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Design of the Life-ring Drone Delivery System (LDDS) for Rip Current Rescue Andrew Hardy Mohammed Rajeh Lahari Venuthurupalli Gang Xiang Sponsor: CATSR - Lance Sherry Support: Expert Drones - Brett Velicovich, Brian Yi Department of Systems Engineering and Operations Research George Mason University 4400 University Drive Fairfax, VA 22030-4444 United States December 9th, 2015 SYST495 Fall 2015 Senior Capstone Project Final Report
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Page 1: SYST495 Fall 2015 Senior Capstone Project Final …report totals and not rescues with specific causes, so the 32,867 is an estimate of the minimum number of rip current rescues that

Design of the Life-ring Drone Delivery System (LDDS)

for Rip Current Rescue

Andrew Hardy

Mohammed Rajeh

Lahari Venuthurupalli

Gang Xiang

Sponsor:

CATSR - Lance Sherry

Support:

Expert Drones - Brett Velicovich, Brian Yi

Department of Systems Engineering and Operations Research George Mason University

4400 University Drive Fairfax, VA 22030-4444

United States

December 9th, 2015

SYST495 Fall 2015

Senior Capstone Project

Final Report

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Table of Contents 1.0 Context Analysis .................................................................................................................. 5

1.1 Beach Analysis ................................................................................................................. 5

1.2 Beach Rescues and Fatalities .......................................................................................... 5

1.2.1 Beach Rescues .......................................................................................................... 6

1.2.2 Beach Fatalities ......................................................................................................... 8

1.3 Rip Currents ....................................................................................................................10

1.3 Drowning Process ...........................................................................................................11

1.4 Lifeguard Rescue Process ...............................................................................................12

1.5 Performance Gap ............................................................................................................13

2.0 Stakeholder Analysis ...........................................................................................................14

2.1 Liability Issues .................................................................................................................15

2.2 Stakeholder Tensions ......................................................................................................15

2.3 Win-Win ...........................................................................................................................16

3.0 problem and Need ...............................................................................................................16

3.1 Problem Statement ..........................................................................................................16

3.2 Need Statement ...............................................................................................................16

3.3 Proposed Design Solution ...............................................................................................17

4.0 Requirements ......................................................................................................................18

4.1 Mission Requirement .......................................................................................................18

4.2 Functional Requirements .................................................................................................18

4.3 Design Requirements ......................................................................................................18

4.4 Ilities Requirements .........................................................................................................19

4.4.1 Usability ....................................................................................................................19

4.4.2 Availability .................................................................................................................19

4.4.3 Reliability ..................................................................................................................19

4.4.4 Resistibility ................................................................................................................19

5.0 Concept of Operations ........................................................................................................20

5.1 Function Flow Block Diagram ..........................................................................................20

5.2 Operational Scenario .......................................................................................................21

6.0 Alternatives .........................................................................................................................22

6.1 Drone Alternatives ...........................................................................................................22

6.2 Flotation Device Alternatives ...........................................................................................22

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7.0 Method of Analysis ..............................................................................................................24

7.1 Simulation Goal ...............................................................................................................24

7.2 Equations ........................................................................................................................24

7.2.1 Power and Thrust ......................................................................................................26

7.2.2 Drag Model ...............................................................................................................28

7.2.3 Life vest Model ..........................................................................................................28

7.2.4 Main Force Model .....................................................................................................29

7.2.5 Rotational Dynamics Model .......................................................................................30

7.2 Design of Experiments for Variables ................................................................................32

7.2.1 Force of Drag ............................................................................................................32

7.2.2 Motor Parameters .....................................................................................................34

7.3 Simulation ........................................................................................................................35

7.3.1 Rip Current and Victim Process ................................................................................35

7.3.2 Lifeguard Rescue Process ........................................................................................36

7.3.3 Drone Dynamics and Control ....................................................................................37

7.3.4 Post MATLAB & Simulink Analysis ............................................................................39

7.4 Simulation Requirements .................................................................................................40

7.4.1 Functional Requirements ..........................................................................................40

7.4.2 Input Requirements ...................................................................................................40

7.4.3 Output Requirements ................................................................................................40

7.5 Simulation Design of Experiments ...................................................................................41

7.5.1 1st DoE: Victims distance from shore before dying ...................................................41

7.5.2 2nd DoE: Best Path, Best Location, Minimum Velocity Needed ................................42

7.5.3 3rd DoE: Drone Design Space Model ........................................................................43

7.5.4 4rd DoE: Guarded and Unguarded Rescue ...............................................................44

7.6 Cost Model ......................................................................................................................45

7.7 Utility Function .................................................................................................................46

8.0 Recommendations and Results ...........................................................................................46

9.0 Statement of Work ..............................................................................................................46

9.1 Scope of Work .................................................................................................................46

9.2 Schedule/Milestones .......................................................................................................47

9.3 Payment Schedule ..........................................................................................................48

9.4 Work Breakdown .............................................................................................................48

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9.4.1 Work Breakdown Structure .......................................................................................48

9.4.2 Critical Tasks ............................................................................................................49

9.4.3 Schedule ...................................................................................................................51

9.4.4 Earned Value ............................................................................................................53

10.0 Project Risk Mitigation .......................................................................................................54

References ................................................................................. Error! Bookmark not defined.

Appendix ...................................................................................................................................56

Appendix A: Federal Drone Regulations ................................................................................56

Appendix C: Matlab Modules .................................................................................................58

Linear Dynamics ................................................................................................................58

Rotational Dynamics ..........................................................................................................62

Main Model ........................................................................................................................65

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1.0 CONTEXT ANALYSIS 1.1 Beach Analysis

In the United States, approximately 42% of the adult population visits the beach every

year [1]. Beach goers visit the beach for activities such as swimming, surfing, scuba, and to just

walk around the beach. While on beaches, they pay for beach services and give revenue to the

owners. There are approximately 6,200 beaches in the United States [2]. In addition, those

beaches are a profitable business for the U.S.; they generate more than $320 billion annual

revenue [3]. The costs to manage and maintain a beach in the United States are less than 4%

of $2.65 billion annual park service budgets. For example, beach patrol in Ocean City, Maryland

operates on a budget $2.3 million [4]. On any sizable beach, there are lifeguards that make sure

beach goers are safe.

1.2 Beach Rescues and Fatalities There are different incidents that lifeguards respond to every year. Each incident can

lead to successful rescues, or in the worse case, fatalities. For the first type beach rescues, we

have considered statistical data from the USLA between 2003 and 2013 [5]. That data includes

rip currents rescues and total rescues. For fatalities, we have considered statistical data from

the USLA between 2003 and 2014 [5]. That data include surf zone fatalities total, rip current

drowning deaths and total drowning deaths. For rip current drowning deaths and total drowning

deaths, we have considered the situation when there was a lifeguard and when there was not a

lifeguard.

Please note, some beach agencies only report totals for fatalities and rescues, but not

the specific causes of rescues. For example, just because a graph says there are only two rip

current rescues that year, does not mean there were only two rip current rescues that year for

all agencies. It means only two rescues from agencies that do report that subcategory. We show

these graphs to reveal the general trends and minimum numbers regarding rescues and

fatalities.

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1.2.1 Beach Rescues

Figure 1 and Figure 2 are the most important graphs on beach rescues [6]. Figure 1

shows that rip currents are the primary cause of rescue in the United States in the last decade

since rip currents accounted for nearly 330,000 or nearly 80%, of rescues. The rescues from

surf, swiftwater, and scuba were 18%, 0%, and 1% respectively. Compared to surf, swiftwater,

and scuba rescues, rip currents are the primary cause of rescue. Figure 2 is a sample from

2012 to emphasize that rip currents are the primary cause of rescue.

Rip Current, 334184, 81%

Surf, 73670, 18%

Swiftwater, 2459, 0% Scuba, 2538, 1%

0

100000

200000

300000

400000

Rescues

Primary Cause of Rescue 2003 – 2012

Rip Current Surf Swiftwater Scuba

Rip Current, 35935, 82%

Surf, 7288, 17%

Swiftwater, 307, 1% Scuba, 272, 0%

0

10000

20000

30000

40000

Rescues

Primary Cause of Rescue 2012

Rip Current Surf Swiftwater Scuba

FIG. 1: CAUSE OF RESCUE TOTALS FOR 2003-2012

FIG. 2: PRIMARY CAUSE OF RESCUE FOR 2012

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Figure 3 shows the amount of rip current rescues from 2003 to 2013, according to the

USLA [5]. When looking at the trend line, rip current rescues are increasing over the years by a

rate of about 900 people per year. Figure 4 shows the total rescues for all causes between 2003

and 2013. The total includes rip currents with swift, surf and scuba rescues. By looking at the

trend line, total rescues are increasing over the years by an increasing rate of about 1160

people per year. When comparing rip current rescues with the total rescues, rip current rescues

are almost half of the total rescues. For example, in 2011 the rescues from rip currents were

32,867 while the total rescues were 63,909 people rescued. Remember that some agencies

report totals and not rescues with specific causes, so the 32,867 is an estimate of the minimum

number of rip current rescues that year.

y = 889.41x - 2E+06

0

10,000

20,000

30,000

40,000

50,000

2000 2005 2010 2015

Num

ber

of P

eo

ple

Year

Rip Current Rescues

y = 1163.4x - 2E+06

0

20,000

40,000

60,000

80,000

100,000

2000 2005 2010 2015

Num

ber

of P

eo

ple

Year

Total Rescues

FIG. 3: RIP CURRENT RESCUES ACROSS THE U.S. FIG. 4: TOTAL RESCUES ACROSS THE U.S.

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1.2.2 Beach Fatalities

Figure 5 shows the fatalities in 2014 in the United States according to the National

Oceanic and Atmospheric Administration (NOAA) [7]. Rip current drowning accounts for 79% of

all beach fatalities. On the other hand, drowning from high surf accounts for 7%, sneaker wave

drowning accounts for 3%, other drowning accounts for 6% and unknown drowning account for

5%. Rip current drowning accounts for the majority of beach fatalities. In addition, according to

NOAA, the 10-year average of annual rip current fatalities is 51 people per year [8]. However,

the United States Life Saving Association (USLA) believes rip current fatalities exceed 100

people every year [9].

