#### Inverting the Jacobian Matrix

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By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

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By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

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Let’s look at how light rays reflected from an object can form an image. We use the simple geometry of a pinhole camera to describe how points in a three-dimensional scene are projected on to a two-dimensional image plane.

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We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

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We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

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As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.

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A critical part of a visual servoing system is establishing correspondence between points in the scene observed by the camera, and points in our desired image of the scene.

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Many technologies have been developed to determine the 3D-structure of the world. RGBD sensors such as the Kinect use structured light, projecting a pattern of light onto the scene and observing how it is distorted. Time of flight sensors measure the time it takes for a pulse of light to travel from the camera to […]

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For a camera moving through the environment we frequently wish to track particular world points from one frame to the next. We’ll do a quick introduction to the very large field of feature detection and matching using Harris corner features.

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Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

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A color camera has many similarities to the human eye. Instead of three types of cone cells a uniform silicon sensor uses a pattern of three color filters known as a Bayer filter.