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Applying Techniques in Supervised Deep Learning to Steering Angle Prediction in Autonomous Vehicles Vinay Sriram, Petar Penkov, James Ye PROBLEM DEFINITION IMAGE PRE-PROCESSING CONVOLUTIONAL NEURAL NETWORK MODEL RESULTS FUTURE WORK • [1] Eliminate top-half of the images, and downsample by a factor of 100. This size captures necessary information for prediction and is of low enough dimensionality to allow training a network to be computationally feasible. • [2] Apply edge-detection: Construct an image based on thresholding and the Sobel kernel operator on input ’ : Define ) , + = −1 0 1 −2 0 2 −1 0 1 ∗ ′, 1 2 1 0 0 0 −1 −2 −1 ∗ ′ • The development of effective autonomous vehicles is a popular application of machine learning and control. • We wish to solve a learning problem predicting steering angles 4 … 6 7 over the course of a road segment from Udacity’s low-resolution images 4 … 6 7 where each 8 is defined by a 640×480×3 RGB tensor. • We partition the driving data with a 70:30 train-to-test ratio such that the test-set contains significant turning. • Introduce more class labels to better approximate angle continuity (for this, more data must be collected to provide a sufficient training volume for higher-magnitude labels). • Introduce additional conv. layers to reduce the bias of the model, and run stochastic gradient descent (on resources with more computational power) for a greater number of epochs for better convergence at local optima. • Compute cross-image gradients that can determine directions of feature change to better predict turn angles. For each (, ) in the output image, set 8B = 255 if either of the following are true, and set 8B =0 otherwise. • Sobel gradient magnitude ) (, ) D + + (, ) D is above some cutoff threshold (preserving only the edges). • Grayscale value of the pixel (, ) is above some cutoff threshold (preserving only white or near-white sections of the image). Together, lane capture is reasonable. ′ We discretize the problem: each steering angle gets a class label ∈ 1,101 , where each label represents a range of ~0.01 rad. Forward Propagation: IJ4 = (I) (I) and IJ4 = I ( I ) with 8 (4) = 8 and ℎ O,P = (QJ4) . Layer has activation func. (I) . Max Pooling [Class Probabilities] [Input Image] [Softmax Layer] [Fully-Connected Layer] [Conv. Layer - ReLu Activation] REFERENCES Cameron, Oliver. Open Sourcing 223GB of Driving Data. Medium, 5 Oct. ‘16. Pomerleau, Dean. Neural Net Perception for Mobile Robot Guidance. (1993) Unsupervised Feature Learning and Deep Learning Tutorial. Stanford. Web. http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks Cost [ examples]: , = 4 6 ∑ 4 D ℎ O,P 8 − 8 D 6 8X4 Training uses the Back-Propagation algorithm to optimize the cost J. The update rule is : ∆ I ∶= ∆ I + O \ with I = I − 4 6 ∆ I . I = I 7 IJ4 ′( I ) O \ = (IJ4) I 7 ^ I = ( ^ I 7 ^ IJ4 )′( ^ I ) O c \ = ∑ I ∗ ( ^ IJ4 ) 6 8X4 For Typical Layers: For Convolutional Layers • For training and testing, we considered in particular highway driving. The conv. neural network was effective at predicting steering angle within reasonable error. • Sobel pre-filtering of images provided very marginal benefits (between 0.001 and 0.007 RMSE on test sets). • RMSE of the above test segment was 0.031 (without Sobel preprocessing) and 0.034 (with preprocessing).

Applying Techniques in Supervised Deep Learning to ...cs229.stanford.edu/proj2016/poster/SriramPenkovYe...benefits (between 0.001 and 0.007 RMSE on test sets). • RMSE of the above

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Applying Techniques in Supervised Deep Learning to Steering Angle Prediction in Autonomous Vehicles

Vinay Sriram, Petar Penkov, James Ye

PROBLEM DEFINITION

IMAGE PRE-PROCESSING

CONVOLUTIONAL NEURAL NETWORK MODEL

RESULTS FUTURE WORK

• [1]Eliminatetop-halfoftheimages,anddownsamplebyafactorof100.Thissizecapturesnecessaryinformationforpredictionandisoflowenoughdimensionalitytoallowtraininganetworktobecomputationallyfeasible.

