Exercise Sheet 10 - Autonomous Systems Lab

Dr. Cédric PradalierInstitut für Robotik und Intelligente SystemeAutonomous Systems LabCLA E 16.1Tannenstraße 38092 Zürichcedric.pradalier@mavt.ethz.chwww.asl.ethz.ch/people/cedricpProblem 1: Neural Network DesignExercise Sheet 10Topics: Artificial Neural NetworksSelect appropriate neural network parameters (number of input, number of output, useof hidden layers, activation functions) for the following applications. Additionally, foreach application, describe an example data set that could be used for training the network.(a) An ANN to predict the voltage on a resistor based on its input electric current.iV(b) An ANN to predict the voltage V 1 and V 2 at the terminals of two resistors basedon their input current i.i2ii1V(c) An ANN to predict the electric current i 1 and i 2 going through two resistors in parallel,based on the voltage V on the circuit terminals.iV1V2(d) An ANN to predict the voltage on a diode based on its input electric current.iV1

(e) A classifier identifying adults based on their age.(f) A cheese factory is starting a new cheese production. They have customers forstrong mouldy cheeses and light clean cheeses, but strong clean cheeses and lightmouldy ones are much less appreciated. They have a sensor deciding if a cheese istasty (strong/light) and another one identifying the presence of mould. They wantto use this input to identify cheeses that are ready to be sold.Problem 2: Matlab ToolboxMatlab comes with a neural network toolbox, which is available in the default ETH installationpackage. In order to learn how to use it, do the tutorial given at the followingweb page:http://www.mathworks.com/products/demos/shipping/nnet/crabclassify.htmlAlternatively, find it using Google, keywords "crabclassify Crab Classification".(a) After training the network ([net,tr] = train(net,physchars,sex);), the toolboxdisplays a graph with 3 curves. Explain the role of each curve. Would it have madesense to stop the learning after 4 epochs?(b) Change the dataset definition so that the crab sex is represented as a binary value(1 = male, 2 = female). Does this change the classification performances?(c) Design a method to test what crab physical characteristic is the most importantfor the classification. Which one is the less important?(d) In the tutorial, a fixed random seed is used in order to ensure that everybody runningthe tutorial will get the same result. Try varying the random seed and observethe consequence on the classification performance. How sensitive is the systemto the initial random conditions? Are your conclusions to the previous questionsensitive to the initial random conditions?Problem 3: Implementation of the backpropagation algorithmIn the class, we have seen how to implement the back-propagation algorithm using thevector based representation of the neural network.Using the crab classification data set, the algorithm described in the slides, and a networkwith 20 internal nodes, implement the back propagation algorithm. How doesyour implementation compares to Matlab toolbox implementation in terms of classificationperformances?2

Problem 4: Neural Network ControllerThe ASL wants to build a remote controlled car piloted by a computer. Some researchhas already been completed and it is possible to know the position and orientation ofthe car at any time. It is now necessary to write a controller to follow trajectories inraces against human pilots.(a) Define the trajectory following problem in a way that can be learned by a neuralnetwork.(b) Propose a network topology that would be suitable for learning the control law.(c) Propose a strategy to train the neural network. How to be sure that the controllerwill give an appropriate control in any situation? Is this feasible?3