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
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