#### All Weeks Robotics: Aerial Robotics Coursera Quiz Answers

## Robotics: Aerial Robotics Week 1 Quiz Answers

### Quiz 1: 1.1 Answers

Q1. Which of these factors has **NOT** contributed to the rapidly-increasing commercial interest in multi-rotor vehicles?

- Mechanical simplicity
- Ability to hover in mid air
**Inexpensive components**- Efficiency in forward flight

Q2. In how many ways can you translate and rotate this robot in free space? Enter your answer as a numeric value (e.g. 1 instead of one).

** Autonomous control Planning to avoid obstacles State estimation**

Q3. How many independent control inputs does the vehicle shown above have?

- 4, since it is similar to a quadrotor, except with more motors
**6, because there are six motors**- 6, because a rigid body has six degrees of freedom

Q4. Based on the lecture content in this course, which of these components are incorporated in commercial products mentioned in lecture such as the DJI Phantom or the Parrot Bebop? (Select all that apply.)

**State estimation****Planning to avoid obstacles**- Mapping
**Autonomous control**

Q5. An Inertial Measurement Unit (IMU) is an important sensor used in aerial robotics. A typical IMU will contain an accelerometer and a rate gyro. Which of the following information does a robot get from an IMU? (Select all that apply. Choose only quantities that are directly reported by the IMU. Do not include quantities that can be computed from the IMU measurements but cannot be obtained directly. Additional research to find information about IMUs is allowed and encouraged!) (Select all that apply)

- Position
- Orientation
- Linear velocity
**Angular velocity****Linear acceleration**- Angular acceleration

Q6. What does Simultaneous Localization And Mapping (SLAM) software do? (Select all that applies.)

**Estimates the location of features in the environments**- Navigates the robot in a cluttered environment
**Estimates the position and orientation of the robot with respect to the environment**- Controls the robot’s flight through the environment
- Causes the robot to avoid obstacles in the environment

### Quiz 2: 1.2 Answers

Q1.

You observe the response of a system shown in the figure below

What should you do to decrease the oscillations in the response?

- Increase the proportional gain (K_p
*Kp*) - Increase the integral gain (K_i
*Ki*) **Decrease the proportional gain (K_p***Kp*)**Increase the derivative gain (K_v***Kv*)

Q3. Assuming we are using the F550 + E310 + 4 cell battery with a 200g onboard computer and a laser (270g), what is the thrust to weight ratio of the platform? (We use the term “weight” and “thrust” loosely. Except for Thrust/Weight and Propeller, all units are in grams)

**2.264**

Q4. don’t all the rotors of a quadrotor spin in the same direction?

- Spinning all rotors in the same direction uses more battery power.
**Spinning all rotors in the same direction will cause the robot to constantly rotate.**- Spinning all rotors in the same direction does not allow the quadrotor to fly upside down.

Q5. Given that a quadrotor consumes 200 W to carry a mass of 1kg, which component contributes more to the quadrotor’s total power consumption?

A 100g computer that consumes 30W for operation or a 200g laser which consumes 20W for operation?

- The computer.
- The laser.
**Both contribute the same to the power consumption.**

## Robotics: Aerial Robotics Week 2 Quiz Answers

### Quiz 1: 2.1 Answers

Q1. Which of the following matrices are rotation matrices?

- \left[ 0.38350.5710−1.39540.57300.59190.02170.9287−0.41191.1105\right]⎣⎢⎡0.38350.5710−1.39540.57300.59190.02170.9287−0.41191.1105⎦⎥⎤
- \left[ (√2)/20−(√2)/2010(√2)/20(√2)/2\right]⎣⎢⎡(2)/20−(2)/2010(2)/20(2)/2⎦⎥⎤
- \left[
*cos*(*θ*)*sin*(*θ*)−*sin*(*θ*)*cos*(*θ*)\right][*cos*(*θ*)*sin*(*θ*)−*sin*(*θ*)*cos*(*θ*)] - \left[ 0.21200.21200.95400.7743−0.6321−0.03160.59630.7454−0.2981\right]⎣⎢⎡0.21200.21200.95400.7743−0.6321−0.03160.59630.7454−0.2981⎦⎥⎤

Q2. What is the ZYZ euler angle representation,(\psi,(*ψ*, \theta,*θ*, \phi)*ϕ*), for the following rotation matrix?

