Position offering letter

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EECS 4200/5200 Term Project (10%) sp21

Modeling of Soft Landing of Mars ‘Perseverance’ Rover

Introduction

On February 18, 2021 the Mars Perseverance Rover landed on Mars’s Jezero Crater. Sent to look

for signs of ancient life and to collect rock samples, the process of landing on Mars safely required

a team of scientists and researchers to derive a series of complex maneuvers. Over the course of

this project, you will take on the role of these scientists and create models of the soft landing

procedure.

Objectives of the Term Project

The term project's primary objective is to impart practical skills necessary to develop a real-world

system model. The student is expected to be able to do the following by the completion of this

term project:

1. To generate a model of a practical system by the laws of the physical sciences governing

the system’s behavior. In this case, it is Translational Motion Mechanical System.

2. Convert the model into a Free Body Diagram with all acting forces presented.

3. Create a Set of Differential Equations pertaining to the diagram.

4. Presentation of the equation in Matrix form with State variables and Output.

5. Develop Signal Flow Graph and defining the System Transfer function.

6. Identification of key design parameters from literatures and reference material and

utilization/application to the modeling process.

7. Calculation of key parameters such as masses, velocities, gravity, etc. Any defined

values from correlating literature (web, text, papers) must be specified regarding author(s),

title, page, date, address (if Web).

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Background

While performing the soft-landing on Mars, the Perseverance rover underwent a series of stages

where numerous elements of the system would provide support ensuring a safe landing. As far as

the soft-landing is concerned, at approximately 12 kilometers from the surface of Mars, the

parachute of the Perseverance rover was deployed to slow its descent. After a reasonable amount

of deacceleration, the heat shield was removed, allowing the cameras onboard the rover to obtain

their first glimpse of the surface of Mars. Further into the descent, the engine of the hover unit was

activated as the backshell containing the connection to the parachute was separated. At this stage

of the descent, the rover’s landing was assisted by the hover unit providing upward thrust to

decrease the velocity at which it fell. Finally, after a predetermined height over the surface was

reached, the hover unit took on the role of a helicopter and hovered in position. Then, the hover

unit behaved like a “skycrane” where it gradually lowered the rover onto the surface.

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Project Description

The project you are assigned is concerned with the soft landing of the Perseverance rover; in other

words, starting with the deployment of the parachute and onwards as it descends. For purposes of

the project, we are to analyze the soft-landing system at the instant in which the parachute is

deployed and the hover unit engines are activated providing upward thrust. In order words,

the backshell is still attached while the heat shield has been removed. Furthermore, we

assume the “skycrane” is already activated with its full length and the rover has touched the

surface. As a student, you are to model this landing system and derive a series of requirements

based upon the description provided below:

1. The masses of the system considered are from the hover unit (M1) and the rover (M2).

The backshell is assumed negligible and can be ignored as a mass (for simplicity).

2. As opposed to the backshell, we will assume the parachute is connected straight to the

hover unit. It can be thought of as a spring (K1), while the “skycrane” the hover unit

uses to lower the rover is also a spring (K2).

3. The parachute provides air resistance relating to the descent which can be thought

of as friction (B1). Likewise, the “skycrane” between the hover and the rover has a

friction of (B2).

4. The force the hover unit exerts to allow the system to hover is described as [ F(t)].

5. Refer to the displacement of the hover unit as y1(t) and the displacement of the rover

as y2(t).

6. Hint: Read through the provided resources to help decrease any difficulties.

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The Perseverance Rover

Backshell, Hover and Rover

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Details of Soft Landing Model

As defined within the objectives, using the masses, friction, spring constants, displacement and

force, you are to create a model illustrating how these components are correlated to one another

(connections, placement, etc.). This diagram will serve as the basis you will use to create a free

body diagram of the system. The diagram must show all relevant forces and interactions. Using

the free body diagram you created, you must derive their associated differential equations. You

may assume all initial conditions to be equal to zero. Next, you are to present these equations in

matrix format in addition to representing the output. You will then prepare a signal flow diagram

of the system which will guide you in presenting a transfer function.

In other words, you are to deliver the following in sequence:

*Notes

Per each of the deliverable below, specify the source of information, type of information you

use, how you apply this information to yield each item of deliverable. If you miss this

description, points will be deducted.

1. Draw a schematic to illustrate this Translational Motion Mechanical system.

2. Create a Free Body Diagram depicting the system (show all the parameters with

directions).

3. Develop a set of differential equations based on this system. Assume all initial

conditions are zero.

4. Convert your differential equation into a state equation formatting.

5. Depict your state equation in matrix format. Also include the output equation as a

matrix too.

6. Draw a Signal Flow Graph (Observable form) using the states you created earlier as a

guide. (mark the state variables on the graph)

7. Prepare a Transfer Function given input F and output y1.

Hint: Use Mason’s Rule based off the signal flow graph you drew previously.

8. Given the provided literature and any other sources you find online (cite your references

as per the instructions in the objectives section), Provide a Table of Key Parameters

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which present a numerical values for M1, M2, K1, K2, B1, B2, Y1 and Y2. Note that

you may not find values for all of them. Present whatever you can find and suggest

reasonable values per each parameter with source of information (title, author, page,

date, web address if from web) if not possible, with justification.

Further Requirements

1) You are to prepare a discussion detailing the procedure you followed to create your

diagrams and how you went about solving them. Furthermore, all necessary calculations

must be shown within your work. A scan representing your illustrations and calculations

is accepted.

2) Present a section titled “Self-Assessment on the Use of Collected Information” where

you collectively include answers to the following:

a. Where do you get the information needed for modeling per each stage?

b. What information you collected?

c. How do you use the information for modeling project and which stage?

d. By including the values you got from the literature, what benefit did you receive from

this project?

3) Finally, provide a short conclusion summarizing the project.

Resources

Here are resources to help you get started. Feel free to resort to anything else you can find.

https://mars.nasa.gov/mars2020/

https://www.nasa.gov/perseverance

https://mars.nasa.gov/resources/25529/mars-2020-perseverance-landing-press-kit/

(It is highly suggested you view the above press kit)

https://www.youtube.com/watch?v=4czjS9h4Fpg&ab_channel=NASA

(This video shows the soft-landing along with each of the steps detailed in the project)

https://openoregon.pressbooks.pub/bodyphysics/chapter/lunar-lander/

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Midterm Project Report

Your project report should be written in a professional manner including the following items in

sequence:

1.Cover page: Course name, Project name, Your name, Date, Pledge (include the paragraph

Below ass you did for Test)

Pledge and Acknowledgement

By writing my name, I pledge that: this is my own work and I do not give or receive any help in

completing this term project. In addition, I acknowledge that there will be a penalty for late

submission.

Name____________________________ Date ___________________

2. Table of Contents

3. Schematic Diagram of Translational Mechanical Motion-Mars Soft Landing Rover

4. Free Body Diagram

5. Set of Differential Equations

6. State Equations with state variables and Output Equation

7. Matrix format of item 6 above

8. Signal Flow Graph marked with all state variables and parameter values

9. Key Parameter Value Table (per each parameter, specify the source as described

in “item 8 of Details of Soft Landing Model”)

10. Signal Flow Graph (Observable Form)

11. Transfer function T(s) for input F and output Y1

12. Discussions

13.Self-Assessment on the use of Collected Information

14. Conclusions

15. List of References (include all references used to identify parameter values and modeling)

*Formatting and Submission

Typed document submitted as a PDF. Scanned pages showing work are accepted.

File name: 4200Projyourname.pdf

Upload to Project link in BB

Due: 5 PM April 27 (Tu), 2021. No Late Submission Accepted !