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Solar System (Particle Filter) Project
Spring 2024 – Deadline: Monday February 26th, 11:59p AOE
Project Description
After completing an intergalactic mission, it’s time for you to return home. The goal of this project is to give you practice implementing a particle filter used to localize a man-made 10.2-meter satellite in a solar system. The satellite has a mass between 1000-100,000 kg. Your satellite is warped through a wormhole and released into your home solar system in approximate circular orbit around the sun. The satellite receives measurements of the magnitude of the collective gravitational pull of the planets in the solar system. Note that this measurement does NOT include the gravitational effects of the sun. Although the gravitational acceleration of other planets can be measured, curiously in your home solar system, the satellite and the planets follow their orbit around the sun and their motion is not affected by other planets.
You will be riding in the satellite which will exit the wormhole somewhere within the solar system. Your satellite will exit possibly as far off as +/- 4 AU in both X and Y, and will be ejected into circular counter-clockwise orbit around the sun, which is located somewhere within +/- 0.1 AU in both X and Y.
The planets in the solar system are also orbiting counter-clockwise around the sun in circular or elliptical orbits.
You also have at most 300 days to locate yourself and the satellite before food and resources run out.
Note that your software solution is limited to 15 seconds of“real”CPU time, which is different from the simulated“satellite time”. Unless your localization and control algorithm is VERY efficient, you will probably not hit the 300-day limit before you run into the CPU timeout. If it takes your localization system more than 100-200 days to determine the satellite location, you may need to improve your localization algorithm.
The gravimeter sensor gives you a (noisy) magnitude of the sum across each planet of the gravitational acceleration on the satellite by that planet, +/- some Gaussian noise.
where v is the gravity magnitude, n is the number of planets, G is the gravitational constant, Mp is the mass of planet p, and r is the vector from the satellite to the planet.
The body.py file (which you should not modify, but may examine or import) implements the simulated planets.
The solar_system.py file (which you should not modify, but may examine or import) contains the model for the sun and planets.
The satellite.py file (which you should not modify, but may examine or import) may be used to simulate a satellite.
The solar_locator.py file contains two functions that you must implement, and is the only file you should submit to GradeScope.
Part A
After warping back to your home solar system, you must localize where you are. The first function is called estimate_next_pos, and must determine the next location of the satellite given its gravimeter measurement and the distance and steering of its next motion. If your estimate is less than 0.01 AU from the target satellite’s actual (x,y) position, you will succeed and the test case will end.
Note that your function is called once per day (time step), and each time your function is called, you will receive one additional data point. It is likely you will need to integrate the information from multiple calls to this function before you will be able to correctly estimate your satellite’s position. The“OTHER”variable is passed into your function and can be used to store data which you would like to have returned back to your function the next time it is called (the next day).
A particle filter may include the following steps and you may want to consider the following questions:
• Initialization
– How many particles do you need such that some cover the target satellite?
• Importance Weights
– How does the sigma parameter affect the probability density function of a gaussian distribution and the weights of the particles?
• Resample
– How many particles should you keep at each timestep and what are the pros/cons to having more/less particles?
• Fuzz
– How much positional fuzzing should you have?
– What percentage of your particles should you fuzz?
• Mimic the motion of the target satellite by utilizing a bicycle motion model
• Estimate
Part B
The second function is called next_angle. The goal of this function is to once again localize the satellite using different target satellite measurement information and to set the angle to send a radio message from the satellite to your home planet.
Unlike in part A where a single gravimeter measurement is taken each timestep, part B will provide multiple percent illumination measurements each timestep. The satellite will take percent illumination readings for each planet in order of closest to furthest from the sun.
The percent illumiation describes what fraction of a planetary body’s 2D face is in sunlight. The phase angle is the angle between sun-planet-satellite and is used to compute the percent illumination. When sun-satellite-planet are in line, the phase angle is 0 degrees, the planet will look like a full moon, and the planet will be 100% illuminated. When sun-planet-satellite are in line, the phase angle is 180 degrees, the planet will look like a new moon, and the planet will be 0% illuminated.
PERCENT_ILLUMINATION = 50 × (1 + cos (PHASE_ANGLE))
Now that you’re back in your home solar system and have localized your satellite, you must send SOS messages back to your home planet, the last/ outer-most planet in the solar system, so that they know to come pick you up. Each message you send contains part of your location and trajectory. It takes 10 messages to fully transmit this data. When your home planet receives your messages they will send a team out to retrieve you and your satellite. The test will end once your home planet has received 10 messages.
The next_angle function will return an absolute angle from the satellite to the home planet in radians as well as the predicted location of the satellite.
Submitting your Assignment
Please refer to the“Online Grading”section of the Syllabus
Calculating your score
The test cases are randomly generated, and your particle filter is likely to also perform differently on different runs of the system due to the use of random numbers. Our goal is that you are able to generate a particle filter system that is generally able to solve the test cases, not one that is perfect in every situation.