Rip Current, 79%

High Surf, 7% Sneaker Wave, 3% Other, 6% Unknown, 5%

0%

20%

40%

60%

80%

100%

Fatalities

Surf Zone Fatalities 2014 Total

Rip Current High Surf Sneaker Wave Other Unknown

FIG. 5: FATALITY PERCENTAGES ACROSS THE U.S 2014

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y = 0.1909x - 379.16

0

5

10

2000 2005 2010 2015

Num

ber

of P

eo

ple

Year

Rip Current Guarded Deaths

Figure 6 and Figure 7 show unguarded (no lifeguards present) deaths between 2003

and 2013, and unguarded drowning deaths from rip currents from 2003 to 2013 [5]. Drowning

deaths from rip currents is slightly increasing at a rate of 0.6 per year. In Figure 7, you can see

the total unguarded drowning deaths from 2003 to 2013. The total includes rip currents with

swift, surf and scuba. The total drowning deaths is mostly stable.

Figure 9 and Figure 8 show guarded drowning deaths according to the USLA from 2003

to 2013 [5]. Guarded (lifeguard present) drowning deaths from rip currents are increasing at a

rate of 0.19 per year. The total deaths includes fatalities caused by rip currents, swiftwater, surf

and scuba. Total drowning deaths is increasing by a rate of 0.67 per year.

y = 0.6x - 1176.2

0

20

40

60

2000 2005 2010 2015

Num

ber

of P

eo

ple

Year

Rip Current Unguarded Deaths

y = 0.0545x - 20.436

0

50

100

150

2000 2005 2010 2015

Num

ber

of P

eo

ple

Year

Total Unguarded Deaths

y = 0.6727x - 1332.4

0

10

20

30

2000 2005 2010 2015Num

ber

of P

eo

ple

Year

Total Guarded Deaths

FIG. 6: UNGUARDED RIP CURRENT DEATHS ACROSS THE U.S. FIG. 7: TOTAL UNGUARDED DEATHS ACROSS THE U.S.

FIG. 9: GUARDED RIP CURRENT FATALITIES 2003-2013 FIG. 8: TOTAL GUARDED FATALITIES 2003-2013

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1.3 Rip Currents Shown by the statistics from section 1.2, beach goers who swim in the waters have to be

careful of rip currents, as they are very dangerous and they drag people away from shore.

Agencies like the USLA and NOAA are actively spreading knowledge about the dangers of rip

currents [10]. Rip currents are strong powerful currents of water that flow away from shore. They

form when waves break near the shoreline, meaning it can occur at nearly every beach.

Beaches usually have multiple rip currents spread across the shoreline.

When waves break near the shoreline, they generate feeder currents that move along

shore [11]. Once this feeder current is deflected offshore, it forms the rip current. This rip current

has a neck and a head area. The neck is the area where the rip current’s speed and strength is

highest. Most drowning deaths happen in the neck area of the rip current. The head of the rip

current is the area where the rip current’s speed and strength starts to weaken.

Shown in Figure 10, rip currents can also form around jetties. Additionally, when waves

travel through sandbars, the water level increases and this is also form rip currents. As the

water level increasers, the pressure increases and this would form faster and stronger rip

FIG. 10: IMAGE OF A LARGE RIP CURRENT NEAR A JETTY

FIG. 11: RIP CURRENT CIRCULATION DIAGRAM

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currents. Some rip currents last for many days or months, while others some last hours or days.

The table below shows the ranges for certain rip current properties [12].

TABLE 1: RIP CURRENT RANGES FOR WIDTH, LENGTH, SPEED

The width of the neck ranges between ten and two hundred feet. The neck length ranges

approximately from one hundred to one thousand feet away from shore. The speed of the rip

current ranges from one to eight feet per second. When the rip current’s speed is below four

feet per second, it is not considered to be dangerous for strong swimmers, but it is dangerous

for the weak swimmers [9]. However, if the speed exceeds four feet per second, this is

considered to be dangerous for all the swimmers.

If swimmers caught in a rip current, it is dangerous for them if they try to fight it by

swimming against the rip current. The best method is to swim parallel to the shoreline to get out

of the neck first, then swim back to shore.

1.3 Drowning Process Drowning is a very common and deadly experience. After the victim is caught in a rip

current, their first reaction is to fight it. The victim tries swimming against the current however

they should float with the current, or swim parallel to the shore.

The main reason for a victim to drown is either because they are exhausted, dehydrated,

or they do not know how to swim. Hence, they start to panic. The body accumulates carbon

dioxide which leads to dry-drowning. Dry-drowning is when the water reaches the airway, and

the lungs start to seal and the water starts to accumulate in the stomach. This eventually leads

to secondary drowning where the victim becomes unconscious and the water flows into the

lungs. In less than a minute the victim will be dead. This is shown in the figure below.

Rip Current Measurements

Width [10,200] feet

Length ~[100,1000] feet

Speed [1,8] feet/second

FIG. 12: DROWNING PROCESS

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1.4 Lifeguard Rescue Process A lifeguard chair is placed every couple meters or miles, depending on how big the

beach is. The beach is separated into multiple zones with one lifeguard chair in the top most

center of each zone. If a drowning victim is spotted in the zone, the lifeguard will radio the

control room, whistle at the adjacent lifeguards to cover their zone and point in the direction of

the victim [13]. The lifeguard then will start running towards the shoreline with either their right

hand up in the air, which means assistance is needed, or pointing and tapping on top of their

head, which means assistance is NOT needed. The lifeguard usually detects the drowning

victim when they first start to panic. The lifeguard swims to the victim, rescues them, guides

them back to the shoreline, and then drags them out of the water. Medical care is provided as

needed afterwards. This entire lifeguard rescue process takes a max of 4 minutes [14]. This

process is shown in the function block diagram depicted below.

FIG. 13: LIFEGUARD RESCUE PROCESS

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1.5 Performance Gap

FIG. 14: GAP BETWEEN SURVIVAL TIME AND RESCUE TIME

There is a gap between victim survival time and lifeguard rescue time. Shown as the

green line above, lifeguards can reach a victim in a maximum of 93 seconds [14]. Victims that

can survive more than 93 seconds are on the right side of that green line. They are safe

because they can survive long enough for lifeguards to come and rescue them. The victims that

cannot survive for more than 93 seconds are in the red shaded area. They are the ones in risk

of drowning. The time of 60 seconds marks the estimated survival time for a weak swimmer that

attempts to fight against the rip current.

60

93

Fighting Against Current

Lifeguard Reach Time

Time (s)

Max Victim Survival Time

*not in scale

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2.0 STAKEHOLDER ANALYSIS There are five main stakeholders: 1) lifeguarding associations, 2) lifeguards, 3) beach

goers, 4) manufacturers, and 5) municipalities.

1. Lifeguarding Associations

Lifeguarding associations are professional lifesaving associations that train dedicated

beach lifeguards and open water rescuers. These associations certify lifeguards and make sure

they are up to date with all four requirements: 1) Yearly licensing, 2) Four hours of in-service

training, 3) Monthly training meetings and, 4) Red ball test. If the individual meets all these

requirements each year they will be certified as a lifeguard.

2. Lifeguards

Lifeguards are strong swimmers who supervise the safety and rescue of swimmers,

surfers, and other water sports participants. Three certified lifeguards were interviewed to help

with research on rip currents, rescue process, and liability issues.

3. Beach Goers

Beach goers are people who go to the beach and use its services. They want the least

restrictions. Instructions given by lifeguards are of no concern. However, they want the

lifeguards to be 100% effective at their jobs. In other words, the beach goers want the lifeguards

to be always alert, well-trained, and to save everyone in time.

4. Manufacturers

Manufacturers are companies that produce equipment for the lifeguards. Some major

companies include Swimoutlet and Marine Rescue Products. A lifeguarding association can

also manufacture rescue products. For an example, the Jeff Ellis & Associates, an international

lifeguard training company, builds their own products such as a rescue board, a lifeguard buoy,

a ring buoy and life jackets.

5. Municipalities

municipality is broken down into owner and operator. The owner can be the county, city,

or state government that owns the beach property. The operator documents the lifeguards

current status of certification and requirements met. They are the ones who pay the lifeguarding

associations, certified agencies(like Jeff Ellis), and lifeguards. Both the owner and operator are

usually the same. However there are some operator businesses that concentrate on the

documentation and financial aspect of lifeguarding that owners may hire.

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2.1 Liability Issues Between these five stakeholders there are liability issues. The body of water, in this case

a beach, is broken down into municipalities which can be looked at as the owner and operator.

The operator keeps the lifeguard certification history, updates are all documented and monitors

the financial status. The lifeguard associations are certified lifeguard agencies. These

associations train lifeguards who are hired by the owner to supervise the safety of the beach

goers.

Lifeguards and certification agencies are always liable if a drowning victim sues a

lifeguard for any injuries during the rescue process. However, if the lifeguards use only the

designated, branded equipment the agencies provide, and the agencies have proof and

correctly document the lifeguard's training and license, there is a very low chance of a

successful lawsuit. Most cases would be settled out of court [13].

2.2 Stakeholder Tensions The below diagram in Figure 15 is a summary of all the interactions, liabilities, and

tensions among the relevant stakeholders. There are tensions between all the stakeholders

such as the lifeguards not doing their jobs correctly and not following what the agencies have

taught them, or the municipalities not having proper documentations stored or the beach goers

not obeying the rules and regulations. The lifeguards protect the beach goers in case of any

emergency. If the beach goers are injured during the rescue process they can sue the

lifeguards. However, at the end of the day, the beach owner is always responsible for any

lawsuits against the lifeguards. The beach owner is protected under the catastrophic umbrella

insurance which is an extra layer of liability protection over and above the beach property in

case the owner is sued because of an accident. If the owners lose the lawsuit, the taxpayers

pay that umbrella insurance.

