# Simulation and intelligent tracking of a robot Information Technology Assessment and Tutor Proposal ## Our Real Student’s Score cards ## Simulation and intelligent tracking of a robot

This ACW deals with modelling and simulating an intelligent robotic tracking system, and consists of 3 parts.

In part I you will be simulating an ideal robot in one dimension.
The next part, you will make this simulation more realistic, by adding white noise (random numbers with zero mean and a standard deviation, with a normal distribution). This is what is implemented in robot simulation software.
The final part is to train an intelligent agent to track this robot.

There  will be a series of compulsory  demonstrations  prior  to  the  final  submission  of  the  report.  This  demonstration  will  be  feedback  on  the  work,  and  also  enables  you  to  make  final  corrections based on yoru feedback.

### Part 1

Consider a mobile robot. This robot gets a series of commands to move to a set of coordinates, from its current coordinates in 1D space. (we can assume that this is the floor). A model of this robot is given by the following simplified model

x=-2x+2U

where X is a set of generalised coordinates as a distance from the origin. U changes with time, and represents the distance from the origin the robot has to travel, and is given by

U={2 for 0

where t is time, and you can take the units to be seconds.

Write a program to simulate this robot. You will need to use different step sizes h for this. Confirm the limiting value of h (see slides from week 2) with the simulation.

Write to file the following, x(k) and U(k), where k is the sample number. You should take your sample interval to be value>0.1 seconds. If h=0.01 seconds, then you should write to file the value every 10th integration (sample interval= h*(number of steps)).

For this part you must

• Produce the code to simulate the system. Include the logic for changing U over the period of the simulation [15+5marks]
• The report for this part of the ACW should include results for different values of step size. Look at the upper limit and lower limit for the step. Confirm this using the theoretical discussion done in class (week 2). [20 Marks]

### Part 2

Assume there is another robot in the vicinity. This second robot has a camera, which uses an intelligent predictive agent to locate and predict the location of the  robot from part I. Such systems are often effected by uncertainty and noise. For this part, we can consider all of this together as a random process, and add this to the values you have written to the file in Part I to simulate the noise.

For Part II you will need to simulate noise as a random process with mean μ=0.0 and a standard deviation σ=0.001. You should do this using the Box-Muller method of generating random numbers in a normal distribution. (See slides from week 3).
Add these numbers to the values of x(t) you have in the file from part I

These marks are distributed as follows

• The code for the random number generation, and adding to the data – to simulate the disturbances. (you need to plot the data) [5 Marks]
• Write up on the random number generation process. You should include a discussion on how and why two normally distributed random numbers are generated starting from one random number in a uniform distribution. This should be approximately 200 words for this (excludes equations etc) [5 Marks]

### Part III

In this part you will need to develop the intelligent agent which predicts the location of the robot from Part I.
Here the the problem is essentially one of being able to predict the next position of the robot. You will need to use the sensor readings, the values of x(t) after noise has been added for this part. The agent has a single neuron which is capable of learning these movements. You have to write a program to train the neuron.

You would need to do the following

• Write the code for the intelligent agent (The basic outline of the code was given to you in lectures 2 and 3.)
• Start with a perceptron and show that the perceptron is not capable of learning this data. You need to explain why.
• Replace the activation function with a logistic sigmoid. Show that the neuron is now capable of learning. Explain why.  (see slides from lectures 2/3)
• Your write-up must include the program code, the diagrams for modeling the neuron(s), and any other information useful for your conclusions.
• You will also need to explain how you would test the agent for unseen data, i.e explain whether it is able to generalize or not.
• In the data you have generated there are a number of step changes. You should test you training by plotting X(n) and X_p(n) (to get similar plots as above). You will find that there is a lag – consider why this is the case and report on this in your submission;
• Discuss  possible ways you could predict both position and velocity, either using a perceptron (or a set of perceptrons) or a multilayered network (you need not implement this part (f)).

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