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In theory, controlling a 6D pose (3D position + 3D orientation) would require 6 joints, and - assuming the robot is carefully designed - the inverse kinematics should be solvable for that case.

Adding a 7th joint, and still targeting a 6D pose, would result in a null space of at least one dimension anywhere in the workspace. Why is this desirable?

My intuition is that it allows controlling the direction of the velocity and that the desired target changes; however, I didn't verify or investigate this so it is at most a best guess.

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Adding a 7th joint, and still targeting a 6D pose, would result in a null space of at least one dimension anywhere in the workspace.

That is basically one the reasons people may wish to use a 7-DOF Robot for a 6-DOF End-Effector. It adds what is called Kinematic Redundancy. Your robot's end effector can reach a certain pose with different joint position sets.

Have a look at the following video for example:

https://www.youtube.com/watch?v=Wm2SdIhd3hU&ab_channel=EnergidTechnologies

As you can see, even though robot moves with changing some of the joint positions, end effector is not moving. You may wish to have multiple joint positions for a single end-effector pose if you have obstacles in the environment, or there is a possibility of your robot to have a self-collision.

Sometimes in industrial environments, these robot arms have limited free-space. Even though a certain configuration can be achieved with multiple joint positions, one of them may cause robot to collide with its surroundings (another robot arms, a vehicle, and etc.).

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  • $\begingroup$ So it is mainly used to be able to avoid obstacles in the workspace? $\endgroup$ Oct 8 at 13:29
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    $\begingroup$ It might be one of the reasons, self collisions are one to look out for as well. I believe some torque related concerns can go into that as well. The lower joints may require higher torques than the ones above, since they carry them as well, which requires higher energy and therefore battery usage. So that kind of concern may go into that as well. $\endgroup$
    – kucar
    Oct 8 at 13:42
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Kinematic redundancy is certainly a good thing to avoid objects in the workplace etc., but we could simply see this as we want an extra degree of freedom for its own sake.

More fundamentally important is that 7DOF avoids gimbal lock situations. That's when some of the degrees of freedom in joint space happen to map to the same movement in object space. Because you still only have the same total number of dimensions in joint space, there's then suddenly one too few to cover all possible movements in object space. If you have one “spare” degree of freedom, this issue can be avoided – the extra DOF can jump in for the one of those that have become identical, and it gives you the choice-freedom to avoid the points where multiple joints might become locked.

Gimbal lock famously was an issue on the Apollo missions, here's a fascinating video about it:

https://www.youtube.com/watch?v=OmCzZ-D8Wdk

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Your question doesn't say if this is in an industrial setting or more general humanoid robot.

In an industrial setting, I think you can get by with as few degrees of freedom as possible. For the most part, the environment, task, and end-effector are all custom designed and singular purpose. So if you can get by with only 3 or 4 DoF then go for it. Extra DoF don't help at all and only increase manipulator cost, weight, and moving parts to fix.

However things get more interesting with more general purpose arms. When I was designing a new humanoid robot I did a study on the best arrangement of joints. It became clear that the usable workspace of the arm was not very large. More joints significantly increases the arm's workspace. This restriction was severe enough that despite having a 7 DoF arm and a holonomic mobile base, we still added a DoF to the torso of the robot.

Also note that just because an arm can reach a point in space, doesn't mean that it will be very usable there. @leftaroundabout brought up a good point about gimbal lock, and @kucar had good points about joint limits and avoiding obstacles in the workspace. But there is also manipulability. For a given end-effector pose, depending on the arm configuration, the arm may have vastly different speed and strength capabilities. More DoF give you more flexibility in choosing the best arm configuration for the job.

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