PEG Breakout

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

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

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

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

Interface of different components

• Position Estimation– X,Y for Pursuer and Evader with delay and

error bound

• Cars Control– Series of speed, angle commands

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

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

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

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)

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

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

Design a policy

• Map one or more pursuer to the evader

• Narrow it to one evader

• Tracking controller that minimizes the distance

Problem

• Loss, delay, – Delay corresponds to speed– Failure model

• Retain your history

• Loss is lack of update

Calibration

Leader Election

Reliable Transport

Error Model

• Using the sensor network to quantify expected capture time

Separate network channel

• Pursuer and Evader

Pursuer can ask network

• Where did the evader go?

Control

• Sensing is distributed

• Stability of the system

• Introduce new constraints

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

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

Control Evader

• Test the problem of both side the same time

• Two matches– Same algorithm

• Control the evader and the pursuer

• Compare algorithms

Magnetometer

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

How to go from one to many?

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

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)

Define Interface for other components to plug in

Kit 3

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