The beach goers provide the revenue for the operator who then provides clean and safe

beaches for the owner. The Life guarding associations train and certify professional lifeguards

who are hired by the operator. These associations also provide legal assistance for the owner,

operator, and lifeguards. Also, the associations, operator, and lifeguards provide feedback

of the equipment the manufactures produce. The associations are looking for the most reliable

and effective equipment whereas the operator is looking for something that is affordable.

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FIG. 15: STAKEHOLDER TENSIONS DIAGRAM

2.3 Win-Win Assume there exists a solution that would decrease the amount of rip current fatalities.

Since there is less fatalities, beaches with the system would be considered safer, thus more

beach goers would come, which is a win for municipalities and for beach goers. The system

could be equipped with any reasonably weighted flotation device, so it is unlikely any

lifeguarding agencies need to buy equipment from a different manufacturer. Thus,

manufacturers should not be affected by the system. Currently, there is no stakeholder that is

again a new system. All stakeholders will receive some benefits if the system is successful.

3.0 PROBLEM AND NEED 3.1 Problem Statement On average, rip currents are the cause of 81% of annual beach rescues, 79% of annual

beach fatalities, and they cause a minimum of 51 deaths per year (USLA 2015)(NOAA

2014)(NOAA 2015). Lifeguards are very good at their job and can reach a victim caught in a rip

current in a max of 93 seconds (Butch 2015). However some victims cannot survive this long,

as some have survival times as low as 60 seconds.

3.2 Need Statement There is a need for a system that can reach and assist a victim in under 60 seconds in

order to increase the victim's survival time. If a victim receives a flotation device in time, they

can survive long enough for the lifeguard to pull them back to shore.

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3.3 Proposed Design Solution We will design a system that will increase the victim survive time during the rip current

rescue process. This will be done by delivering a flotation device to the victim while they are in

the water. Once a victim has the flotation device, they will be able to survive long enough for the

lifeguard to rescue them. The delivery will be done by the use of an unmanned aerial drone.

Tether Hold/Release System

Tethered Lifesaving Device

Front and Down Cameras

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4.0 REQUIREMENTS *We are current revising our requirements to be more organized and relevant to our

components.

4.1 Mission Requirement MR.1 - The LDDS system shall reduce the average annual number of rip current deaths by a

minimum of X%.

4.2 Functional Requirements F.1 The system shall hover at a minimum altitude of 3m above the ground.

F.1.1 The system shall hover at an altitude of 3m with a minimum payload of 2.268kg.

F.2 The system shall be operable within X m of the home point.

F.3 The system shall reach a victim within X seconds.

F.3.1 The system shall increase the victim survival time by an average of X seconds, if

the system does reach the victim.

F.4 The system shall be able to restock its payload within X seconds.

F.5 The system shall be able to deploy its payload within X seconds.

F.6 The system shall do the entire rescue process at a maximum time of X seconds.

F.7 The system shall be able to hover within a horizontal distance of 0.5m from the target.

4.3 Design Requirements DR.1 The system shall attach the lifesaving device to the drone through a tether.

DR.1.1 The system may have a disconnect method to cut or release the tether in order

to deliver the lifesaving device.

DR.1.2 The system shall have a tether release system that weighs under X kg.

DR.1.3 The system shall be able to release the tether within X seconds of the request to

release.

DR.2 The system shall have a camera system pointing downward.

DR.3 The system shall have a camera system pointing forward.

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4.4 Ilities Requirements

4.4.1 Usability

U.1 The system shall be usable by a person that has less than 12 hours of training.

4.4.2 Availability

A.1 The system shall be available to at least any beach on U.S territory

A.1.1 The system shall comply with all federal drone regulations (see Appendix A)

A.2 The system shall be available for rescues over 95% of the time.

A.3 The system shall be usable in X rescues a day when balanced charged.

A.4 The system shall have a minimum lifetime of 5 years

4.4.3 Reliability

RE.1 The system will have MTBF of X months

RE.2 The system shall have a tether system error MTBF of 7 days

4.4.4 Resistibility

RS.1 The system shall resist sand conditions of an average beach.

RS.2 The system shall resist humidity conditions of an average beach.

RS.3 The system shall resist temperature conditions of an average beach

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5.0 CONCEPT OF OPERATIONS *We are currently revising our concept of operations to meet questions from the faculty

presentation.

5.1 Function Flow Block Diagram The lifeguard process and the drone system are independent, meaning the lifeguard

rescue process is outside of our system boundary. If the lifeguard for some reason is not able to

reach the victim the drone will still continue and drop the ring buoy. If the drone is not able to

drop the ring buoy, the lifeguard will still reach the victim. The drone process will start and

simultaneously take place in the 90 seconds the lifeguard has to swims to the drowning victim.

The controller receives what zone the victim is and finds the exact coordinates the victim is. The

controller will then command the drone to lift off. After the drone leaves the home point to the

given coordinates, there is a decision mark if the drone reaches the victim on time. If the drone

reached the victim in time, it will continue the process of dropping the ring buoy near the

drowning victim and releasing the tether when the victim grabs it, and then the drone returns to

its home point. This will modify the victim’s survival time. However, if the drone does not reach

the victim on time, the drone will directly go back to its home point.

FIG. 16: RESCUE PROCESS WITH THE LDDS SYSTEM

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21

5.2 Operational Scenario Precondition: Lifeguard has identified a drowning victim. Lifeguard is prepared for rescue

process. Lifeguard informs the controller about the section number or victim’s general direction.

Victim is located somewhere on the rip current and is attempting an escape method. Drone is

ready to deploy. Flotation device is stocked on drone.

Primary: Stage 1

1. Controller is informed by lifeguard of general area of the victim

2. Controller takes off drone and confirms victim location by eyesight if near tower

3. The system takes off to a height of X meters.

4. The system accelerates to X m/s towards the section given.

5. Controller confirms specific location relative to drone in that section through camera or

eyesight

6. The system maintains X m/s towards the victim's location.

7. Once the system is within X m of the victim’s location, system shall decelerate to victim’s

speed and position. At the same time, the system will reduce height until the flotation

device is just above the water (confirmed by controller).

Primary: Stage 2

8. The system drops the flotation device when it is 5m away from the victim and positions it

by the victim.

9. Once the victim is about to grab the flotation device, system detaches the tether.

10. The system maintains a X m hover over victim until lifeguard has reached the victim.

a. Controller uses camera to visually determine victim state (active or passive)

Primary: Return

11. Once lifeguard has reached the victim, or drone has been determined to be of no further

use, or drone has reached critical battery charge, system will be flown back to the home

point.

12. System lands on home point.

Post-Condition: Lifeguard is enacting the rest of rescue process starting with rescuing the

victim. Drone has landed back at the home point and awaits restocking of ring buoy. Victim is

being helped by the lifeguard.

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6.0 ALTERNATIVES We have three sets of alternatives we are looking to evaluate to ensure that the LDDS

drone system will be the most effective.

6.1 Drone Design Alternatives For the design of the LDDS drone system we must consider how big a battery the

system actually has to carry, the larger the battery the more flight time the drone will have.

However, with the increase in size comes an increase in weight. We wish to ensure that the

drone can devote the majority of its carrying capacity to the flotation device and related

components so the lightest battery possible while still ensuring we have enough flight time

necessary to perform the mission is required.

The size of the motors increases the lift the drone can generate, however larger motors

would require the drone to be both larger and heavier to take the resultant increased forces. We

need motors that are big enough to provide the necessary carrying capacity for the done while

not turning it into a helicopter.

Another way to increase the drone carrying capacity is to increase the number of motors

that are on the drone, so we wish to find the minimum number of motors and the optimum

configuration of motors while not turning the drone into a motor pile.

6.2 Drone location alternatives There are three considered locations that it could be station for use in the updated

rescue process. First is in a central control room. This would allow the drone to be sheltered

from the elements and be near its charging station. However, the drone would be forced to

travel a farther distance to reach any drowning persons. Second is to station the drone near the

lifeguard towers. This would reduce the travel time to drowning persons, but it exposes the

drone to the elements and removes it from maintenance and charging areas. Third is to have

the drone stationed out in the ocean. This is only being considered as a method of ensuring

compliance with potential FAA regulations.

6.3 Flotation Device Alternatives Alternatives for the life saving device are listed in the table below. It compares the four

most popular and reasonable floating devices in order to conclude the best alternative for the

drone to carry and deliver to the drowning victim. The quantitative factors being compared are

weight, dimensions, buoyancy, and cost [15]. The most reasonable one is the ring buoy as it is

cost effective and the victim has a better chance of grasping it, and it has been recommended

by our stakeholders. The effectiveness and usability are the ratings from a professional lifeguard

which is purely opinion based. The best alternative is found by performing an AHP analysis. The

weights for each factor is found however calculations to find the best alternative by using these

weights is still in process (TBA).

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TABLE 2: FLOTATION DEVICE ALTERNATIVES

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7.0 METHOD OF ANALYSIS 7.1 Simulation Goal The goal of our simulations is to verify that the LDDS system meets the mission

requirement of reducing fatalities. The LDDS system works best with a lifeguard, however 75%

of all fatalities are in unguarded areas. Thus, we will perform simulations to check the LDDS

system's performance for both unguarded and guarded rescues.

To make sure the simulation is close to reality, we will have design of experiments on

verifying the properties of the drone.

7.2 Equations In order to analysis the feasibilty of the system, we shall use a MATLAB simulation to

test a drone's ability to fly to a moving target, which represents the victim in a rip current. In

order to do that, we first detail the equations and notations we will use. We used Andrew's work

and last year's NSPDAV team works for our equations [16] [17].

Drones, or Unmanned Aerial Vehicles, have an even number of motors (four, six, or

eight). Half the motors spin counterclockwise and the other half spin clockwise. By having

motors that spin in different ways, the drone can controll rotation about its axises. For example,

this figure shows the top view of the drone. Clockwise rotation is stronger, thus the drone body

must be rotating counterclockwise.

