#### 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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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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The workspace of a robot arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm.

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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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Let’s recap the important points from the topics we have covered about light, wavelength, spectrums, light sources, reflection, reflectance functions, cone cells, tristimulus and chromaticity space.

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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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As the illumination level changes so do the red, green and blue tristimulus values, but they are linearly related. We can separate brightness from chromaticity which is a two dimensional representation of color. We discuss briefly the effect of gamma encoding on the color reproduction process.

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A robot manipulator may have any number of joints. We look at how the shape of the Jacobian matrix changes depending on the number of joints of the robot.

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To move a robot smoothly from one pose to another we need smooth and coordinated motion of all the joints. The simplest approach is called joint interpolated motion but it has some limitations.