Mercurial Hosting > traffic-intelligence
changeset 240:d2b68111f87e
added module for extrapolation
author | Sarah@Sarah-PC.polymtl.ca |
---|---|
date | Fri, 13 Jul 2012 17:08:31 -0400 |
parents | 93c26e45efd8 |
children | 942455aff829 |
files | python/extrapolation.py |
diffstat | 1 files changed, 173 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/python/extrapolation.py Fri Jul 13 17:08:31 2012 -0400 @@ -0,0 +1,173 @@ +########## +# Extrapolation Hypothesis +########## + +import sys + +sys.path.append("G:/0-phdstart/Code/traffic-intelligence1/python") + +import moving + +#Default values +FPS= 25 # No. of frame per second (FPS) +vLimit= 25/FPS #assume limit speed is 90km/hr = 25 m/sec +deltaT= FPS*5 # extrapolatation time Horizon = 5 second + +def ExtrapolationPosition (movingObject1, instant,deltaT): + ''' extrapolation hypothesis: constant velocity''' + return movingObject1.getPositionAtInstant(instant) + movingObject1.getVelocityAtInstant(instant). multiply(deltaT) + +def motion (position, velocity, acceleration): + ''' extrapolation hypothesis: constant acceleration''' + from math import atan2,cos,sin + vInit= velocity + vInitial= velocity.norm2() + theta= atan2(velocity.y,velocity.x) + vFinal= vInitial+acceleration + + if acceleration<= 0: + v= max(0,vFinal) + velocity= moving.Point(v* cos(theta),v* sin(theta)) + position= position+ (velocity+vInit). multiply(0.5) + else: + v= min(vLimit,vFinal) + velocity= moving.Point(v* cos(theta),v* sin(theta)) + position= position+ (velocity+vInit). multiply(0.5) + return(position,velocity) + +def motionPET (position, velocity, acceleration, deltaT): + ''' extrapolation hypothesis: constant acceleration for calculating pPET ''' + from math import atan2,cos,sin,fabs + vInit= velocity + vInitial= velocity.norm2() + theta= atan2(velocity.y,velocity.x) + vFinal= vInitial+acceleration * deltaT + if acceleration< 0: + if vFinal> 0: + velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta)) + position= position+ (vInit+ velocity). multiply(0.5*deltaT) + else: + T= fabs(vInitial/acceleration) + position= position + vInit. multiply(0.5*T) + elif acceleration> 0 : + if vFinal<= vLimit: + velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta)) + position= position+ (vInit+ velocity). multiply(0.5*deltaT) + else: + time1= fabs((vLimit-vInitial)/acceleration) + velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta)) + position= (position+ (velocity+vInit). multiply(0.5*time1)) + (velocity.multiply (deltaT-time1)) + elif acceleration == 0: + position= position + velocity. multiply(deltaT) + + return position + +def timePET (position, velocity, acceleration, intersectedPoint ): + ''' extrapolation hypothesis: constant acceleration for calculating pPET ''' + from math import atan2,cos,sin,fabs + vInit= velocity + vInitial= velocity.norm2() + theta= atan2(velocity.y,velocity.x) + vFinal= vInitial+acceleration * deltaT + if acceleration< 0: + if vFinal> 0: + velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta)) + time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x))) + else: + time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x))) + elif acceleration> 0 : + if vFinal<= vLimit: + velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta)) + time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x))) + else: + time1= fabs((vLimit-vInitial)/acceleration) + velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta)) + time2= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x))) + if time2<=time1: + time= time2 + else: + position2= (position+ (velocity+vInit). multiply(0.5*time1)) + time= time1+fabs((intersectedPoint.x-position2.x)/( velocity.x)) + elif acceleration == 0: + time= fabs((intersectedPoint.x-position.x)/(velocity.x)) + + return time + +def motionSteering (position, velocity, deltaTheta, deltaT ): + ''' extrapolation hypothesis: steering with deltaTheta''' + from math import atan2,cos,sin + vInitial= velocity.norm2() + theta= atan2(velocity.y,velocity.x) + newTheta= theta + deltaTheta + velocity= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta)) + position= position+ (velocity). multiply(deltaT) + return position + +def MonteCarlo(movingObject1,movingObject2, instant): + ''' Monte Carlo Simulation : estimate the probability of collision''' + from random import uniform + from math import pow, sqrt, sin, cos,atan2 + N=1000 + ProbOfCollision = 0 + for n in range (1, N): + # acceleration limit + acc1 = uniform(-0.040444,0) + acc2 = uniform(-0.040444,0) + p1= movingObject1.getPositionAtInstant(instant) + p2= movingObject2.getPositionAtInstant(instant) + v1= movingObject1.getVelocityAtInstant(instant) + v2= movingObject2.getVelocityAtInstant(instant) + distance= (p1-p2).norm2() + distanceThreshold= 1.8 + t=1 + while distance > distanceThreshold and t <= deltaT: + # Extrapolation position + (p1,v1) = motion(p1,v1,acc1) + (p2,v2) = motion(p2,v2,acc2) + distance= (p1-p2).norm2() + if distance <=distanceThreshold: + ProbOfCollision= ProbOfCollision+1 + t+=1 + POC= float(ProbOfCollision)/N + return POC + +def velocitySteering(velocity,steering): + from math import atan2,cos,sin + vInitial= velocity.norm2() + theta= atan2(velocity.y,velocity.x) + newTheta= theta + steering + v= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta)) + return v + +def MonteCarloSteering(movingObject1,movingObject2, instant,steering1,steering2): + ''' Monte Carlo Simulation : estimate the probability of collision in case of steering''' + from random import uniform + from math import pow, sqrt, sin, cos,atan2 + N=1000 + L= 2.4 + ProbOfCollision = 0 + for n in range (1, N): + # acceleration limit + acc1 = uniform(-0.040444,0) + acc2 = uniform(-0.040444,0) + p1= movingObject1.getPositionAtInstant(instant) + p2= movingObject2.getPositionAtInstant(instant) + vInit1= movingObject1.getVelocityAtInstant(instant) + v1= velocitySteering (vInit1,steering1) + vInit2= movingObject2.getVelocityAtInstant(instant) + v2= velocitySteering (vInit2,steering2) + distance= (p1-p2).norm2() + distanceThreshold= 1.8 + t=1 + while distance > distanceThreshold and t <= deltaT: + # Extrapolation position + (p1,v1) = motion(p1,v1,acc1) + (p2,v2) = motion(p2,v2,acc2) + distance= (p1-p2).norm2() + if distance <=distanceThreshold: + ProbOfCollision= ProbOfCollision+1 + t+=1 + POC= float(ProbOfCollision)/N + return POC + +