\left[0.69270.7165−0.0824−0.71460.69730.05640.09780.01980.995\right]⎣⎢⎡0.69270.7165−0.0824−0.71460.69730.05640.09780.01980.995⎦⎥⎤

Recall that this rotation matrix can be seen as a combination of three rotations:

\left[cos(*ψ*)sin(*ψ*)0−sin(*ψ*)cos(*ψ*)0001\right]\left[cos(*θ*)0−sin(*θ*)010sin(*θ*)0cos(*θ*)\right]\left[cos(*ϕ*)sin(*ϕ*)0−sin(*ϕ*)cos(*ϕ*)0001\right]⎣⎢⎡cos(*ψ*)sin(*ψ*)0−sin(*ψ*)cos(*ψ*)0001⎦⎥⎤⎣⎢⎡cos(*θ*)0−sin(*θ*)010sin(*θ*)0cos(*θ*)⎦⎥⎤⎣⎢⎡cos(*ϕ*)sin(*ϕ*)0−sin(*ϕ*)cos(*ϕ*)0001⎦⎥⎤

- (0.7,(0.7, 0.4,0.4, 0.2)0.2)
- (0.9,(0.9, 0.1,0.1, 0.1)0.1)
- (0.1,(0.1, 0.1,0.1, 0.2)0.2)
- (0.2,(0.2, 0.1,0.1, 0.6)0.6)

Q3. At a given time t*t*, the rotation matrix R has the value:

R = \left[0.6750.2474−0.6951−0.17240.96890.17750.717400.6967\right]*R*=⎣⎢⎡0.6750.2474−0.6951−0.17240.96890.17750.717400.6967⎦⎥⎤.

The angular velocity \hat{\omega}^b*ω*^*b* at that same time t*t* is:

\hat{\omega}^b=\left[01−0.9689−100.24740.9689−0.24740\right]*ω*^*b*=⎣⎢⎡01−0.9689−100.24740.9689−0.24740⎦⎥⎤.

What is \hat{\omega}^s*ω*^*s*?

- \left[00.8742−1.0736−0.87420−0.28831.07360.28830\right]⎣⎢⎡00.8742−1.0736−0.87420−0.28831.07360.28830⎦⎥⎤
- \left[0.81470.90580.12700.91340.63240.09750.27850.54690.9575\right]⎣⎢⎡0.81470.90580.12700.91340.63240.09750.27850.54690.9575⎦⎥⎤
- \left[00.6967−1−0.696700.71741−0.71740\right]⎣⎢⎡00.6967−1−0.696700.71741−0.71740⎦⎥⎤
- \left[01−0.9689−100.24740.9689−0.24740\right]⎣⎢⎡01−0.9689−100.24740.9689−0.24740⎦⎥⎤

Q4. Given the following rotation matrix, what is the corresponding axis-angle representation assuming the angle is restricted to \left[0,\;\pi\right][0,*π*]?

\left[0.2919−0.643−0.70810.643−0.41610.643−0.7081−0.6430.2919\right]⎣⎢⎡0.2919−0.643−0.70810.643−0.41610.643−0.7081−0.6430.2919⎦⎥⎤

- u=\left[\sqrt{2}/2,\; 0,\; -\sqrt{2}/2 \right]^T
*u*=[2/2,0,−2/2]*T*, \phi=2*ϕ*=2 - Not enough information is given to uniquely determine the axis-angle representation
- u=\left[-\sqrt{2}/2,\; 0,\; \sqrt{2}/2 \right]^T
*u*=[−2/2,0,2/2]*T*, \phi=2*ϕ*=2 - u=\left[-\sqrt{2}/2,\; 0,\; \sqrt{2}/2 \right]^T
*u*=[−2/2,0,2/2]*T*, \phi=0.8*ϕ*=0.8 - u=\left[\sqrt{2}/2,\; -\sqrt{2}/2,\;0 \right]^T
*u*=[2/2,−2/2,0]*T*, \phi=0.8*ϕ*=0.8

Q5. the following rotation matrix, what is the corresponding axis-angle representation assuming the angle is restricted to \left[0,\;\pi\right][0,*π*]?

\left[−1/32/3−2/32/3−1/3−2/3−2/3−2/3−1/3\right]⎣⎢⎡−1/32/3−2/32/3−1/3−2/3−2/3−2/3−1/3⎦⎥⎤

- u=\left[-\sqrt{3}/3,\; \sqrt{3}/3,\; -\sqrt{3}/3 \right]^T
*u*=[−3/3,3/3,−3/3]*T*, \phi=.2*ϕ*=.2 - u=\left[-0.9066,\; 0.9066,\; 0.9066 \right]^T
*u*=[−0.9066,0.9066,0.9066]*T*, \phi=.2*ϕ*=.2 - Not enough information is given to uniquely determine the axis-angle representation
- u=\left[-0.9066,\; -0.9066,\; -0.9066 \right]^T
*u*=[−0.9066,−0.9066,−0.9066]*T*, \phi=\pi*ϕ*=*π* - u=\left[\sqrt{3}/3,\; \sqrt{3}/3,\; -\sqrt{3}/3 \right]^T
*u*=[3/3,3/3,−3/3]*T*, \phi=\pi*ϕ*=*π*

Q6. Recall the transformation from the in-video exercises:

Assuming \mathbf{p}**p** and \mathbf{q}**q** represent the vectors from the origin to the points P and Q respectively, which of the following are correct expressions for the cross-product of the rotated vectors \mathbf{p}’\times \mathbf{q}’**p**′×**q**′?

