#### Task and Configuration space

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We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

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We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

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A characteristic of inverse kinematics is that there is often more than one solution, that is, more than one set of joint angles gives exactly the same end-effector pose.

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For a redundant robot the inverse kinematics can be easily solved using a numerical approach.

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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.

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A robot joint controller is a type of feedback control system which is an old and well understood technique. We will learn how to assemble the various mechatronic components such as motors, gearboxes, sensors, electronics and embedded computing in a feedback configuration to implement a robot joint controller.

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The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.

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Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations.

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We learn how to use information from three magnetometers to determine the direction of the Earth’s north magnetic pole.