Robot Kinematics - Inverse Kinematics Quiz
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Questions and Answers

What is a characteristic of independent joint PID control?

  • It requires complex models for implementation.
  • It is sensitive to modeling errors.
  • It is robust to modeling errors. (correct)
  • It involves only end-effector control.

Which of the following orders the given tasks by computational expense from least to most expensive?

  • Forward kinematics < Jacobian calculation < Inverse kinematics (7 DoF manipulator, numerical) < Inverse kinematics (4 DoF SCARA robot)
  • Forward kinematics < Inverse kinematics (4 DoF SCARA robot) < Jacobian calculation < Inverse kinematics (7 DoF manipulator, numerical) (correct)
  • Jacobian calculation < Forward kinematics < Inverse kinematics (4 DoF SCARA robot) < Inverse kinematics (7 DoF manipulator, numerical)
  • Inverse kinematics (4 DoF SCARA robot) < Jacobian calculation < Forward kinematics < Inverse kinematics (7 DoF manipulator, numerical)

What action will be taken if the battery level is adequate?

  • Shut down temporarily.
  • Replace the batteries.
  • Do main task. (correct)
  • Perform maintenance.

What can be assumed about the AUV in relation to the charger?

<p>It is already near the charger. (A)</p> Signup and view all the answers

How is 'Failure' interpreted in a condition node?

<p>As 'False'. (A)</p> Signup and view all the answers

What is a requirement for traversing edges in the RRT* algorithm?

<p>Your vehicle must traverse any edge in both directions. (A)</p> Signup and view all the answers

Which sensor is classified as proprioceptive?

<p>Accelerometer. (D)</p> Signup and view all the answers

What does the prediction step in a localization system do?

<p>Increases position uncertainty. (C)</p> Signup and view all the answers

For a differential drive robot, what is true about the motors?

<p>Each wheel is driven by a separate motor. (C)</p> Signup and view all the answers

Which condition must be satisfied for an algorithm to be considered valid for calculating the inverse kinematics of a manipulator?

<p>The algorithm must meet the criterion of $|ε| &lt; desired tolerance$. (A)</p> Signup and view all the answers

For a 7 DoF serial link manipulator, which properties can be controlled independently?

<p>Translational and angular velocity of the end effector. (D)</p> Signup and view all the answers

Which statement regarding the formulation of forward kinematics in a serial link manipulator is true?

<p>Closed form can always be formulated if DH parameters are known. (C)</p> Signup and view all the answers

Which of the following is generally true regarding manipulator dynamics?

<p>The required joint torques depend on the current configuration of the robot. (A)</p> Signup and view all the answers

What is the maximum number of controllable degrees of freedom for the end effector pose for a robot with 7 revolute joints?

<p>6 degrees of freedom with revolute joints. (D)</p> Signup and view all the answers

What does the Jacobian relate in manipulator kinematics?

<p>It determines the relationship between joint velocities and end-effector velocities in task space. (C)</p> Signup and view all the answers

Which joint actuation option provides the highest precision for end effector positioning?

<p>Brushless DC motor and optical encoder. (A)</p> Signup and view all the answers

In grasping tasks, what type of grasp is suitable for adjusting cylindrical beverage cans?

<p>Force closure. (C)</p> Signup and view all the answers

What must be considered when making a statement about the inverse kinematics for a serial link manipulator?

<p>The joint configuration may result in no solution. (D)</p> Signup and view all the answers

Which statement is true about formulating forward kinematics for a serial link manipulator?

<p>A closed form can always be generated if the DH parameters are known. (A)</p> Signup and view all the answers

The joint torques necessary for a specific end effector acceleration are constant, regardless of the robot's configuration.

<p>False (B)</p> Signup and view all the answers

Independent joint PID control is robust to modeling errors.

<p>True (A)</p> Signup and view all the answers

What happens if the battery level is not okay?

<p>Recharge (A)</p> Signup and view all the answers

What is the maximum number of controllable degrees of freedom for the end effector pose with a 7 DoF robot using revolute joints?

<p>6</p> Signup and view all the answers

What is the computational cost order from least to most expensive for manipulator kinematics?

<p>Forward kinematics, Jacobian calculation, Inverse kinematics (4 DoF SCARA robot), Inverse kinematics (7 DoF manipulator, numerical)</p> Signup and view all the answers

The __________ relates joint velocities to end-effector velocities in task space.

<p>Jacobian</p> Signup and view all the answers

A multi-rotor drone can perform __________ landing and takeoff.

<p>vertical</p> Signup and view all the answers

Match the following types of joint actuation with their precision for positioning an end effector:

<p>Brushless DC motor and optical encoder = Highest precision Stepper motor in direct drive configuration = Moderate precision Permanent magnet DC motor and a potentiometer = Lower precision Pneumatic cylinder with a strain gauge air pressure sensor = Lowest precision</p> Signup and view all the answers

Match the sensor with its classification (1 for proprioceptive, 2 for exteroceptive):

<p>RGB-D = 2 Gyro = 1 Accelerometer = 1 Radar = 2</p> Signup and view all the answers

For a 7 DoF manipulator, what types of movement can the end effector's pose control independently?