- \mathbf{p}\times \mathbf{q}
**p**×**q** - g_*\left(\mathbf{p}\times \mathbf{q}\right)
*g*∗(**p**×**q**) - g_*(\mathbf{p})\times g_*(\mathbf{q})
*g*∗(**p**)×*g*∗(**q**)

## Robotics: Aerial Robotics Week 3 Quiz Answers

### Quiz 1: 3.1 Answers

Q1. In the nested feedback control loop

- The inner loop corresponds to orientation and the outer loop corresponds to position.
- The inner loop corresponds to position and the outer loop corresponds to orientation.

Q2. arg\min_{x(t)} \int_0^T \|x^{(5)}(t)\|^2dt*arg*min*x*(*t*)∫0*T*∥*x*(5)(*t*)∥2*dt* is an k*k*th degree polynomial trajectory where k=*k*=**1 point**

- 3
- 5
- 7
- 9
- 11

Q3. Which of the following are simplifying assumptions we made when designing the controller in this module?

- Roll and pitch angles are close to zero
- Quadrotor is very small
- Quadrotor is near equilibrium
- Angular velocities are close to zero

## Robotics: Aerial Robotics Week 4 Quiz Answers

### Quiz 1: 4.1 Answers

Q1. What sensors would you rely on for state estimation in an office building with vertical walls without too much clutter due to furniture when the lighting is poor?

- IMU
- GPS
- Cameras
- Laser Scanners

Q2. Given a desired thrust vector \mathbf{t} = \sin(30^\circ) \cos(45^\circ) \mathbf{a}_1 + \sin (30^\circ) \sin (45^\circ)\mathbf{a}_2+ \cos( 30^\circ) \mathbf{a}_3**t**=sin(30∘)cos(45∘)**a**1+sin(30∘)sin(45∘)**a**2+cos(30∘)**a**3 and a desired yaw angle, \psi_{des} = 45^\circ*ψ**des*=45∘. Compute the desired rotation matrix, R_{des}*R**des*.

- \left[
- −0.50.86600010.8660.50
- \right]⎣⎢⎡−0.50.86600010.8660.50⎦⎥⎤
- \left[
- .866−0.3536−0.353600.70710.7071−0.3536−0.61240.6124
- \right]⎣⎢⎡.866−0.3536−0.353600.70710.7071−0.3536−0.61240.6124⎦⎥⎤
- \left[
- 0.08100.13130.988−0.85090.525300.988−0.84070.1543
- \right]⎣⎢⎡0.08100.13130.988−0.85090.525300.988−0.84070.1543⎦⎥⎤
- \left[
- 0.70710.70710−0.61240.61240.50.3536−0.35360.866
- \right]⎣⎢⎡0.70710.70710−0.61240.61240.50.3536−0.35360.866⎦⎥⎤
- \left[
- 0.14640.1464−0.5−0.50.50.7071−0.14640.14640.5
- \right]⎣⎢⎡0.14640.1464−0.5−0.50.50.7071−0.14640.14640.5⎦⎥⎤
- \left[
- 0.61240.6124−0.5−0.70710.707100.35360.35360.866
- \right]⎣⎢⎡0.61240.6124−0.5−0.70710.707100.35360.35360.866⎦⎥⎤

Q3. What is the rotation matrix that describes the attitude error if the current rotation matrix is given by R*R* and the desired rotation matrix is R_{des}*R**des*:

R = \left[

0.72440.64240.250.1294−0.4830.8660.6771−0.595−0.433

\right]*R*=⎣⎢⎡0.72440.64240.250.1294−0.4830.8660.6771−0.595−0.433⎦⎥⎤

R_{des} = \left[

010001100

\right]*R**des*=⎣⎢⎡010001100⎦⎥⎤

- \left[
- 0.7244−0.35760.250.1294−0.483−0.134−0.3229−0.5950−0.433
- \right]⎣⎢⎡0.7244−0.35760.250.1294−0.483−0.134−0.3229−0.5950−0.433⎦⎥⎤
- \left[
- 0.6424−0.483−0.5950.250.866−0.4330.72440.12940.6771
- \right]⎣⎢⎡0.6424−0.483−0.5950.250.866−0.4330.72440.12940.6771⎦⎥⎤
- \left[
- −0.72440.3576−0.25−0.12940.4830.1340.32290.5950.433
- \right]⎣⎢⎡−0.72440.3576−0.25−0.12940.4830.1340.32290.5950.433⎦⎥⎤
- \left[
- 0.64240.250.7244−0.4830.8660.1294−0.595−0.4330.6771
- \right]⎣⎢⎡0.64240.250.7244−0.4830.8660.1294−0.595−0.4330.6771⎦⎥⎤

Q4. What sensors are most likely to fail when operating indoors in a building with glass walls?

- Laser Scanners
- IMU
- GPS
- Cameras

Q5. What sensors are most likely to fail when the robot is flying outdoors, close to the ground near the wall of a tall building?

- IMU
- GPS
- Cameras
- Laser Scanners