Homework 3 - Localizing a stationary robot

MAE 4180/5180, ECE 4772/5772, CS 3758
Autonomous Mobile Robots
Homework 3 - 
A document containing the answers and figures should be uploaded to Gradescope as HW3writeup.pdf.
All the code and the files needed to run the code are to be uploaded to Canvas as a zip file named
HW3code.zip. Note, the code zip file should contain ONLY .m files and files containing data (if needed) and
not any other file (writeup, assignment, etc). Specific functions, as indicated below, should be uploaded
to their corresponding assignments on Canvas.
Notes about autograded assignments:
• We highly recommend you develop and debug the autograded functions in Matlab. The error messages
that the autograder provides are not as explicit as in Matlab
• You may submit as many times as you like until the deadline
• Make sure to also include the functions in the zip file you upload to Canvas
• Reusing code: We encourage you to reuse your prior functions in the new functions. For the autograded assignments, if you want to use a previous function you have written (for example robot2global),
simply copy-paste it below the function you are writing
Localizing a stationary robot (80 Points)
A point robot is standing in place in the map described in HW3map.mat which contains the coordinates of
all walls in the environment: [x1, y1, x2, y2]. The file stationary.mat contains the sensor measurements for
the robot. Each line contains the range measurements in the global North, East, South and West directions.
The maximum range of the sensor is less than 3 meters (a measurement of NaN indicates no obstacle within
the sensing range).
Assume that there is no uncertainty in the angle and that the North and South ranges have noise that
is distributed N(0,0.1) and the East and West ranges have noise that is distributed N(0,0.3). All range
measurements are independent of each other.
Grid localization (30 points)
1. Write the function gridLocalizationStationary.m that returns the pdf representing the location of
the robot. This function should accept as input the size of the grid (n × m) where n is the number
of cells along the X dimension and m the number fo cells along the Y dimension. Explain how you
addressed the measurement issue discussed in class (with respect to where is the measurement?).
2. Assume a 10x10 grid. What is your initial distribution?
3. Plot the pdf - the initial one and the final one (after incorporating all measurements). You may find
the function plotGridBelief.m useful.
4. Calculate and plot a pdf for a grid size of 40x22. Plot the final pdf. Do you get the same possible
robot location(s) as in part 3? explain.
Kalman filter (30 points)
1. Write the function KFStationary.m that estimates the position of the robot using a Kalman Filter.
2. What is your prediction step. Do you need one?
3. How is the update performed? (write the equation)
4. What are you choosing as your initial distribution? why those values?
5. Plot the initial and final position and covariance estimates (1 σ) on the map. (Hint: for plotting the
ellipse, do not forget the functions posted at the beginning of the semester on Canvas)
6. Try a different initial distribution. How does that affect the position estimate?
7. Would an EKF be more appropriate for this problem? explain.
Test function (autograded) (10 points)
1. Edit the test function on Canvas TestFunHW3.m look for comments that begin with ‘STUDENTS’ and
follow the directions. Course staff will use this function to test your code with different inputs and we
are using the autograder as a way to ensure the test function runs. We are NOT testing for correctness
of the algorithm.
Make sure the zip file you submit on Canvas contains this function and all of the functions
necessary to run it.
Location estimate (10 points)
1. For both filters, would you be able to estimate the location exactly given perfect range information?
Explain. (5 points)
2. You are told that the robot’s y coordinate is less than 8. Based on the various pdfs found in the
previous sections, can you estimate the true position of the robot? Explain (no need to run the filters)
(5 points)
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