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annotate python/extrapolation.py @ 245:bd8ab323c198

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corrected issue with predictPosiont static method
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Tue, 17 Jul 2012 13:25:34 -0400
parents 5027c174ab90
children 59f547aebaac
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1 #! /usr/bin/env python
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2 '''Library for moving object extrapolation hypotheses'''
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3
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4 import moving
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5
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6 class ExtrapolatedTrajectory:
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7 '''Class for extrapolated trajectories with lazy evaluation
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8 if the predicted position has not been already computed, compute it
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9
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10 it should also have a probability'''
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11 def predictPosition(self, nTimeSteps):
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12 return None
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13
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14 class ExtrapolatedTrajectoryConstant(ExtrapolatedTrajectory):
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15 '''Extrapolated trajectory at constant speed or acceleration
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16 TODO add limits if acceleration
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17 TODO generalize by passing a series of velocities/accelerations'''
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18
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19 def __init__(self, initialPosition, initialVelocity, initialAccleration = 0, probability = 1):
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20 self.initialPosition = initialPosition
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21 self.initialVelocity = initialVelocity
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22 self.initialAccleration = initialAccleration
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23 self.probability = probability
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24 self.predictedPositions = {}
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25 self.predictedVelocities = {}
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26
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27 def predictPosition(self, nTimeSteps):
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28 if not nTimeSteps in self.predictedPositions.keys():
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29 self.predictedPositions[nTimeSteps] = moving.predictPosition(nTimeSteps, self.initialPosition, self.initialVelocity, self.initialAcceleration)
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30 return self.predictedPositions[nTimeSteps]
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31
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32 # Default values: to remove because we cannot tweak that from a script where the value may be different
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33 FPS= 25 # No. of frame per second (FPS)
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34 vLimit= 25/FPS #assume limit speed is 90km/hr = 25 m/sec
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35 deltaT= FPS*5 # extrapolatation time Horizon = 5 second
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36
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37 def motion (position, velocity, acceleration):
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38 ''' extrapolation hypothesis: constant acceleration'''
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39 from math import atan2,cos,sin
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40 vInit= velocity
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41 vInitial= velocity.norm2()
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42 theta= atan2(velocity.y,velocity.x)
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43 vFinal= vInitial+acceleration
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44
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45 if acceleration<= 0:
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46 v= max(0,vFinal)
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47 velocity= moving.Point(v* cos(theta),v* sin(theta))
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48 position= position+ (velocity+vInit). multiply(0.5)
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49 else:
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50 v= min(vLimit,vFinal)
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51 velocity= moving.Point(v* cos(theta),v* sin(theta))
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52 position= position+ (velocity+vInit). multiply(0.5)
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53 return(position,velocity)
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54
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55 def motionPET (position, velocity, acceleration, deltaT):
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56 ''' extrapolation hypothesis: constant acceleration for calculating pPET '''
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57 from math import atan2,cos,sin,fabs
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58 vInit= velocity
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59 vInitial= velocity.norm2()
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60 theta= atan2(velocity.y,velocity.x)
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61 vFinal= vInitial+acceleration * deltaT
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62 if acceleration< 0:
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63 if vFinal> 0:
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64 velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
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65 position= position+ (vInit+ velocity). multiply(0.5*deltaT)
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66 else:
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67 T= fabs(vInitial/acceleration)
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68 position= position + vInit. multiply(0.5*T)
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69 elif acceleration> 0 :
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70 if vFinal<= vLimit:
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71 velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
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72 position= position+ (vInit+ velocity). multiply(0.5*deltaT)
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73 else:
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74 time1= fabs((vLimit-vInitial)/acceleration)
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75 velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta))
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76 position= (position+ (velocity+vInit). multiply(0.5*time1)) + (velocity.multiply (deltaT-time1))
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77 elif acceleration == 0:
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78 position= position + velocity. multiply(deltaT)
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79
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80 return position
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81
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82 def timePET (position, velocity, acceleration, intersectedPoint ):
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83 ''' extrapolation hypothesis: constant acceleration for calculating pPET '''
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84 from math import atan2,cos,sin,fabs
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85 vInit= velocity
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86 vInitial= velocity.norm2()
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87 theta= atan2(velocity.y,velocity.x)
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88 vFinal= vInitial+acceleration * deltaT
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89 if acceleration< 0:
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90 if vFinal> 0:
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91 velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