FIG. 17: DIAGRAM FOR A COUNTERCLOCKWISE ROTATION

There is also two frames of reference we need to consider. The drone has its own

reference, or point-of-view. While the controller, standing still on a beach, has his own

reference; his own left, forward, and up. We define the drone's point-of-view as the body-frame,

and the controller or beach's point-of-view as the inertia-frame.

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FIG. 18: MOTOR NUMBERS AND ROTATIONS FOR DIFFERENT PLATFORMS

We first define the motor numbers, and spins in Figure 18. The simulation will focus on

hexacopters and octocopters.We define odd-numbered motors to be spinning clockwise and

even-numbered motors to be counterclockwise. Although this might seem contrary to the figure,

these notations are for viewing the drone from the bottom-up. Thus, clockwise means, from the

bottom view, it is rotating clockwise. We define the axis of the body-frame drone as the

following: the front side as the positive X-axis, the left side as the positive Y-axis, and the top

side as the positive Z-axis (the Z axis is point out of the screen in ).

We will define the position of the drone in X-Y-Z coordinates. The orientation of the

drone will be in the Euler angles of φ-θ-ψ, or roll-pitch-yaw.

There is three axis of rotations. They can rotate around their X-axis (roll), the Y-axis (pitch), and

the Z-axis (yaw) as shown below.

FIG. 19: AXES OF ROTATION

In order to transform body-frame forces into inertia-frame forces, we will use

transformational matrices. For example, force-inertia = Rotational-matrix*force-body. There are

respective transforms for φ-θ-ψ (roll-pitch-yaw). We only need the product of the three rotational

matrices in order to a full transform using the three values of φ-θ-ψ.

X

Y 1

2

3

4

2

5

4

3

1

6

X

Y

4

7

3

5

1

2

8

6

X

Y

http://theboredengineers.com/2012/05/the-quadcopter-basics/

X Y

Z

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cossin0

sincos0

001

cos0sin

010

sin0cos

100

0cossin

0sincos

R

R

R

coscoscossinsin

cossincossinsinsinsinsincoscossincos

cossincossinsincossinsincossincoscos

RRRR

coscossin0

cossincos0

sin01

Z

Y

X

Additionally there is a transform matrix to convert derivatives of Euler angles to inertia-

frame angular velocities. Shown below:

7.2.1 Power and Thrust

We first assume that the propeller motor torque is proportional to the current difference.

Show below:

Where τ is motor torque, I is the current, I0 is the no-load current when the motor is not

spinning, and Kt as the proportionality constant. We assume I0 is negligible. We also assume

that the voltage difference is the sum of the voltage drop across internal resistance and a term

that involves the angular velocity of the propellers. Because the faster the propeller spins, the

more voltage it uses.

Where V is voltage, I is the current, Rm is the internal resistance, Kv is the proportionality

constant, and ω is the angular velocity of the motor's propeller. For the simulation, we assume

Rm is negligible. Also note that motor manufacturers list Kv publicly, but that is the inverse of the

Kv we are using. Their equation for Kv is Kv*V = ω, while we have V = Kv*ω. We simply need to

do 1/Kv of the manufacturer’s value to get our version of Kv.

)( 0IIKt

vm KIRV

(1)

(2)

(3)

(5)

(6)

(7)

(4)

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27

From the two equations before (6) (7), we gain terms for current and voltage, thus we

can find power.

We now assume that motor torque is proportional to the motor's thrust, thus,

Where τ is the motor torque, Kτ is a proportionality constant, T is thrust, P is power

generated, Kv and Kt are proportionality constants, and ω is motor propeller angular velocity.

The table below summarizes all the proportionality constants we have shown.

Variable

1

Relation Variable

2

Proportionality

Coefficient

Equation

τ ∝ I Kt τ = Kt * I

τ ∝ T Kτ τ = Kτ * T

V ∝ ω Kv V = Kv* ω

TABLE 3: PROPORTIONALITY CONSTANTS Each motor has a propeller. Each propeller spins, pushing air downwards. The air in turn

push upwards. This is the general idea of how motors provide an upward force. The thrust

equation we use is listed below:

Where T is thrust, D is diameter of the propeller, rho is the air density, and P is power.

Notice that we have a power term (10), thus we can use our earlier power equation to substitute

into the thrust equation (11). The new thrust equation is listed below.

t

v

K

KP

TK

KKP

TK

t

v

3

1

22 ]2

[ PDT

22 )(2

t

v

K

KKDT

(8)

(9)

(10)

(11)

(12)

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28

Where Kv, Kτ, and Kt are proportionality constants, and ω is propeller angular velocity. In

the body frame, the drone only provides thrust upwards. Moving is possible when the drone is

titled, but to the drone it always provide thrust force in the positive Z-axis. Also each motor

follows the thrust equation, and so the motor’s thrusts can be added together. The follow shows

that idea.

Where ωi is the ith motor.

7.2.2 Drag Model

We will use the follow drag equations.

Where FD is force due to drag, PD is the power due to drag, CD is the coefficient of drag

of the drone, ρ is the air density, v is the velocity of the drone, and A is the cross sectional area

of the drone. Since there are three surfaces normal to the X-Y-Z axes, there are three

components to the force of drag, shown below:

Where the coefficient of drag, area, and velocities are decomposed into their X,Y, and Z

components.

7.2.3 Life vest Model

For the flotation device, we will model the force of gravity and the vector sum of the drag

force on the device, the force of gravity is of course F = mg, while the force of drag is from the

equation of drag (14).

2

2 0

0

*)(2

i

t

vbody

K

KKDT

AvCP

AvCF

DD

DD

3

2

2

1

2

1

(13)

(14)

(15)

2

2

2

00

00

00

2

1

z

y

x

DZ

DY

DX

D

v

v

v

Az

Ay

Ax

C

C

C

F (16)

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29

7.2.4 Main Force Model

With the force of drag(14), force of thrust (13), force of gravity, force due to the tether

rope, and force due to the life vest, this will lead up to the equation of

𝑚𝑎 = ∑ 𝐹𝑖

Where m is the mass of the drone system, a is the acceleration, and F is the various

forces acting on the drone. Expanding on this equation, we have:

Where x,y,z is the coordinate position of the drone, g is the gravitational constant (9.81

m/s/s), R is the rotational matrix(4), TB is the thrust in body-frame, FD is the force of drag, and

Flifevest is the force due to the life vest or flotation device. Here is a summation of our forces in a

free body diagram, shown below.

FIG. 20: FREE BODY DIAGRAM, SIDE VIEW OF DRONE SYSTEM

(17)

(18) lifevestDbody FFRT

mgz

y

x

m

0

0

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30

7.2.5 Rotational Dynamics Model

The torque on the body of the drone is from the motors. Each motor has spinning

propellers that push air horizontally, but the air also pushes back. This creates a force at a

distance away from the center of the drone, which is the definition of torque. The torque is given

by

𝜏𝐷 = 𝑟 × 𝐹𝐷

Where r is the distance between the motor and the drone’s center of mass. We already

know the force of drag from above. We also know that velocity = radius * angular velocity, thus

we can derive a torque equation based on angular velocity. However we also note that torque =

moment of inertia * angular acceleration. However, it is a small enough value that we can later

consider negligible in equation (21).

Where τZ is the torque around the body Z-axis, Iz is the moment of inertia about the body

Z-axis. Now that we know torques are related to the angular velocity squared, we can find the

torques about the X-Y-Z axes.

For roll, the torque is given as torque = force * distance. The distance is the distance

from the motor to the center of mass. We assume the drone is symmetrical, thus the distance is

the same for all motors. When rolling, drones usually increase the thrust of one motor while

decreasing the other motor in the pair in order to maintain the same body thrust while also

creating a torque form that difference of thrust. Thus, the torque from one motor minus the

torque from the opposite motor creates the body’s rolling torque.

For pitch, it is the same as roll, however it involves the other pair of motors on the drone.

For yaw, we add up all the motor’s torques (21). Since two motors spin counterclockwise

and two spin clockwise, two of the terms must be negative. We denote the even numbered

motors contributing to clockwise spin, thus the terms involving even numbered motors are

negative.

Where L is the distance from a motor to the center of mass. This equation is for a

quadcopter, however similar equations exist for the hexacopter and octocopter. These

equations are based on Figure.

ZZ

D

DD

Ib

rACrb

rACr

2

2

22

)(2

1

)()(2

1

)(

)(

)(

2

4

2

3

2

2

2

1

2

4

2

2

2

3

2

1

b

Lk

Lk

yaw

pitch

roll

B

(19)

(20)

(21)

(23)

(22)

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31

We will be using Euler’s equation for torque in order to get the angular acceleration of

the system.

Where τ is the body’s torque, I is the moment of inertia, and w is the angular velocity of

the drone. This equation does not directly give us roll, pitch, or yaw, thus we need to expand on

it. Since we assume the drone is symmetric, the moment of inertial about the X-Y-Z axes are

independent of each other, shown below in that equation. If we modify the equation to solve for

angular acceleration, we get the other equation below.

Where τφ, τθ, and τψ are the torques in their respective rotations (22), Ixx, Iyy, Izz is the

moment of inertia about their respective axes, and ωx, ωy, ωz are the angular velocities about

their respective axes. Once we have the angular accelerations, we can use the transformation

matrix to get the Euler angle derivatives (5). Integrate those to get the Euler angles. To find

moment of inertia for the X,Y, and Z axes we will use the general equation for moment of inertia

around the center of mass,

(26)

(27)

(28)

(29)

)(

)(

)(

2

6

2

5

2

4

2

3

2

2

2

1

2

6

2

5

2

3

2

2

2

4

2

1

b

Lk

Lk

yaw

pitch

roll

B

)(

)(

)(

2

8

2

7

2

6

2

5

2

4

2

3

2

2

2

1

2

8

2

7

2

4

2

3

2

6

2

5

2

2

2

1

b

Lk

Lk

yaw

pitch

roll

B(25)

(24)

)( II

yx

ZZ

YYXX

zx

YY

XXZZ

zy

XX

ZZYY

ZZ

YY

XX

z

y

x

ZZ

YY

XX

I

II

I

II

I

II

I

I

I

II

I

I

I

I

1

1

1

1 ))((

00

00

00

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32

Where mi is the mass of component i, ri is the distance from the center of mass for

component i, and rc is the distance between the edge of the object and the center of mass.

