Simulazioni svolte Robotica

EXAM BOOK

Exam Rules:

• Test duration: 2h30m. This test comprises 10 multiple-choice questions and 2 open

answer problems

• The exam is closed notes, closed books. You can keep with you a single A4 sheet with

notes or formulas. Both sides can be written.

• No extra paper is allowed. Please consult with the instructor or the TA before using or

asking for extra paper.

• Calculators without internet connection are admitted, tablets or PCs are forbidden.

• Multiple choice questions do not need any justification, open answer problems do require

justifications to elucidate the process of formulation of the solution.

• Solutions to multiple choice questions must be reported in the grid in this page.

• Any cheating attempt will not be tolerated. You will be immediately disqualified from the

exam and reported to the University committee for academic dishonesty.

ANSWER GRID

Question 1 2 3 4 5 6 7 8 9 10

Answer

Question 1

With reference to the robot in the photograph:

a) it is a spherical robot, with a joint sequence RRP

b) it is a cartesian robot, with a joint sequence PPR

c) it is a cartesian robot, with a joint sequence PPP

d) it is a cylindrical robot, with a joint sequence RPP

Question 2

The Euler angles:

a) constitute a minimal representation of the orientation of a rigid body in the 3D space, and

consists of 3 parameters

b) constitute a minimal representation of the position and orientation of a rigid body in the

3D space, and consists of 4 parameters

c) do not constitute a minimal representation of the position and orientation of a rigid body

in the 3D space

d) are the components of the unit vectors of a reference system with respect to the unit

vectors of another reference system

Question 3 rd nd

For a certain configuration of a manipulator, the element in the 3 row and 2 column of the

Jacobian is zero. This implies that:

a) the manipulator is redundant

b) the third joint variable has no effect on the second variable of the task space

c) the second joint variable has no effect on the third variable of the task space

d) the manipulator is in a singular configuration

Question 4

The relationship between analytical and geometrical Jacobian:

a) is established through a block-diagonal matrix that depends on the current configuration

b) is established through a constant block-diagonal matrix

c) is established through a system of ordinary differential equations

d) is established through a system of partial differential equations

Question 5

The kinetic energy of a manipulator:

a) is a linear function of the joint velocities

b) is a differential function of the joint velocities

c) is a quadratic function of the joint velocities, with in general constant coefficients

d) is a quadratic function of the joint velocities, with in general variable coefficients, which

depend on the robot configuration

Question 6

The following equations:

a) represent the kinematical model of a manipulator

b) represent the dynamical model of a manipulator in space state, where x are the joint

1

positions and x are the joint velocities

2

c) represent the dynamical model of a manipulator in space state, where x are the joint

2

positions and x are the joint velocities

1

d) represent the static equilibrium conditions for a manipulator

Question 7

The decentralized joint control

a) assumes that the robot model is linear and coupled, and controls each joint in order to

increase the transmission ratio of the gearbox

b) assumes that the robot model is nonlinear and decoupled, and add a specific term to the

individual controllers to compensate at least the gravitational term

c) cancels the robot nonlinear dynamics through an inner loop that uses the inverse

dynamical model of the robot. Then, controls individually the joints of the obtained

linearized model

d) assumes that the robot model is linear and decoupled, and controls each joint separately

with a linear controller. All the terms that are neglected are considered as disturbances

Question 8

A bicycle-like robot:

a) has the same kinematic model irrespective of the fact that is forward- or backward-driven

b) never possesses an instantaneous curvature center

c) has an instantaneous curvature center that depends on the bicycle configuration

d) has only holonomic constraints

Question 9

The aim of stereoscopic vision is:

a) to reconstruct colors using pairs of grey-scale images

b) to duplicate images using pattern recognition algorithms

c) to divide images in two specular images in order to improve image filtering

d) to reconstruct a missing third coordinate (using the depth) starting from the analysis of

two images of the same scene taken from slightly different point of views

Question 10

The gradient operator:

a) is a local derivative operator used to filter images

b) is a local derivative operator used to enhance the image quality

c) is a local derivative operator used to reveal edges and contours in images

d) is a global derivative operator used to equalize the image histogram

SCRATCH PAPER

Problem 1

Write the dynamical model of a manipulator in its compact form. Comment on the role and

meaning of each of the terms that constitute the model. Comment on the role of an increase of

the transmission ratios of motors on each of the terms

Answer here – Turn page for the next problem

Problem 2

In image processing, state the difference between edge detection and image segmentation.

Then, describe the two main techniques used for image segmentation.

