Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

380
Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
380
Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

300
In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
300
Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

441
Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...
441
Equation of Motion: Rotation About a Fixed Axis01:18

Equation of Motion: Rotation About a Fixed Axis

196
Consider a flywheel, having an uneven mass distribution, rotating steadily around a fixed axis. As this rotation occurs, the center of mass of the flywheel traces a circular path. Understanding the acceleration of this center of mass requires observing both its tangential and normal components.
The tangential component is dependent on the direction of the angular acceleration of the flywheel. The tangential component of the acceleration propels the flywheel along its path. On the other hand,...
196
Rotation of Asymmetric Top01:11

Rotation of Asymmetric Top

818
By definition, a spherically symmetric body has the same moment of inertia about any axis passing through its center of mass. This situation changes if there is no spherical symmetry. Since most rigid bodies are not spherically symmetric, these require special treatment.
The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...
818
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

337
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
337

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

RenAIssance: A Survey Into AI Text-to-Image Generation in the Era of Large Model.

IEEE transactions on pattern analysis and machine intelligence·2025
Same author

Leveraging machine learning for taxonomic classification of emerging astroviruses.

Frontiers in molecular biosciences·2024
Same author

Accuracy Differences in Cannabis Retailer Information Ascertained from Webservices and Government-Maintained State Registries Across US States Legalizing the Sale of Cannabis in 2019.

Cannabis (Albuquerque, N.M.)·2023
Same author

Population-based Long-term Outcomes for Squamous Cell Carcinoma of the Nasal Cavity.

American journal of clinical oncology·2023
Same author

Practical Design Considerations for Performance and Robustness in the Face of Uncertain Flexible Dynamics in Space Manipulators.

Frontiers in robotics and AI·2021
Same author

Impact of a Patient Support Program on Patient Beliefs About Neovascular Age-Related Macular Degeneration and Persistence to Anti-Vascular Endothelial Growth Factor Therapy.

Patient preference and adherence·2021

Related Experiment Video

Updated: May 22, 2025

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects
06:36

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects

Published on: October 18, 2024

856

Certifiably optimal rotation and pose estimation based on the Cayley map.

Timothy D Barfoot1, Connor Holmes1, Frederike Dümbgen1

  • 1Robotics Institute, University of Toronto, Toronto, ON, Canada.

The International Journal of Robotics Research
|March 17, 2025
PubMed
Summary

We developed new convex relaxations for rotation and pose estimation, guaranteeing global optimality even with noise. This method uses Semidefinite Programs (SDPs) for accurate trajectory and pose averaging.

Keywords:
Cayley mapLagrangian dualityRotation estimationpose estimationquadratically constrained quadratic programsemi-definite program

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

42.6K
A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
12:39

A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers

Published on: January 18, 2020

7.5K

Related Experiment Videos

Last Updated: May 22, 2025

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects
06:36

Author Spotlight: Insights into the Analysis of Human Interaction with 3D Virtual Objects

Published on: October 18, 2024

856
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

42.6K
A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
12:39

A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers

Published on: January 18, 2020

7.5K

Area of Science:

  • Robotics and Computer Vision
  • Optimization and Mathematical Programming

Background:

  • Existing methods for rotation and pose estimation often assume specific noise models, like the matrix von Mises-Fisher distribution.
  • Anisotropic noise in the Lie algebra is a common alternative representation for rotational uncertainty.

Purpose of the Study:

  • To introduce novel convex relaxations for rotation and pose estimation problems.
  • To provide a posteriori guarantees of global optimality for these estimation tasks.
  • To address both basic averaging and complex trajectory estimation problems.

Main Methods:

  • Formulating estimation problems based on a noise model using the Cayley map.
  • Converting these problems into Quadratically Constrained Quadratic Programs (QCQPs).
  • Relaxing QCQPs to Semidefinite Programs (SDPs) solvable by interior-point methods, leveraging Lagrangian strong duality.

Main Results:

  • Successful formulation of SDP relaxations for rotation averaging, pose averaging, and trajectory estimation.
  • Demonstration of the practical applicability and effectiveness of the proposed SDP relaxations.
  • Identification and handling of redundant constraints within the SDP formulations.

Conclusions:

  • The proposed convex relaxations offer a robust approach to rotation and pose estimation.
  • These methods provide a posteriori guarantees of global optimality under practical noise conditions.
  • The work expands the toolkit for solving complex estimation problems with guaranteed optimal solutions.