In robotics, vision and graphics, rotation matrix is one of the most popular mathematical representations of the rotational motion. It is simple but sometimes may cause confusions. In this post, I will construct a rotation matrix from stratch and talk about its key properties. For brevity, all vectors are column vectors and all coordinate frames are right-handed unless otherwise stated.

My work “Estimating 3D Motion and Forces of Person-Object Interactions From Monocular Video” was shortlisted among the best paper finalists at the Conference on Computer Vision and Pattern Recognition 2019 (CVPR 2019) that took place in Long Beach (CA, USA) in summer.

The paper introduces a new approach for automatic reconstruction of 3D motion and actuation forces of a person interacting with an object from a single RGB video. The objective is to enable robots to learn how to manipulate tools by watching instructional videos that are available at, for example, Youtube. The approach was developed in collaboration with researchers from LAAS-CNRS in Toulouse.

The project Webpage is available online.

The following Python function converts a 3 x nf matrix, axisAngles, whose columns are axis-angles, to a 4 x nf matrix of quaternions under the (x,y,z,w) convention. Note that the quaternions should always have norm 1.