7.2 Design of Experiments for Variables

7.2.1 Force of Drag

The purpose of this experiment is to determine the force of drag acting upon the

Spreading Wings S900 while the drone is in flight. This is needed to accurately create a

simulation of said drone. To determine the force of drag we need to perform a flight test of the

drone and collect some of its telemetry for the flight.

The force of drag has been broken down into two components vertical and horizontal.

Each of these tests will be performed at different speeds to determine the change in the

coefficient of drag with the change in velocity of the drone.

In order to find the coefficient of drag of the drone, we need to collect from this

experiment: pitch, roll, velocity of the wind, and velocity of the drone. We would also like to have

recorded how far above the ground and how far from home the drone is. All of this data would

be required to be timestamped. The velocity, altitude, and distance of the drone would also be

used to verify that the flight went as expected.

Inputs Outputs

Procedure Height

Flig

ht

Sp

ee

d

Pitc

h

Ro

ll

Ve

locity

Win

d

Speed

Altitu

de

Dis

tanc

e

Horizonta

l

CD test

fly 30 m north

fly 30 m east

fly 30 m south

fly 30 m west

Maintain

constant 10

m

# 1 1 m/s

# 2 5 m/s

# 3 10 m/s

# 4 15 m/s

Vertical

CD test

Ascend 30 m

Descend 30 m

At least 10 m

above

ground

# 1 1 m/s

# 2 5 m/s

TABLE 4: FORCE OF DRAG DOE

(30)

(31)

i

ii

c

iii

m

rmr

IrmI2

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For each leg of the test there are three sections, a section where the drone accelerates to

the required velocity, the section where the test will be performed, and a section where it

decelerates and/or turns. The data will be gathered from the test section, where the drone will

follow the flight procedure. All of the data must be ether timestamped or otherwise linked

together. We would prefer the data in some giant data stream for the entire flight which we

would parse later, but an excel file with data from the relevant sections would be acceptable.

FL = FT ∗ cos(θ)

FF = FT ∗ sin(θ)

When the drone is in a state of forward flight maintaining a constant velocity and height,

the drone is generating a force of thrust that is counteracting both the force of gravity and force

of drag on the drone. This force of thrust consists of the force of lift, which is counteracting the

force of gravity, and the forward force, which is counteracting the force of drag. Therefore if we

know the pitch/roll of the drone at a specific velocity we can recompose the force of lift with the

pitch/roll to find the force of drag. With the force of drag we can find the coefficient of drag.

FD = FF

FD = FT ∗ sin(θ) ; FT =FL

cos(θ)

FD = FL ∗ tan(θ) ; FL = m ∗ g

FD = m ∗ g ∗ tan(θ)

CD =2 ∗ FD

ρ ∗ v2 ∗ A

This would only net us the horizontal force of drag. To find the vertical force of drag if we

consider the conservation of energy.

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The force of drag is the loss of energy due to friction with the air divided by the distance

traveled. This is equal to the potential energy at point 1 subtracted by the kinetic energy at point

2.

FD = [(mgh1) − (1

2⁄ mv2)]

h1

CD =2 ∗ FD

ρ ∗ v2 ∗ A

7.2.2 Motor Parameters

The purpose of this experiment is to determine certain information about the brushless

DC electric motors used on the Spreading Wings S900 for our simulation. Those parameters

are: the no load current, the torque constant, and a way to relate torque to thrust The properties

of: the torque-speed curve [18], the power-speed curve [18], and the torque-current curve [19] of

a DC electric motor will allow us to determine those values.

The torque-current curve is a line that relates the torque that the motor outputs with the

current that the motor draws. It can be found by applying a fixed amount of torque to the motor

and measuring the current that is being drawn. From the torque-current curve we will be able to

determine the no-load current (a point on the line). The slope of the torque-current curve is the

torque constant. [19]

To relate the torque to the thrust of the drone, we need to find both the power-speed

curve, and the torque-speed curve. The thrust of the drone is related to the mechanical power

output of the motor. The mechanical power output of the motor is for a given speed is the

power-speed curve. [20] The power-speed curve is derived from the torque-speed curve, the

power of the motor at a given speed is the area of a square with one corner at the origin and

another on the torque-speed curve. [18]

In order to find these curves we need to know the torque, current, and speed of the

motor at a fixed voltage. The procedure we will follow is: [20]

1) Apply Fixed Voltage to motor, which is not to exceed motor rated voltage

2) Run the motor without a load applied to its shaft.

a. The RPM of the motor will be recorded

i. used in finding the torque-speed curve

b. The current the motor is drawing will also be recorded

i. used in finding the torque-current curve

3) Apply torque to the shaft of the motor

a. Record the torque

i. used in finding the torque-speed curve and the torque-current curve

b. Record the current

i. used in finding the torque-current curve

These steps will be repeated for additional voltages to determine if/how the data changes.

For this DOE we would require: 1) electric motor of the S900, 2) adjustable voltage

supply, 3) ammeter, 4) ohm meter, 5) adjustable torque load, 6) non-contact tachometer.

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35

Inputs

Outputs

Voltage Torque Current Speed (RPM)

TABLE 5: MOTOR PARAMETER DOE

7.3 Simulation The three processes we will simulate are:

1. Rip Current and Victim Process

2. Drone dynamics and control

3. Lifeguard Rescue Process

7.3.1 Rip Current and Victim Process

FIG. 21: SIMULATION DIAGRAM OF RIP CURRENT EFFECTS ON VICTIM STATE

This simulation will calculate the position of the victim over time. There is three methods

of escape methods (float, swim parallel to shore, swim toward shore). The white block is the

integration block, showing that position is the integral of velocity.

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36

Each method would be represented as a velocity. For example, swimming toward the

shore can be represented as an 2 m/s velocity in the negative x-axis direction. The rip current

velocity will be randomly chosen between its minimum and maximum possible velocity. The

distribution of chosen methods was developed after talking with a lifeguard stakeholder [14].

The distributions are shown below:

victVelo is the victim's velocity which is decomposed into horizontal and vertical

swimming speed. A and B are the ranges for the human swimming speed. We will develop this

further over Winter break. A is negative and B is negative, thus a victim is always represented

as possibly swimming toward shore or swimming toward the guard tower.

Rip current properties include rip current width, length, position on the shore, and current

velocity. The width, length, and current velocity ranges are shown in the Context #. Position on

shore will be a uniform distribution between 0m and 750m.

Using the rip current properties This process's output is the victim’s position, which will

later act as the waypoint input for the drone and for the lifeguard.

7.3.2 Lifeguard Rescue Process

FIG. 22: LIFEGUARD MODEL

This process calculates the lifeguard position over time. The lifeguard simulation will be

inputted the victim position as a waypoint. The victim position will be randomly modified to be at

a position at a later time due to the delay of lifeguards identifying victims. The time to identify

can be a distribution, but the maximum is 10 seconds [14]. It will also input the rip current

properties because lifeguards jump into the rip current to get to the victim quickly. Using the

165.0,

65.04.0,

4.00,

)(

)1,0(

xparallel

xfloat

xfight

xescape

uniformx

parallelescapeB

floatescape

fightescapeA

escapevictVelo

],,0[

],0,0[

],0,[

)(

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37

victim as the target and the rip current as a boost, the lifeguard will attempt to reach the victim

before they drown. The lifeguard velocity is also a range, the minimum swimming speed to be a

lifeguard is publicly available and we can estimate the max velocity using the fact that 90

seconds is the max time to reach. Once the lifeguard has reached the victim, we will add a

delay time to simulate the time needed for the lifeguard to help the victim and grab hold of the

them.

The rescue process after the lifeguard reaches the victim is outside the scope of the

drone system. It is up to the lifeguard from here on out to help the victim, thus we will not

simulate the rescue process beyond this point.

7.3.3 Drone Dynamics and Control In order to test the drone’s abilities to fly and accelerate when carrying a life ring, we

must simulate the electrical and mechanical properties of the drone under flight. The simulation

will follow the following diagrams.

FIG. 23: DYNAMCIS AND CONTROL MODEL

FIG. 24: ROTATIONAL DYNAMICS MODEL

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FIG. 25: THRUST/THROTTLE/TRANSLATIONAL MODEL

The controller will be simulated as GPS flight. This means that the drone autonomously

hovers when there is no input, there is a maximum velocity and tilt, and that it maintains altitude

while in horizontal movement.

The way the first model works is that the target's position is used as a waypoint. Using

the drone's current state and the victim's position, the controller outputs voltages to the motors.

The motors provide some thrust and torque on the drone, which is used to calculate errors in

the PID controls.

The controller is programmed to use Euler angle errors to adjust the voltage, but how do

we convert errors in velocity and position to errors in angles? The velocity error could be any

value in the interval [-∞,∞], and the wanted angle can be any value that is within the tilt limits set

by the drone's controller. Thus there needs to be a relation between the velocity domain and

wanted angle range. The most simple relation is:

)1(

)1(bx

bx

e

ea

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FIG. 26: CONTROL RELATION BETWEEN VELOCITY AND WANTED ANGLE

Where a is the tilt angle limit in radians, and b is a coefficient. The higher the value of b

is, the more we want to tilt to get the right velocity.

The waypoint is the position of the victim. Using its position and various errors

calculated, we can control the drone to be the same position and velocity as the waypoint. Once

it reaches that waypoint and stays at it for a set period of time, we record the time.

7.3.4 Post MATLAB & Simulink Analysis

FIG. 27: MAIN SIMULATION MODEL

The above model shows how we will derive successful rescues with and without the

drone. Calculate Victim Position is referred in. Calculate Lifeguard Position is referred in.