Answer here 01PEEQW – Robotics – Exam Simulation

Prof. Alessandro Rizzo

Surname _____________ Name__________________

EXAM BOOK

Exam Rules:

• Test duration: 2h15m. This test comprises 10 multiple-choice questions and 2 open

answer problems

• The exam is closed notes, closed books. You can keep with you a single A4 sheet with

notes or formulas. Both sides can be written.

• No extra paper is allowed. Please consult with the instructor or the TA before using or

asking for extra paper.

• Calculators without internet connection are admitted, tablets or PCs are forbidden.

• Multiple choice questions do not need any justification, open answer problems do require

justifications to elucidate the process of formulation of the solution.

• Solutions to multiple choice questions must be reported in the grid in this page.

• Any cheating attempt will not be tolerated. You will be immediately disqualified from the

exam and reported to the University committee for academic dishonesty.

ANSWER GRID

Question 1 2 3 4 5 6 7 8 9 10

Answer

2018wxlhhwa

Question 1

A kinematic chain

a) Consists of a variable number of motors and gearboxes

b) Consists of links and joints, considered only as geometrical entities

c) Consists of links and joints, including friction coefficients and masses

d) Consists of control algorithms for robot movement

Question 2

The task space:

a) is the subset of the cartesian space that can be reached by the TCP

b) is the subset of the joint space that can be reached by the TCP

c) is the subset of the cartesian velocities that can be covered by the TCP

d) is the subset of the joint velocities that can be covered by the TCP

Question 3

In a kinematic chain, link i is related to link i-1 through the following homogeneous matrix:

3

1 0 0 0

0 1 0

""#$

= & +

0 0 1 "

1

0 0 0

a) Link i is a rotation link

b) Link i is a prismatic link

c) The matrix above is not a homogeneous transformation matrix

d) None of the above

Question 4

The geometric Jacobian of a two-link planar arm is

The manipulator:

a) Has no singularities

b) Has an infinite number of singularities p

c) Has two singularities, for q =0 and q =

1 1 p

d) Has two singularities, for q =0 and q =

2 2

Question 5

A planar manipulator in a fully-extended configuration:

a) is in a singular configuration

b) is not in a singular configuration

c) has a maximum number of degrees of freedom in the task space

d) spans a 2-dimensional space in the task space

Question 6

Given the (true) relationship calling the joint forces/torques and the task space

̇ = ()̇ ,

forces, the kineto-static duality implies:

a) =

#$

b) =

5

c) =

5

d) =

Question 7

In the trajectory planning problem:

a) The path is the geometrical description of the desired set of point in the task space, the

trajectory is the path plus the time law to follow the path

b) The trajectory is the geometrical description of the desired set of point in the task space,

the path is the trajectory plus the time law to follow the path

c) The path is a synonymous for control law of the robot

d) The path has nothing to do with the trajectory planning problem

Question 8

The schematic in the figure

a) Refers to the task space control scheme

b) Refers to the joint space control scheme

c) Refers to the combined task-and-joint space control scheme

d) Is not a control scheme

Question 8

Nonholonomic constraints:

a) Reduce the accessibility to the space of configurations

b) Do not alter the accessibility to the space of configurations

c) Are always integrable

d) Imply the existence of corresponding kinematic constraints

Question 9

A non-slipping constraint in wheeled robots:

a) Is a nonholonomic constraint

b) Is a holonomic constraint

c) Is a kinematic constraint

d) Is a dynamical constraint

Question 10

The following stencil:

a) computes the Gradient in a pixel

b) computes the Laplacian in a pixel

c) computes the average of the light intensity in a 3x3 neighborhood

d) computes median filtering in a pixel

Problem 1

Derive the pure rolling constraint for the unicycle illustrated in the figure (Note: derive means that

I want to see some form of calculations/reasoning/proofs etc. – if you copy the constraint from

your notes the corresponding grade is zero)

Problem 2

Describe the perspective transformation problem in robotic vision and derive the homogeneous

transformation matrix related to it.

The perspective transformation problem in robotic vision consists in establishing a

correspondence between 3D points in the real world and 2D points in the image plane. To solve

this problem, we assume the pin-hole model for the camera, whereby light can pass from the 3D

world to the image plane through a single, tiny hole, placed inside the camera lens. Due to the

assumption that light travels along straight lines, the image plane will exhibit a flipped (upside-

down and mirrored) image with respect to reality. Let us call X,Y,Z the 3D coordinates of a point,

l

x,y the coordinates of the same point in the image plane, the focal length, t