Search Results for: rotation matrix

We learn the mathematical relationship between angular velocity of a body and the time derivative of the rotation matrix describing the orientation of that body.

We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object.   In the MATLAB example starting at 3:48 I use the Quaternion class.  For Toolbox version 10 (2017) please use UnitQuaternion instead.

We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.

We learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.

The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.

We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.