# Quaternions and Rotations *

@inproceedings{Jia2015QuaternionsAR, title={Quaternions and Rotations *}, author={Yan-Bin Jia}, year={2015} }

Up until now we have learned that a rotation in R3 about an axis through the origin can be represented by a 3×3 orthogonal matrix with determinant 1. However, the matrix representation seems redundant because only four of its nine elements are independent. Also the geometric interpretation of such a matrix is not clear until we carry out several steps of calculation to extract the rotation axis and angle. Furthermore, to compose two rotations, we need to compute the product of the two…

## 47 Citations

### Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra

- MathematicsISPRS Int. J. Geo Inf.
- 2020

The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering and its solution was investigated for specific data using three different methods.

### An Algorithm for Quaternion–Based 3D Rotation

- Mathematics, Computer ScienceInt. J. Appl. Math. Comput. Sci.
- 2020

A new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications, and the proposed algorithm can compute the same result in only 14 real multiplier cases.

### Survey of Higher Order Rigid Body Motion Interpolation Methods for Keyframe Animation and Continuous-Time Trajectory Estimation

- Mathematics2018 International Conference on 3D Vision (3DV)
- 2018

This survey carefully analyze the characteristics of higher order rigid body motion interpolation methods to obtain a continuous trajectory from a discrete set of poses and concludes that split interpolation in R3 × SU(2) is preferable for most applications.

### On the Orientation Planning with Constrained Angular Velocity and Acceleration at Endpoints

- Computer Science2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2018

To impose the unitariness condition critically required for quaternion representation of orientation, an on-line update mechanism is developed which successively reparameterizes the polynomials constructing the spline, towards suppressing distortions that the normalization operation might incur.

### A Pose-Graph Optimization tool for MATLAB

- Computer Science
- 2018

This paper presents the development and implementation of a pose-graph optimization tool for MATLAB that consists in generating a graph from the poses of the robot and from the constraints of measurements between poses, followed by the optimization of this graph to obtain a consistent trajectory.

### Distributed Dual Quaternion Based Localization of Visual Sensor Networks

- Mathematics2019 18th European Control Conference (ECC)
- 2019

An estimation scheme that exploits the unit dual quaternion algebra to describe the sensors pose is proposed that is beneficial in the formulation of the optimization scheme allowing to solve the localization problem without designing two interlaced position and orientation estimators, thus improving the estimation error distribution over the two pose components and the overall localization performance.

### Building up an Inertial Navigation System Using Standard Mobile Devices

- Computer Science
- 2017

This paper presents the development of a PNS (Pedestrian Navigation System), which utilizes accelerometer, gyroscope and magnetometer data to enable accurate positioning and combines the most promising techniques and describes improvements.

### Inscribed Tverberg‐type partitions for orbit polytopes

- MathematicsMathematika
- 2022

Tverberg's theorem states that any set of t(r,d)=(r−1)(d+1)+1$t(r,d)=(r-1)(d+1)+1$ points in Rd$\mathbb {R}^d$ can be partitioned into r subsets whose convex hulls have non‐empty r‐fold intersection.…

### Bendable Cuboid Robot Path Planning with Collision Avoidance using Generalized Lp Norms

- MathematicsArXiv
- 2017

This work reformulated the optimal safe path planning problem for rigid and deformable cuboid robots as a two stage optimization problem, where the safety constraint depends on a point on the robot which is closest to the obstacle in the obstacle's distance metric.

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