How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]
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We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.
We can also derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame.
For real robots such as those with 6 joints that move in 3D space the inverse kinematics is quite complex, but for many of these robots the solutions have been helpfully derived by others and published. Let’s explore the inverse kinematics of the classical Puma 560 robot.
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 […]
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.
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.