Search Results for: conic section

What are the consequences of representing a three-dimensional scene using only two-dimensions? The appearance of parallel lines converging and circular objects being elliptical should be surprising but we take this for granted.

If your knowledge of dynamics is a bit rusty then let’s quickly revise the basics of second-order systems and the Laplace operator. Not rusty? Then go straight to the next section.

We have a quick revision of the skew-symmetric matrix. If you’re comfortable with this topic then go straight on to the next section.

We repeat the process of the last section but this time consider it as an algebraic problem.

A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]

We summarise the important points from this lecture.

A number of strategies exist to reduce the effect of these coupling torques between the joints, from introducing a gearbox between the motor and the joint, to advanced feedforward strategies.

For a redundant robot the inverse kinematics can be easily solved using a numerical approach.

Much of what we know about robots comes from fiction. Let’s look at fictional robots and the underlying reality.

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.