it to one evader • Tracking controller that minimizes the distance

14. Problem • Loss, delay, • Delay corresponds to speed • Failure model • Retain your history • Loss is lack of update

15. Calibration

16. Leader Election

17. Reliable Transport

18. Error Model • Using the sensor network to quantify expected capture time

19. Separate network channel • Pursuer and Evader

20. Pursuer can ask network • Where did the evader go?

21. Control • Sensing is distributed • Stability of the system • Introduce new constraints

22. Demo • Step 1: • Move the pursuer • Calibrate Position estimation and error bound • Using magnetometer to track pursuer • Eventually, we have multiple • Localize pursuer with beacons • Modulating the magnetic field on the pusrsuer • Or use the sound • Time of flight will work • On line calibration on localization • data out of sensor network

23. Step 2 • Pursuer’s computation • Where to compute • Depends on the algorithm • MATLAB simulation with traces and run with the same code in real • Step 2: • Algorithms make assumption of lossy updates • Give errors of the current estimate

24. Control Evader • Test the problem of both side the same time • Two matches • Same algorithm • Control the evader and the pursuer • Compare algorithms

25. Magnetometer • No centering • Precision Navigation • PNI • Digital output • Set/reset • No drift • Measure absolute filed • Little resistor

26. How to go from one to many?

27. How to model your time delay? • Jitter • Correct sensor network data • Model the sensor network • *** implement the car • Need to run and characterize the sensor network

28. Kit Upgrade • Multiple evader/multiple pursuer • But single hop to the robot • Drives the challenge of localization: • Pursuer tracked by audio • Magnetometer is very unreliable for distance estimate • Proximity may be fine • Unless you use an AC magnetic field • Detect • Needs a localization that supports multiple agents (3 MAX)

29. Define Interface for other components to plug in

30. Kit 3

31. Distributed Mapping • Map of objects • Map of probabilistic of where the evader is • Accelerometer • Coarse estimation of where you are from magentometer • Accelerometer gives high frenquency data • Many robots map out the space through localization of each other