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92 time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
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93 else:
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94 time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x)))
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95 elif acceleration> 0 :
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96 if vFinal<= vLimit:
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97 velocity= moving.Point(vFinal* cos(theta),vFinal* sin(theta))
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98 time= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
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99 else:
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100 time1= fabs((vLimit-vInitial)/acceleration)
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101 velocity= moving.Point(vLimit* cos(theta),vLimit* sin(theta))
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102 time2= fabs((intersectedPoint.x-position.x)/(0.5*(vInit.x+ velocity.x)))
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103 if time2<=time1:
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104 time= time2
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105 else:
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106 position2= (position+ (velocity+vInit). multiply(0.5*time1))
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107 time= time1+fabs((intersectedPoint.x-position2.x)/( velocity.x))
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108 elif acceleration == 0:
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109 time= fabs((intersectedPoint.x-position.x)/(velocity.x))
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110
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111 return time
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112
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113 def motionSteering (position, velocity, deltaTheta, deltaT ):
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114 ''' extrapolation hypothesis: steering with deltaTheta'''
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115 from math import atan2,cos,sin
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116 vInitial= velocity.norm2()
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117 theta= atan2(velocity.y,velocity.x)
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118 newTheta= theta + deltaTheta
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119 velocity= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta))
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120 position= position+ (velocity). multiply(deltaT)
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121 return position
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122
243
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123 def MonteCarlo(movingObject1,movingObject2, instant):
244
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124 ''' Monte Carlo Simulation : estimate the probability of collision'''
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125 from random import uniform
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126 from math import pow, sqrt, sin, cos,atan2
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127 N=1000
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128 ProbOfCollision = 0
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129 for n in range (1, N):
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130 # acceleration limit
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131 acc1 = uniform(-0.040444,0)
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132 acc2 = uniform(-0.040444,0)
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133 p1= movingObject1.getPositionAtInstant(instant)
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134 p2= movingObject2.getPositionAtInstant(instant)
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135 v1= movingObject1.getVelocityAtInstant(instant)
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136 v2= movingObject2.getVelocityAtInstant(instant)
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137 distance= (p1-p2).norm2()
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138 distanceThreshold= 1.8
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139 t=1
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140 while distance > distanceThreshold and t <= deltaT:
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141 # Extrapolation position
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142 (p1,v1) = motion(p1,v1,acc1)
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143 (p2,v2) = motion(p2,v2,acc2)
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144 distance= (p1-p2).norm2()
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145 if distance <=distanceThreshold:
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146 ProbOfCollision= ProbOfCollision+1
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147 t+=1
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148 POC= float(ProbOfCollision)/N
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149 return POC
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150
243
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151 def velocitySteering(velocity,steering):
244
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152 from math import atan2,cos,sin
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153 vInitial= velocity.norm2()
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154 theta= atan2(velocity.y,velocity.x)
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155 newTheta= theta + steering
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156 v= moving.Point(vInitial* cos(newTheta),vInitial* sin(newTheta))
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157 return v
243
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158
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159 def MonteCarloSteering(movingObject1,movingObject2, instant,steering1,steering2):
244
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160 ''' Monte Carlo Simulation : estimate the probability of collision in case of steering'''
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161 from random import uniform
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162 from math import pow, sqrt, sin, cos,atan2
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163 N=1000
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164 L= 2.4
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165 ProbOfCollision = 0
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166 for n in range (1, N):
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167 # acceleration limit
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168 acc1 = uniform(-0.040444,0)
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169 acc2 = uniform(-0.040444,0)
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170 p1= movingObject1.getPositionAtInstant(instant)
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171 p2= movingObject2.getPositionAtInstant(instant)
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172 vInit1= movingObject1.getVelocityAtInstant(instant)
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173 v1= velocitySteering (vInit1,steering1)
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174 vInit2= movingObject2.getVelocityAtInstant(instant)
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175 v2= velocitySteering (vInit2,steering2)
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176 distance= (p1-p2).norm2()
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177 distanceThreshold= 1.8
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178 t=1
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179 while distance > distanceThreshold and t <= deltaT:
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180 # Extrapolation position
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181 (p1,v1) = motion(p1,v1,acc1)
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182 (p2,v2) = motion(p2,v2,acc2)
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183 distance= (p1-p2).norm2()
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184 if distance <=distanceThreshold:
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185 ProbOfCollision= ProbOfCollision+1
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186 t+=1
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187 POC= float(ProbOfCollision)/N
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diff changeset
188 return POC
243
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189
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190