#### Second Order Dynamic Systems

lesson

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.

lesson

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 we apply a sequence of 3D rotations to an objects we see that the order in which they are applied affects the final result.

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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.

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The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

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In order to determine the size and distance of objects in the scene our brain uses a number of highly evolved tricks. Let’s look at some of these.

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When it comes to describing a blob we can do more than just area, centroid position and bounding box. By looking at second order moments we can compute an ellipse that has the same moments of inertia as the blob, and we can use its aspect ratio and orientation to describe the shape and orientation […]

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We will learn about how we make the the robot joints move to the angles or positions that are required in order to achieve the desired end-effector motion. This is the job of the robot’s joint controller and in this lecture we will learn how this works. This journey will take us in to the […]

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We will learn how to create coordinate frames that have smoothly changing position and orientation over time.

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We start by considering the effect of gravity acting on a robot arm, and how the torque exerted will disturb the position of the robot controller leading to a steady state error. Then we discuss a number of strategies to reduce this error.