1 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). 2 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. 3 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 t ...

1. 1
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

2. 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).

3. 2
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

4. 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.
3
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

5. 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

6. as y2(t).
6. Hint: Read through the provided resources to help decrease
any difficulties.
4
The Perseverance Rover
Backshell, Hover and Rover
5
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

7. 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).

8. 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
6
which present a numerical values for M1, M2, K1, K2, B1, B2,

9. 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

10. 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/
https://mars.nasa.gov/mars2020/

11. https://www.nasa.gov/perseverance
https://mars.nasa.gov/resources/25529/mars-2020-perseverance-
landing-press-kit/
https://www.youtube.com/watch?v=4czjS9h4Fpg&ab_channel=
NASA
https://openoregon.pressbooks.pub/bodyphysics/chapter/lunar -
lander/
7
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

12. ___________________
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)

13. *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
!