You will receive seven points for each successful test case, even though there are 20 test cases in total (10 in part A, 10 in part B). This means that you only need to successfully complete 15 of the 20 test cases to receive a full score on this assignment. Your maximum score will be capped at 100, although if you are able to solve more than 15 test cases you can brag about it.
Testing Your Code
NOTE: The test cases in this project are subject to change.
We have provided you a sample of 10 test cases where the first two test cases are easier than the actual test cases you will be graded with because they have no measurement noise. These test cases are designed to allow you to test an aspect of the simulation. Test cases 3-10 are more representative of the test cases that will be used to grade your project.
To run the provided test cases on the terminal: python testing_suite_full.py
We will grade your code with 10 different“secret”test cases per part that are similar, but not an exact match to any of the publicly provided test cases. These“secret”test cases are generated using the generate_params_planet.py file that we have provided to you. You are encouraged to make use of this file to generate additional test cases to test your code.
We have provided a testing suite similar to the one we’ll be using for grading the project, which you can use to ensure your code is working correctly. These testing suites are NOT complete as given to you, and you will need to develop other test cases to fully validate your code. We encourage you to share your test cases (only) with other students on Ed.
By default, the test suite uses multi-processing to enforce timeouts. Some development tools may not work as expected with multi-processing enabled. In that case, you may disable multi-processing by setting the flag DEBUGGING_SINGLE_PROCESS to True. Note that this will also disable timeouts, so you may need to stop a test case manually if your filter is not converging.
You should ensure that your code consistently succeeds on each of the given test cases as well as on a wide range of other test cases of your own design, as we will only run your code once per graded test case. For each test case, your code must complete execution within the proscribed time limit (15 seconds) or it will receive no credit. Note that the grading machine is relatively low powered, so you may want to set your local time limit to 3 seconds to ensure that you don’t go past the CPU limit on the grading machine.
Academic Integrity
You must write the code for this project alone. While you may make limited usage of outside resources, keep in mind that you must cite any such resources you use in your work (for example, you should use comments to denote a snippet of code obtained from StackOverflow, lecture videos, etc).
You must not use anybody else’s code for this project in your work. We will use code-similarity detection software to identify suspicious code, and we will refer any potential incidents to the Office of Student Integrity for investigation. Moreover, you must not post your work on a publicly accessible repository; this could also result in an Honor Code violation [if another student turns in your code]. (Consider using the GT provided Github repository or a repo such as Bitbucket that doesn’t default to public sharing.)
Frequently Asked Questions (F.A.Q.)
• Q How can I simplify this problem to make thinking about it easier?
– A Take a look at this video that uses a particle filter to solve a 1D problem that has a lot of similarities to this one: Particle Filter explained without equations – https://www.youtube.com/watch?v=aUkBa1zMKv4
• Q Are you SURE this can be solved using a particle filter?
– A Yes. See https://mediaspace.gatech.edu/media/t/1_c1f99rxe
• Q What is fuzzing?
– A Fuzzing is the process of perturbing (a percentage of) the particles with the intention of diversifying your hypotheses (covering a wider search area). Fuzzing is also known as dithering or roughening (sometimes called jittering). It is discussed in these papers: Sample Impoverishment, PF: Tutorial, Roughening Methods
• Q How can I turn on the visualization?
– A Near the top of testing_suite_full.py set PLOT_PARTICLES=True. When PLOT_PARTICLES is set to True, you will be presented with a visualiza-tion. While debugging wih visualization, you may consider also setting DEBUGGING_SINGLE_PROCESS=True to allow the test case to run beyond the‘TIME_LIMIT’.
• Q What is each color/object in the visualization?
– A Red triangle is the target satellite. White triangles are the particles. Cyan square is your estimated (x,y) for the satellite. Lime circles are planets, and magenta circle with a skyblue trail is the home planet.
• Q Can I pause the visualization?
– A There is a pause button in the upper right corner of the visualization that will pause the screen for PAUSE_DURATION seconds. To pause the first time step, set PAUSE_FIRST=True. Pausing frequently and/or for long durations may require adjustments to the‘TIME_LIMIT’.
• Q How can I change the TIME_LIMIT?
– A There are additional ALL CAPS variables near the top of the testing_suite_full.py file. They are by default set to the same values used by the grader, but you can toggle the True/False values to enable/disable verbose logging and the visualization, and increase the timeout value (logging & visualization slow things down). If your computer is faster than that of Gradescope and iterates through more timesteps, you may consider decreasing the TIME_LIMIT while developing your solution.
• Q Why is my local score different from my Gradescope score?
– A The gradescope test cases are different from the student provided test cases in testing_suite_full.py. The gradescope machine may be slower or faster than your machine, causing it to iterate through more or less time steps before timing out. You’re encouraged to submit early and often – a failing solution on your local computer might do better on Gradescope and vice versa.
• Q Why do I get different results locally when the visualization is on vs off?
– A Since visualization slows things down, with visulization off your solution may get through more timesteps than with visulization on, and those extra timesteps could be where your solution succeeds.