• [2]Applyedge-detection:Constructanimage𝑋 basedonthresholdingandtheSobelkerneloperatoroninput𝑋’:

Define 𝑆), 𝑆+ =−1 0 1−2 0 2−1 0 1

∗ 𝑋′,1 2 10 0 0−1 −2 −1

∗ 𝑋′

• Thedevelopmentofeffectiveautonomousvehiclesisapopularapplicationofmachinelearningandcontrol.

• Wewishtosolvealearningproblempredictingsteeringangles 𝛼4…𝛼6 7 overthecourseofaroadsegmentfromUdacity’s low-resolutionimages 𝑋4 …𝑋6 7 whereeach𝑋8 isdefinedbya640×480×3 RGBtensor.

• Wepartitionthedrivingdatawitha70:30train-to-testratiosuchthatthetest-setcontainssignificantturning.

• Introducemoreclasslabelstobetterapproximateanglecontinuity(forthis,moredatamustbecollectedtoprovideasufficienttrainingvolumeforhigher-magnitudelabels).

• Introduceadditionalconv.layerstoreducethebiasofthemodel,andrunstochasticgradientdescent(onresourceswithmorecomputationalpower)foragreaternumberofepochsforbetterconvergenceatlocaloptima.

• Computecross-imagegradientsthatcandeterminedirectionsoffeaturechangetobetterpredictturnangles.Foreach(𝑖, 𝑗) intheoutputimage,set𝑋8B = 255 ifeither

ofthefollowingaretrue,andset𝑋8B = 0 otherwise.• Sobelgradientmagnitude 𝑆)(𝑖, 𝑗)D + 𝑆+(𝑖, 𝑗)D isabove

somecutoffthreshold(preservingonlytheedges).• Grayscalevalueofthepixel(𝑖, 𝑗) isabovesomecutoff

threshold(preservingonlywhiteornear-whitesectionsoftheimage).Together,lanecaptureisreasonable.

𝑋′ 𝑋

Wediscretizetheproblem:eachsteeringanglegetsaclasslabel𝑥 ∈ 1,101 ,whereeachlabelrepresentsarangeof~0.01rad.ForwardPropagation:𝑧 IJ4 = 𝑊(I)𝑎(I) and𝑎 IJ4 = 𝑓I(𝑧 I )with𝑎8

(4) = 𝑥8 andℎO,P = 𝑎(QJ4).Layer𝑙 hasactivationfunc.𝑓(I) .

MaxPooling

[ClassProbabilities]

[InputImage]

[SoftmaxLayer] [Fully-ConnectedLayer] [Conv.Layer- ReLuActivation]

REFERENCESCameron,Oliver.OpenSourcing223GBofDrivingData.Medium,5Oct.‘16.

Pomerleau,Dean.NeuralNetPerceptionforMobileRobotGuidance.(1993)

UnsupervisedFeatureLearningandDeepLearningTutorial.Stanford.Web.http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks

Cost[𝑚 examples]:𝐽 𝑊, 𝑏 = 46∑ 4

DℎO,P 𝑥8 − 𝑦8

D68X4

TrainingusestheBack-Propagation algorithmtooptimizethecostJ.Theupdateruleis:∆𝑊 I ∶= ∆𝑊 I + 𝛻O \ 𝐽

with𝑊 I = 𝑊 I − 𝛼 46∆𝑊 I .

𝛿 I = 𝑊 I 7𝛿 IJ4 𝑓′(𝑧 I )

𝛻O \ 𝐽 = 𝛿(IJ4) 𝑎 I 7

𝛿^I = 𝑢𝑝𝑠𝑎𝑚𝑝𝑙𝑒(𝑊 I 7𝛿^

IJ4 )𝑓′(𝑧^I )

𝛻Oc\ 𝐽 = ∑ 𝑎 I ∗ 𝑟𝑜𝑡(𝛿^

IJ4 )68X4

ForTypicalLayers:

ForConvolutionalLayers

• Fortrainingandtesting,weconsideredinparticularhighwaydriving.Theconv.neuralnetworkwaseffectiveatpredictingsteeringanglewithinreasonableerror.

• Sobelpre-filteringofimagesprovidedverymarginalbenefits(between0.001and0.007RMSEontestsets).

• RMSEoftheabovetestsegmentwas0.031(withoutSobelpreprocessing)and0.034(withpreprocessing).

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