Calculate Drone Position is referred in . At the end, using the lifeguard and drones position over

time, we can calculate the survival of the victim. The green block will evaluate whether the

victim survived until the drone reached them, whether the lifeguard reached the victim in time,

whether the drone dropped the ring buoy in time, and then record the time it took for the

lifeguard and drone to reach the victim. Depending on the drone simulation and if it deployed

the life ring on time at the right position, the victim survival time will be modified.

After the simulation of the processes is over, we generate a random victim survival time.

Repeat for several trials to generate survival rate for with-drone and without-drone processes,

along with average time to reach victim, average successful rescue, and average drone velocity.

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7.4 Simulation Requirements The simulation requirements are currently being redone to be better organized.

7.4.1 Functional Requirements

SR.1 The system shall be able to fly towards a waypoint and maintain position within 0.5m of

the waypoint.

SR.2 The system shall have one run simulated under 1 minute.

SR.3 The system shall simulate wind and weight interactions with the drone.

SR.4 The system shall model drone rotational and translational dynamics.

SR.5 The system shall model the lifeguard-victim rescue process until the lifeguard reaches the

victim.

SR.5.1 The system shall model the three victim escape methods (swim parallel to neck,

swim against the neck, and float)

SR.5.2 The system shall model riptides of length 100/200/300/400/500 meters.

SR.5.3 The system shall model the lifeguard speed on land and on water as an average

velocity of X m/s and Y m/s respectively.

7.4.2 Input Requirements

IR.1 The system shall inputted a victim swimming method. It will pick between floating,

swimming parallel against the shore, and swimming parallel to shore.

IR.1.1 The system shall model the swimming methods as velocities. The choice will be

based on a discrete random distribution.

IR.1.2 The system shall be inputted a random victim survival time based on the

swimming method chosen.

IR.2 The system shall be inputted a random rip current speed. The speed will be chosen by a

random X distribution with mean X and variance X.

7.4.3 Output Requirements

OR.1 The system shall output the victim position over time.

OR.2 The system shall output the lifeguard position over time.

OR.3 The system shall output the drone position over time.

OR.4 The system shall output 1 or 0 depending if the lifeguard rescue time is under victim

survival time.

OR.4.1 The system shall detect if the drone reached the victim before the lifeguard and

increase victim survival time by X seconds.

.

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7.5 Simulation Design of Experiments In order to gather meaning results from the simulation, we need to run it through

experiments. Each experiment gives outputs that flow into the next experiments.

7.5.1 1st DoE: Victims distance from shore before dying

Using the victim escape method, escape velocity, and survival time distributions we

have, we will general a distribution for distance travelled by the victim while they are surviving.

The distributions will be generated using ARENA.

Input Output

Rip Current Speeds Rand. Victim Properties Distance Travelled Distribution

1m/s 50reps

2m/s 50reps

3m/s 50reps

4m/s 50reps

5m/s 50reps

6m/s 50reps

7m/s 50reps

8m/s 50reps

Rand. Uniform(1,8) 50reps

Whether we use a specific distribution for the selected rip current velocity, or use a

randomized one for all velocities, will be decided in the next semester.

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7.5.2 2nd DoE: Best Path, Best Location, Minimum Velocity Needed

This experiment is to find the necessary minimum velocity, best location to set up a

drone, and the best path a drone should take

Inputs Outputs

Drone Location

Random: 1. Rip

position 2. Victim

speed 3. Rip length 4. Identified

Victim

Drone Velocity

Path % reached within 30 sceonds

% reached within 60 seconds

% reached within 90 seconds

Base Hexacopter

Location A (Main Control

Room) 20 reps

12m/s Fly Straight

Go Around

10m/s Fly Straight

Go Around

Location B (Lifeguard

Tower) 20 reps

12m/s Fly Straight

Go Around

10m/s Fly Straight

Go Around

Location C (On a Rescue

ship) 20 reps

12m/s Fly Straight

Go Around

10m/s Fly Straight

Go Around

The DoE does expand to another octocopter platform, and the velocities of 14,8, and

16m/s, and 6 m/s. Using the distribution of victims in each of the 20 reps, we can determine

the best location and best path. The minimum velocity will be set if more than 90% are saved in

under 60 seconds. This percentage might change as the team deliberates more over Winter

break.

Since the flight speed and flight path might have some issues and have no clear winner,

we will need a utility test to determine the best speed and path. This function will be completed

over the Winter break.

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7.5.3 3rd DoE: Drone Design Space Model

We now need to find the power needed for the drone's weight. There is a circle of

feedback where the more weight we add, the more thrust we need, more thrust means more

power, more power means bigger battery, and bigger battery means more weight. Thus, we

need to know what power we need and what battery alternatives we can use in this drone

system. The following DoE is for that purpose:

Inputs

Outputs

Drone Properties and Base

Weight Added Payload Maneuvers

Power Needed to Maintain

Maneuver

Base Hexacopter

1kg

Hover

Const. Velo. Lv. Flight

Accelerating Lv. Flight

3kg

Hover

Const. Velo. Lv. Flight

Accelerating Lv. Flight

Base Octocopter

1kg

Hover

Const. Velo. Lv. Flight

Accelerating Lv. Flight

3kg

Hover

Const. Velo. Lv. Flight

Accelerating Lv. Flight

By varying the weight and flight maneuver, we will find the power needed to do that

maneuver. We can then plot our design space in a line graph between Total weight vs. Power

needed. There will be three functions to plot for the three maneuvers. For constant velocity

flight, we will use the minimum velocity needed found in DoE 2.

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44

7.5.4 4rd DoE: Guarded and Unguarded Rescue

Finally, we evaluate all the alternatives to possible improvements to rip current rescue.

The alternatives considered include:

1. Lifeguard 2. Lifeguard with LDDS 3. Lifeguard with ATV 4. Lifeguard with ATV with LDDS 5. Lifeguard with Boat 6. Lifeguard with Boat with LDDS

Inputs Outputs

Rescue

Alternatives

Rip Current

Properties

Distribution

Victim

Distribution % Saved

Avg. Time

to Reach

Avg.

Energy

Usage

Lifeguard Rand. 100 reps 0

Lifeguard with

LDDS Rand. 100 reps

Lifeguard with

ATV Rand. 100 reps 0

Lifeguard with

ATV with LDDS Rand. 100 reps

Lifeguard with

Boat Rand. 100 reps 0

Lifeguard with

Boat with LDDS Rand. 100 reps

We will then determine which alternative gives the most utility, using the utility function

below:

SG = percent guarded lives saved (%)

SUG = percent unguarded lives saved (%)

TR = mean time to reach victim (sec)

E = mean battery energy usage per rescue (kWh/Rescue)

Once the experiment is done after Winter break, we will finish these utility functions.

ETSSu ERTUGsUGGsG

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7.6 Cost Model To calculate the net present cost of a drone system, we will consider the costs within a

two year lifecycle. We will assume inflation is equal to the 2015 inflation rate and is constant

over the two years. We will convert annual costs to a present value costs. Here is the model of

how we will calculate costs:

FIG. 28: HIERARCHICAL COST MODEL

Evaluation of non-drone alternatives will only include two factors: (1) Acquisition Cost,

(2) Annual Upkeep cost (boat or ATV maintenance, if any).

Lifecycle Cost (2yrs)

System Acquisition Cost

Drone Platform

Camera System

Tether Release System

Tether

Environment Protection Equipment

Battery Acquisition

Location Setup

User manual/Training

Operations and Support Cost

Annual Repair Cost

Annual Maintenance Cost

Annual Battery Recharging Cost

Controller’s salary

Disposal Cost

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46

7.7 Utility Function To evaluate the best alternative to completing the mission requirement, we will use the

utility function and the experiment done in section 7.4.4, as well as the cost model from section

7.6.

Below is a table of the weights and values for all the alternatives. Using 7.5.4 DoE#4

results, we will create a graph on utility vs. cost and determine the best result is.

SG SUG TR) E

Weights: Utility:

Alternatives

Lifeguard

Lifeguard with LDDS

Lifeguard with ATV

Lifeguard with ATV with LDDS

Lifeguard with Boat

Lifeguard with Boat with LDDS

Graph here:

8.0 RECOMMENDATIONS AND RESULTS We have done no experiments, thus there is no recommendations as of yet. We will refine this

over the Winter break.

9.0 STATEMENT OF WORK 9.1 Scope of Work The scope of the work we will do includes:

1. Testing the economical and physical feasibility of the LDDS system.

a. Evaluate feasibility using location, flotation device, and platform alternatives.

2. Analyzing current stakeholder and current rescue processes.

3. Simulating drone delivery using drone mechanics.

4. Design a drone that can help lifeguards with the rescue process.

5. Estimating life-cycle costs and benefits of such a system.

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9.2 Schedule/Milestones Milestones Dates

Fall Brief 1 9/21/2015

Fall Brief 2 10/5/2015

Preliminary Project Plan 10/21/2015

Fall Brief 3 10/26/2015

Fall Brief 4 11/09/2015

Faculty Presentation 11/20/2015

Proposal Final Reports

Proposal Final Report Slides

Draft Conference Paper

Draft Poster

12/09/2015

Milestones (SYST 495 Spring 2016) Dates

Spring Brief 1 2/2016

Spring Brief 2 2/2016

Spring Brief 3 3/2016

SIEDS Abstract Due 2/2016

SIEDS Notification 3/2016

SIEDS Manuscript Due 4/2016

SIEDS Conference 4/2016

Registration for Keith Memorial Capstone

Conference Before 4/2016

GDRKMC Conference 5/2016

SCHEDULE MILESTONES

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9.3 Payment Schedule The average salary of an Entry-Level Systems Engineer in Fairfax is 63,000 per year

[21]. Assuming 50 work weeks and 40 hours a week, this is 27.50/hour. We will round this up to

$30 for simplicity. We will assume an overhead multiplier of 2.00. Thus, the total charge is

$60.00 per hour per person [21] [22].

9.4 Work Breakdown

9.4.1 Work Breakdown Structure

The Major Tasks in our Work Breakdown Structure (WBS) are: 1) Management, 2)

Research, 3) Concept of Operations (Con-Ops), 4) Requirements, 5) Alternatives, 6) Analysis,

7) Design of Experiment (DOE), 8) Simulation, 9) Presentations, 10) Documentation.

