#### Multi-dimensional trajectory

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We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

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We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

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We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.

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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. For RTB10.x please note that the mask value must be explicitly preceded by the ‘mask’ keyword. For example: >> q = p2.ikine(T, [-1 -1], ‘mask’, [1 1 0 0 0 0])

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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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To simplify the inverse kinematics most robots have a spherical wrist, a particular mechanical wrist design. For robots where the inverse kinematics is too hard to figure out we can solve the problem numerically, treating it as an optimisation problem.

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We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.

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We repeat the process of the last section but this time consider it as an algebraic problem.

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So far we have worked out the torques on a robot’s joints based on joint position, velocity and acceleration. For simulation we want the opposite, to know its motion given the torques applied to the joints. This is called the forward dynamics problem.

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We revisit the important points from this masterclass.

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We summarise the important points from this masterclass.