#### Analyzing a 2-joint planar robot arm

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We consider a robot, which has two rotary joints and an arm.

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We consider a robot, which has two rotary joints and an arm.

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

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Time varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.

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Let’s learn how to import a color image into MATLAB and see how the data is organized as a matrix with three dimensions.

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Once a digital image exists as a matrix in the MATLAB workspace we can manipulate it to extract information that a robot could use. We will discuss some fundamental algorithms that operate on single images.

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When a camera moves in the world, points in the image move in a very specific way. The image plane or pixel velocity is a function of the camera’s motion and the position of the points in the world. This is known as optical flow. Let’s explore the link between camera and image motion.

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We describe the velocity coupling terms of the robot as a matrix which represents how the torque on one joint depends on the velocity of other joints.

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We describe inertia of the robot as a matrix which represents how inertia of a joint depends on the position of all the joints, and how the torque on one joint depends on the acceleration of other joints.

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We can factorise the joint torque expression into an elegant matrix equation with terms that describe the effects of inertia, Coriolis and centripetal and gravity effects.

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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.