Of these tasks the stakeholder analysis, DOE, and especially the simulation are the

heart of the project. It is crucial that we properly understand the stakeholders and what they

want otherwise any design we come up with would never end up adopted as a life saving

device. Without the simulation we will be unable to effectively trade off design alternatives.

Similarly the DOE’s will be necessary to complete the simulation and verify its functionality.

FIG. 29: WBS HIERARCHY

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9.4.2 Critical Tasks

FIG. 30: CRITICAL PATHS

We are considering a task as a critical task if it has a slack less than 2 days. This is a

margin of error as in that time an unplanned for homework assignment or test could lead to

slippage of the task for our project.

# WBS TASK NAME START FINISH

18 3.2.3 RESCUE PROCESS DIAGRAMS 10/8/15 1/23/16

21 4.2 FUNCTIONAL REQUIREMENTS 10/30/15 11/27/15

22 4.3 DESIGN REQUIREMENTS 10/31/15 11/27/15

29 5.1.4 EVALUATE DRONE BATTERY ALTERNATIVES 3/31/16 4/2/16

31 5.1.6 EVALUATE DRONE MOTOR ALTERNATIVES 3/17/16 3/19/16

33 5.1.8 EVALUATE DRONE ROTOR ALTERNATIVES 3/19/16 3/23/16

35 5.1.10 EVALUATE DRONE LOCATION ALTERNATIVES 3/14/16 3/17/16

36 5.1.11 RESEARCH DRONE CONFIGURATION ALTERNATIVES 10/1/15 10/3/15

37 5.1.12 EVALUATE DRONE CONFIGURATION ALTERNATIVES 10/3/15 10/27/15

40 5.2.2 EVALUATE FLOTATION DEVICE ALTERNATIVES 10/15/15 4/28/16

52 6.3 SENSITIVITY ANALYSIS 3/25/16 4/3/16

56 6.4.3 SIMULATION RISK ANALYSIS 11/27/15 12/5/15

77 8.1.7 CREATE RIP CURRENT MODEL 2/13/16 2/27/16

79 8.1.9 CREATE GUI 2/27/16 3/14/16

80 8.2 SIMULATION TESTING 3/14/16 3/25/16

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81 8.3 PERFORM SENSITIVITY TESTS 3/25/16 4/3/16

89 9.2.1 FACULTY PRESENTATION CREATION 11/14/15 11/19/15

90 9.2.2 FACULTY PRESENTATION 11/20/15 11/20/15

97 9.4.3 SPRING BRIEF 3 3/14/16 3/14/16

102 10.1.2 PROPOSAL FINAL REPORT 12/9/15 12/9/15

104 10.2.1 DRAFT CONFERENCE PAPER 12/9/15 12/9/15

105 10.2.2 DRAFT POSTER 12/9/15 12/9/15

106 10.2.3 FINAL REPORTS AND STUFF 11/23/15 12/8/15

TABLE 6: CRITICAL PATH

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9.4.3 Schedule

Our project schedule involved researching context, dealing with stakeholders, creating the

requirements, con-ops, and building the core of the simulation in 490. Over winter break we plan

to perform necessary flight tests to enable the simulation to be completed, (we have had trouble

coordinating with ExpertDrones). We also plan to finish addressing the comments and concerns

from the faculty presentations and otherwise ensure we are ready to go for 495. 495 will involve

finishing up the simulation, performing the tradeoffs for the alternatives, establishing

documentation of the updated rescue process and everything else we need to do to bring the

project to completion.

FIG. 31: GANTT CHART

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FIG. 32: CPI AND SPI

FIG. 33: CV AND SV

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9.4.4 Earned Value

From the start of our project up until the week of faculty presentations. Our actual cost

(ACWP) while in the past it was above our earned value (BCWP) it is currently below our

earned value (BCWP). Our planned value (BCWS) was equal to our BCWP it is currently below

our BCWP.

FIG. 34: ACTUAL COST, EARNED VALUE, AND PLANNED VALUE FOR AUG 31 TO OCT 18

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10.0 PROJECT RISK MITIGATION

Risk Severit

y

Likelihoo

d Detectability

Scor

e Mitigation

Simulation

Control

Structure is not

done by Nov.

15th (2 weeks

behind

schedule)

8 10 1 80

Revert to old model with no

control. Manually adjust

voltages in order to get the

right distance and other values

needed.

Simulation

Testing is

Delayed by X

days beyond

scheduled due

date

10 3 5 150

Do primary analysis of the

drone’s effectiveness in

reducing fatalities. Forgo all

other simulation tests until we

find time again.

Evaluate life

saving device

alternatives is

not done, ring

buoy information

is wrong

9 3 5 135

Find other life saving devices

with accurate information about

them and evaluate them.

Gather accurate

information

about force,

pitch, roll, yaw,

velocity, height

and wind speed

7 4 4 112

Perform the flight experiment

again until we get accurate

data. Use pocket money to get

program and tablet that can

watch the instruments.

Unable to

acquire tools to

perform

experiments

10 6 1 60 Use the University’s lab

experiments to get the tools.

TABLE 7: PROJECT RISKS, RPN, AND MITIGATION

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APPENDIX

Appendix A: Federal Drone Regulations Source: http://www.faa.gov/uas/

Current Advisories

UAS flight altitude below 400 ft.

UAS weighs under 55 lbs.

Maintain visual line of sight of the UAS

• Spotter allowed

– Minimum 1 spotter per UAS

UAS operator must have a pilot's license

UAS may not be operated in restricted airspace

• (grey area)

• not applicable to government

UAS may not be operated for commercial purposes

No Overhead Operation !!!

Proposed Regulations

UAS flight altitude below 500 ft.

UAS weighs under 55 lbs.

UAS may not exceed 100 mph

Maintain visual line of sight of the UAS

• Spotter allowed

– Minimum 1 spotter per UAS

UAS operator:

• Be licensed

• Report incidents in less than 10 days

• Make UAS available for inspection

3 mile visibility from control station

Inspect UAS prior to flight

No Overhead Operation !!!

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Appendix B: Base Hexacopter Parameters

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Appendix C: Matlab Modules

Linear Dynamics

What comes into the system is the four voltages (v1, v2, v3, v4). They will be inputted into

volt2thrust in order to get a value for the thrust in body form. In the linear motion model, we will

use the equation above to calculate the acceleration. Note that mass of drone is separated

outside, for sensitivity analysis purposes. After integrating the acceleration for position and

velocity, these values will be used to calculate various other forces. Position will be used to

calculate the tether force. Velocity will be used to calculate the drag forces on the drone and on

the life vest.

Voltage to Thrust Conversion (volt2thrust)

function THRUST = volt2thrust(v1,v2,v3,v4)

%#codegen

%Function to convert voltage into the thrust force vector in inertia

frame

%All units are metric unless specified

%constants

Kv = 1; %porportionality constant between propeller voltage and

angular velocity

Kτ = 1; %porportionality constant between propeller torque and current

KT = 1; %porportionality constant between propeller thrust and torque

D = 1; %propeller diameter. Adjusted by propeller properties

rho = 1; %density of air (humid or dry). Probably need to be a

function

%V = Kv * w assuming internal resistance = 0

w1 = v1/Kv;

w2 = v2/Kv;

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w3 = v3/Kv;

w4 = v4/Kv;

W = [0;0;(w1^2+w2^2+w3^2+w4^2)];

k = pi/2*rho*D^2*(Kv/Kτ/KT);

%ThrustBody = thrust vector in body frame

thrustBody = k * W;

%THRUST = thrust vector in inertia frame

THRUST = thrustBody;

Linear Motion Model (DroneState)

function [ax,ay,az] =

DroneState(Fthrust,Frope,Fdrag,Flifevest,EULER,massDrone)

%#codegen

%--------------------------------------------------

%rotation matrix for converting body-frame thrust to inertia-frame

thrust

roll=EULER(1);

pitch=EULER(2);

yaw=EULER(3);

Ryaw = [cos(yaw) sin(yaw) 0;-1*sin(yaw) cos(yaw) 0;0 0 1];

Rpitch = [cos(pitch) 0 -1*sin(pitch);0 1 0; sin(pitch) 0 cos(pitch)];

Rroll = [1 0 0;0 cos(roll) sin(roll);0 -1*sin(roll) cos(roll)];

RotMat = Ryaw*Rpitch*Rroll;

THRUST = RotMat*Fthrust;

%-------------------------------------------------

Fx = 0 + THRUST(1,1) + Frope(1,1) + Fdrag(1,1) + Flifevest(1,1);

Fy = 0 + THRUST(2,1) + Frope(2,1) + Fdrag(2,1) + Flifevest(2,1);

Fz = -massDrone*9.81 + THRUST(3,1) + Frope(3,1) + Fdrag(3,1) +

Flifevest(3,1);

ax = Fx/massDrone;

ay = Fy/massDrone;

az = Fz/massDrone;

Force of Rope (RopeState)

function Frope = RopeState(x,y,z)

%#codegen

h = 1; %vertical difference between ends

L = 1; %horizontal difference between ends

mu = 1; %weight/length density of rope

S = 1; %arc length of rope

%first find absolute distance between ends

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LEN = sqrt(x^2+y^2+z^2);

S = 1.1*LEN; %assumption: arc length is porportional to absolute

distance

lamda = sqrt(S^2-d^2)/(L^2);

Fg = [0;0;-mu*LEN];

Fh = 0;

%if lamda is <1, equation will not work, must approximate by straight

%length?

if lamda<=1

theta = asin(sqrt(x^2+y^2)/LEN);

Fh = Fg(3)*tan(theta);

else

syms u

Y = solve(sinh(u)/u == lamda);

Fh = mu*L/(2*Y);

end

HorizV = Fh*[-x;-y;0]/sqrt(x^2+y^2);

Frope = Fg+HorizV;

% Frope = [0;0;0];

end

Force of Drag (Fdrag)

function Fdrag = Fdrag(vx,vy,vz)