<p>Both translational and angular motion (C)</p> Signup and view all the answers

Form closure is the most suitable grasp type for picking up greased parts.

<p>False (B)</p> Signup and view all the answers

If 'Do main task' takes a long time, the AUV might pause execution to recharge its batteries.

<p>True (A)</p> Signup and view all the answers

What defines the relationship between joint torques and end-effector wrenches?

<p>Jacobian transpose</p> Signup and view all the answers

A condition can have more return statuses than an action.

<p>False (B)</p> Signup and view all the answers

The velocity of the end effector can be determined using the Jacobian's relation to __________.

<p>joint velocities</p> Signup and view all the answers

Which of the following statements regarding the RRT* algorithm is true?

<p>The RRT* algorithm can produce a tree structure. (B)</p> Signup and view all the answers

The update step in a localization system is associated with __________ uncertainty.

<p>decreasing</p> Signup and view all the answers

Which of the following grasp types is suitable for adjusting cylindrical beverage cans?

<p>Force closure (C)</p> Signup and view all the answers

To drive forward, you would give +V voltage to both motors of a differential drive robot.

<p>False (B)</p> Signup and view all the answers

Flashcards

Numerical Inverse Kinematics

A numerical method to solve for joint angles given the desired end-effector pose. Often used when a closed-form solution is not available.

Jacobian Matrix

The relationship between joint velocities and end-effector velocities. It is a matrix that maps joint space to task space.

Degrees of Freedom (DoF)

The specific type of joint configuration where the end-effector's position and orientation are fully determined.

Forward Kinematics

The process of determining the end-effector position and orientation based on the joint angles.

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Form Closure

A grasp where the object is completely surrounded by the gripper and cannot move without the gripper changing its shape.

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Force Closure

A grasp which ensures that the object cannot move regardless of forces applied.

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Caging Grasp

A grasp where the gripper encloses the object like a cage, preventing it from escaping but allowing it to move slightly.

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Controllable Degrees of Freedom

The ability of a manipulator to control both translational and angular velocity of the end-effector independently.

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Manipulator Dynamics

The torques required to achieve a specific acceleration of the end-effector depend on the robot's current configuration.

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Denavit-Hartenberg (DH) Parameters

A method for representing a manipulator's geometry and joints using a set of parameters.

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Independent Joint PID Control and Modeling Errors

Independent joint PID control is not robust to modeling errors. Even small errors in the model can lead to significant tracking errors.

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End-Effector Force Control with Joint Sensors

It is not possible to implement end-effector force control using only joint sensors. You need additional sensors (e.g., force/torque sensors) at the end-effector to measure forces.

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Computational Expense of Kinematics

The order of computational expense, from least to most expensive, is: Forward kinematics, Jacobian calculation, Inverse kinematics (4 DoF SCARA robot), Inverse kinematics (7 DoF manipulator, numerical).

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Condition Node Status Values

A condition in a behavior tree returns fewer status values than an action.

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Condition Node Failure Status

A condition node returning

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RRT* Algorithm and Edge Traversal

The RRT* algorithm generates a tree structure where you can traverse any edge in both directions.

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A* Algorithm and Solution Existence

A* does not guarantee to inform you if no valid solution exists. It might get stuck in a local minimum.

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Differential Drive Robot Motor Configuration

In a differential drive robot, each wheel is driven by a separate motor.

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Differential Drive Robot Forward Motion

To drive a differential drive robot forward, you typically apply positive voltage to one motor and negative voltage to the other.

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Multi-Rotor Drone Characteristics

Multi-rotor drones are best described by the following characteristics: Vertical landing and takeoff, ability to stand still in the air, and high maneuverability.

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Independent Joint PID Control

A control strategy where each joint has its own independent PID controller. This approach is susceptible to errors in the robot's model, leading to inaccurate tracking.

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End-Effector Force Control

The ability to achieve accurate force control at the robot's end-effector requires sensors placed at the end-effector, not only at the joints.

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Computational Expense of Robotics

Forward kinematics is the simplest calculation, involving basic geometry, while inverse kinematics, especially for complex robots and numerical methods, requires more intensive processing.

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Forward Kinematics (Closed Form)

For a serial link manipulator, given the Denavit-Hartenberg (DH) parameters, we can always calculate the end-effector position and orientation. This calculation is known as forward kinematics and it's always possible to find a closed-form solution.

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Forward Kinematics (Numerical)

For a serial link manipulator, given the DH parameters, we can always numerically approximate the end-effector position and orientation for any given set of joint angles. This method is used when a closed-form solution is not available or too complex.

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Jacobian Transpose

The Jacobian transpose links joint torques to the end-effector wrenches (forces and moments). This relationship helps us determine the forces needed at the joints to achieve a desired force or moment at the end-effector.

