#### Reachability and Singularity

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For real robots there are a few extra things to think about. Is a particular point actually reachable? Our old friend, singularity or gimbal lock reappears in the wrist.

lesson

For real robots there are a few extra things to think about. Is a particular point actually reachable? Our old friend, singularity or gimbal lock reappears in the wrist.

lesson

A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]

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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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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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By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

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We revisit the important points from this masterclass.

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We summarise the important points from this masterclass.

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The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.

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We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.