%#codegen

%force of drag depending on its air resistance

%pulls drone BACKWARDS

Cd = 0.02; %coefficent of drag for the lifevest

rho = 1; %air density

A = 1; %cross sectional area of lifevest

%backwards = negative of current velocity vector

Vsqr = sqrt((vx^2)+(vy^2)+(vz^2)); %total velocity magnitude

%unit vector direction of velocity

mag = sqrt(vx^2+vy^2+vz^2);%magnitude of total velocity

if mag==0

mag=1;

end

unitV = [vx;vy;vz]*-1/mag;

Fmag = Cd*rho*A*Vsqr^2; %magnitude of drag force

Fdrag = Fmag.*unitV;

% Fdrag=[0;0;0];

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Force of Lifevest (LifevestState)

function Flife = LifevestState(vx,vy,vz)

%#codegen

%force of drag depending on its air resistance

%pulls drone BACKWARDS

Cd = 1; %coefficent of drag for the lifevest

rho = 1; %air density

A = 1; %cross sectional area of lifevest

%backwards = negative of current velocity vector

Vsqr = sqrt((vx^2)+(vy^2)+(vz^2)); %total velocity magnitude

%unit vector direction of velocity

mag = sqrt(vx^2+vy^2+vz^2);%magnitude of total velocity

if mag==0

mag=1;

end

unitV = [vx;vy;vz]*-1/mag;

Fdrag = Cd*rho*A*Vsqr^2;

FDRAG = Fdrag.*unitV;

%force of weight depending on mass

vestMass = 1; %mass of the lifevest

Fgrav = [0;0;vestMass*-9.81]; %pulls drone DOWN

Flife = FDRAG + Fgrav;

% Flife = [0;0;0];

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Rotational Dynamics

Similar to the linear motion model, we take in four voltages (v1, v2, v3, v4) to calculate the

angular velocities of each rotor. The velocities and the derivative (acceleration) will be used to

calculate the torques in the main rotational model (21). Since we need the Euler angles instead

of angular velocity, we need to convert angular velocity to Euler angle derivatives. Then we

integrate the Euler angles into roll, pitch, and yaw which we can use for the rotation matrices in

the linear motion model (4)(17).

voltage to motor angular acceleration and velocty

function Wmotor = volt2motorW(v1,v2,v3,v4)

%#codegen

Kv = 1; %porportionality constant between voltage and motor angular

velocity

w1=v1/Kv;

w2=v2/Kv;

w3=v3/Kv;

w4=v4/Kv;

Wmotor = [w1,w2,w3,w4];

motor angular velocity to torque in body frame

function [Troll,Tpitch,Tyaw] = w2τ(W,Wdot)

%#codegen

Kv=1; %proportionality constant between motor voltage to angular

velocity

Kτ = 1; %porportionality constant between propeller torque and current

KT = 1; %porportionality constant between propeller thrust and torque

L=1; %distance between motor and center of body frame.

D=1; %diameter of propeller

rho=1; %density of air

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Cd=1; %coefficent of drag for propeller wings

A=1; %proeller cross section

r=D/2; %radius of propeller. Do not change

Iz = 1; %moment of inertia for propellers

%equations for constants we will need for τ

k = pi/2*rho*D^2*(Kv*Kτ/KT);

b = 0.5*r*rho*Cd*A*r^2;

%assume w1 and w3 are right and left motors respectively.

% assume w2 and w4 are back and front motors respectively.

%grab angular motor velocities

w1 = W(1);

w2 = W(2);

w3 = W(3);

w4 = W(4);

%τ of roll pitch and yaw based on angular velocities

Troll = L*k*(w1^2-w3^2);

Tpitch = L*k*(w2^2-w4^2);

Tyaw = b*(w1^2-w2^2+w3^2-w4^2);%+Iz*(Wdot(1)-Wdot(2)+Wdot(3)-Wdot(4));

Rotational Motion Model

function [wdotx,wdoty,wdotz] =

RotationMotion(Troll,Tpitch,Tyaw,eulerDot,euler)

%#codegen

%moment of inertias in the X/Y/Z-axis of the drone body frame

Ixx = 1;

Iyy = 1;

Izz = 1;

I = [Ixx 0 0; 0 Iyy 0; 0 0 Izz];

roll = euler(1);

pitch = euler(2);

yaw = euler(3);

rollDot = eulerDot(1);

pitchDot = eulerDot(2);

yawDot = eulerDot(3);

τ = [Troll;Tpitch;Tyaw];

%First generate rotation matrix for angular velocity and thetaDot

eulerDot2Ω = [1 0 -sin(pitch);

0 cos(roll) sin(roll)*cos(pitch)

0 -sin(roll) cos(roll)*cos(pitch)];

%convert the euler Dots to angular velocities in inertia frame

Ω = eulerDot2Ω*[rollDot;pitchDot;yawDot];

W = [Ω(1);Ω(2);Ω(3)];

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%use rotational motion equations now

Wdot = inv(I)*(τ - cross(W,I*W));

wdotx=Wdot(1);

wdoty=Wdot(2);

wdotz=Wdot(3);

Convert body angular velocity to Euler angle velocity

function [eulerDotRoll,eulerDotPitch,eulerDotYaw] =

w2eulerDot(wx,wy,wz, euler)

%#codegen

roll = euler(1);

pitch = euler(2);

yaw = euler(3);

%rotational matrix for EULERDOT to W. need to inverse it to get

%the relevant transformation matrix

E2W = [1 0 -sin(pitch);

0 cos(roll) sin(roll)*cos(pitch);

0 -sin(roll) cos(roll)*cos(pitch)];

eulerDot = E2W\[wx;wy;wz];

eulerDotRoll = eulerDot(1);

eulerDotPitch = eulerDot(2);

eulerDotYaw = eulerDot(3);

Euler Angle PID Controller

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Position PID Controller

Main Model

The model will take in the waypoint position (and velocity, but we do not use this) and

calculate the PID errors based on current drone position. The position error will be used to

calculate the wanted Euler angles. For example, if we want to accelerate in the X-direction and

we want to go at max velocity, we need to a large magnitude of pitch. On the other hand, if we

need to slow down, we need to pitch in the opposite direction. We assume the drone will have a

max angle of roll-pitch-yaw. Many controls on drones set the max angles at 45 or 30 degrees.

We chose 30 degrees as it is more common of a limit.

After calculating the wanted angle, we calculate the angle PID error. Both errors will be used

in the actuator, which converts the error readings into voltage. We simply added the errors to

the hover voltage (voltage needed to hover, stay in the same position), in order to get the next

time step’s voltage. We must adjust the PID gains in order for voltage to make sense of the

errors.

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set the desired Euler angle

function eulerWanted = setWantedAngles(Eposi)

%#codegen

Ex = Eposi(1);

Ey = Eposi(2);

%no error for yaw currently!

%--------------------------------------------------------------------

%Now we set next iteration's wanted eulers based on error

%The angles we want

Wroll = 0;

Wpitch = 0;

Wyaw = 0;

if (Ex>0) Wpitch=-(pi/6 - exp(-0.05*Ex+log(pi/6))); end

if (Ex<0) Wpitch= (pi/6 - exp( 0.05*Ex+log(pi/6))); end

if (Ey>0) Wroll= (pi/6 - exp(-Ey+log(pi/6))); end

if (Ey<0) Wroll=-(pi/6 - exp( Ey+log(pi/6))); end

%no current controls for yaw

% eulerWanted = [Wroll*abs(Ey)/10;Wpitch*abs(Ex)/10;Wyaw];

eulerWanted = [Wroll;Wpitch;Wyaw];

Main Control Actuator

function [v1,v2,v3,v4] = PIDHumanControl( Eposi, Eeuler,mass)

%#codegen

maxVoltage = 10; %Maximum voltage of the rotors

%voltage totally based on error.

v1=0;

v2=0;

v3=0;

v4=0;

%Set the angles we want to go for-------------------------------------

--

%The specific errors in the X,Y,Z axis of the inertia frame below.

Ex = Eposi(1);

Ey = Eposi(2);

Ez = Eposi(3);

Eroll = Eeuler(1);

Epitch = Eeuler(2);

Eyaw = Eeuler(3);

%if roll error is positive, we need to roll more in positive radians.

And

%so on for the other angles

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%---------------------------------------------------------------------

----

%how much thrust is needed to hover? (assuming 0 angles)

Kv = 1; %porportionality constant between propeller voltage and

angular velocity

Kτ = 1; %porportionality constant between propeller torque and current

KT = 1; %porportionality constant between propeller thrust and torque

D = 1; %propeller diameter. Adjusted by propeller properties

rho = 1; %density of air (humid or dry). Probably need to be a

function

k = pi/2*rho*D^2*(Kv/Kτ/KT);

vHover = Kv*sqrt(mass*9.81/(4*k));

%---------------------------------------------------------------------

%Ex+Ey+Ez is the throttle of the motors. More distance error, more

thrust!

%The Eeulers is the turning force of the drone, more roll needed, more

%rolling we must adjust for

%verison 1

v1 = vHover + Ez + Eroll + Eyaw;

v2 = vHover + Ez + Epitch - Eyaw;

v3 = vHover + Ez - Eroll + Eyaw;

v4 = vHover + Ez - Epitch - Eyaw;

%-------------------------------------------------------------------

%set the limits of voltage based on porportions

%first find the minimum and maximum raw voltage.

minV = min([v1,v2,v3,v4]);

%if minimum voltage is less than zero, add that minimum to every

voltage so the minimum is now zero

if (minV<0)

v1 = v1-minV;

v2 = v2-minV;

v3 = v3-minV;

v4 = v4-minV;

end

%if the highest voltage is greater than the max voltage, divid

everything

maxV = max([v1,v2,v3,v4]);

%so everything is still porportional

if (maxV>maxVoltage)

v1 = v1*maxVoltage/maxV;

v2 = v2*maxVoltage/maxV;

v3 = v3*maxVoltage/maxV;

v4 = v4*maxVoltage/maxV;

end

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68

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