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Controllable DoFs for 7 DoF RRRRRRR

For a 7 DoF serial link manipulator with revolute joints (RRRRRRR), its end-effector's position and orientation can be fully controlled. This means we have the ability to control 6 degrees of freedom independently (3 for position and 3 for orientation).

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Controllable DoFs for 7 DoF PPPPPPP

The maximum number of controllable degrees of freedom for the end-effector pose of a 7 DoF robot with prismatic joints (PPPPPPP) is 3. This limitation stems from the fact that prismatic joints only allow for linear movement, not rotational movement.

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Inverse Kinematics (Numerical)

Inverse kinematics involves finding the joint angles that produce a desired end-effector pose. For a serial link manipulator, if we know the DH parameters, we can find a numerical approximation for these joint angles. This numerical method allows us to solve inverse kinematics problems even when there's no closed-form solution.

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Joint Actuation and Precision

The type of actuator and sensor used significantly impacts the precision of end-effector positioning. A brushless DC motor with an optical encoder offers the highest precision, followed by a stepper motor in direct drive configuration, then a permanent magnet DC motor with a potentiometer, and finally a pneumatic cylinder with a strain gauge sensor.

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Study Notes

Question 1

  • Inverse kinematics algorithms numerically calculate a manipulator's inverse kinematics using a Denavit-Hartenberg (DH) description.
  • The algorithm calculates until the error is less than a desired tolerance.

Question 2

  • For a 7-DOF (RRRRRRR) serial link manipulator, the translational and angular velocity of the end effector can be controlled independently.

Question 3

  • Forward kinematics of a serial link manipulator can be formulated numerically if DH parameters are known.
  • Forward kinematics can be calculated using a closed form if DH parameters are known.
  • Numerical approximation for inverse kinematics is possible if DH parameters are known.

Question 4

  • Numerical approximation for inverse kinematics of a serial link manipulator is possible if DH parameters are known.
  • Joint torques required for a specific end-effector acceleration depend on the robot's current configuration.

Question 5

  • A 7-DOF robot has a maximum of 6 degrees of freedom for the end effector pose.

Question 6

  • The Jacobian relates joint velocities to end-effector velocities in task space.
  • The Jacobian transpose relates joint torques to end-effector wrenches.

Question 7

  • Brushless DC motor with optical encoder provides the highest precision.
  • Stepper motors in direct drive configurations offer high precision.
  • Permanent magnet DC motors with potentiometers provide slightly less precision.
  • Pneumatic cylinders with strain gauge air pressure sensors hold the lowest precision.

Question 8

  • Caging grasp is for picking up trash.
  • Form closure is used for picking up greased parts.
  • Force closure is used for adjusting cylindrical beverage cans.

Question 9

  • Independent joint PID control is robust to modeling errors.
  • End-effector force control can be implemented using only joint sensors, given good kinematic and dynamic models.

Question 10

  • Forward kinematics calculations are computationally inexpensive.
  • Jacobian calculations are moderately expensive.
  • Inverse kinematics calculations for a 4-DOF robot (less complex) are more expensive.
  • Inverse kinematics calculations for a 7-DOF robot (complex) are the most expensive.

Question 11

  • If battery level is low, the robot enters recharge mode.
  • If battery level is satisfactory, the robot continues its primary task.

Question 12

  • The AUV should be near the charger when docking.
  • If primary task takes time, the AUV could pause for charging.

Question 13

  • The number of return states for a condition is fewer than for an action.
  • For a condition node, "Failure" equates to "False".

Question 14

  • The RRT* algorithm produces a tree structure with traversable edges in both directions.

Question 15

  • The A* algorithm terminates if no valid solution exists.

Question 16

  • Each wheel of a differential drive robot is driven by a separate motor.
  • For a differential drive robot, forward motion requires opposite voltages to the motors.

Question 17

  • Multi-rotor drones excel at vertical takeoff, hovering, and high maneuverability.

Question 18

  • RGB-D is exteroceptive.
  • Accelerometer is proprioceptive.
  • Gyro is proprioceptive.
  • Radar is exteroceptive.

Question 19

  • Localization system steps are not described; the question lacks a list of matching statements.

Question 20

  • Occupancy grid memory requirements increase cubically with dimension.

Question 21

  • Kalman filter state representation uses a Gaussian distribution.

Question 22

  • Loop closures are essential in Simultaneous Localization And Mapping (SLAM).
  • Proprioceptive sensors aren't always superior for loop closure detection compared to exteroceptive sensors.

Question 23

  • Current SLAM systems can cover extended environments.

Question 24

  • Accelerometers are best for collision detection.

Question 25

  • Exploration often targets areas at the boundary of known and unknown space.
  • Occupancy grids are frequently used for exploration.

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Answers Re-exam DD2410 2022 PDF

Description

This quiz covers key concepts in robot kinematics, particularly focusing on inverse kinematics algorithms and their application to 7-DOF manipulators. Explore topics such as Denavit-Hartenberg parameters, forward kinematics, and the relationship between joint torques and end-effector acceleration. Test your understanding of how these principles are applied in robotic systems.

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