#### Second Order Dynamic Systems

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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.

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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.

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Diadic operations involve two images of the same size and result in another image. For example adding, subtracting or masking images. As a realistic application we look at green screening to superimpose an object into an arbitrary image.

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

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An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

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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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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.

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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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Robots today are ubiquitous in manufacturing but they can do much, much more.

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Frequently we want a trajectory that moves smoothly through a series of points without stopping.