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Control Systems Engineering > Robotics and Control 1 > Flashcards

Robotics and Control 1 Flashcards

1
Q

What characterizes a RIGID BODY?

A

The distance between any 2 points remains constant in time

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2
Q

What is a POSE?

A

The combination of position and orientation

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3
Q

Are rotations COMMUTATIVE?

A

No

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4
Q

The composition of successive rotations about the CURRENT FRAME is obtained through…

A

…post multiplication of the rotation matrices

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5
Q

The composition of successive rotations about the FIXED FRAME is obtained through…

A

…pre multiplication of the rotation matrices

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6
Q

The Minimal Representation for SO(m) requires…

A

…[m (m - 1) / 2] parameters

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7
Q

What is the Euler’s rotation theorem?

A

Any 2 indipendent orthonormal coordinate frames can be aligned by a sequence of 3 elementary rotations about coordinate axes where no two successive rotations are about the same axis

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8
Q

What are the angles of the Roll-Pitch-Yaw representation?

A

ZYX angles along the fixed frame

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9
Q

What is the Axis Angle Representation representation?

A

It is a non-minimal representation of a rotation of a given angle about a given axis in space

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10
Q

An Axis Angle Representation can be decomposed into…

A

…5 elementary rotations

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11
Q

What is an Elementary Rotation?

A

It is the rotation about one of the frame axes

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12
Q

What is a Skew Symmetric Matrix?

A

It’s a matrix that, if summed to it’s transpose, equals 0

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13
Q

What is the TRACE of a matrix?

A

It is the sum of its diagonal elements which is also equal to the sum of its eigenvalues

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14
Q

What is a QUATERNION?

A

A quaternion is a hypercomplex number written as a scalar plus a vector

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15
Q

What is a COORDINATION TRANSFORMATION?

A

It is a transformation that combines translation and rotation

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16
Q

What are LINKS?

A

It is a series of rigid bodies connected by joints

17
Q

What is an OPEN KINEMATIC CHAIN?

A

A kinematic chain is a series of links and joints, it is open when there is a single sequence of links that connects the 2 ends of the chain

18
Q

How many DEGREES OF FREEDOM does an OPEN KINEMATIC CHAIN possess?

A

As many as the number of joints

19
Q

What is a CONFIGURATION?

A

It is the complete specification of the location of every point on the manipulator

20
Q

What is a CONFIGURATION SPACE?

A

It is the set of all possible configurations

21
Q

What is a WORKSPACE?

A

It is the volume that includes all the points reachable by the end effector

22
Q

What does DIRECT KINEMATICS mean?

A

It means that the description of the pose of the end-effector is a function of the joint variables

23
Q

What is the TWIST ANGLE between 2 axes?

A

It is the angle between their projection on the plane pi, which is orthogonal to their common normal

24
Q

What is the TWIST ANGLE between 2 axes?

A

It is the angle between their projection on the plane pi, which is orthogonal to their common normal

25
Q

What is the REACHABLE WORKSPACE?

A

It is the set of all positions that can be reached with at least one orientation

26
Q

What is the DEXTERIOUS WORKSPACE?

A

It is the set of all positions that can be reached with any orientation

27
Q

What defines the KINEMATIC REDUNDANCY of a manipulator?

A

A manipulator is redundant in respect to a task if the number of degrees of freedom is higher is greater than the variables needed to describe that task

28
Q

What makes a manipulator INTRINSECALLY REDUNDANT?

A

A manipulator is intrinsecally redundant if the number of degrees of freedom (dimension of the configuration space) is higher than the dimension of the operational space

29
Q

What is the ANALYTICAL METHOD for inverse kinematics?

A

The analytical method involves a geometric inspection and the resolution of polynomial equations, it is the preferred method if applicable

30
Q

What is the NEWTON METHOD for inverse kinematics?

A

The newton method is an iterative method with quadratic convergence towards the solution, it has problems near singularities and the initial guess must be at least close to the solution

31
Q

What is the GRADIENT METHOD for inverse kinematics?

A

The gradient method is an iterative method with linear convergence towards the solution, it requires an adequate stepsize, too small and the method is slow, too big and the algorithm overshoots. It has problem near singularities only if the solution is also part of the null space

32
Q

What differentiates INFINITESIMAL ROTATIONS from standard finite rotations?

A

Infinitesimal rotations do commute unlike other finite rotations

33
Q
A

Control Systems Engineering (1 decks)

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