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I first state my humble probably wrong opinion on the connection of these concepts: In gravity compensation mode, each joint has equilibrium as its set point, a human demonstrator can effortlessly move the robot arm to conduct a task like pick up a ball, during this process, the orientation, angular speed and acceleration of the joint is recorded, as well as the Torque (Gravity Compensation torque plus the anti-torque the human exerted). An inverse dynamic model, mapping from (orientation, angular speed, acceleration) to Torque can be built. At reproduction phase, the path is planned by a motion encoder trying to reproduce the demonstrated trajectory, then the inverse dynamics learned is used to exert torque to achieve each point in the planned path. Is the statement correct?

Question1 : If one sees a multi-joint robot (the industry robot for production line) sitting there without power input, there is mechanical constraint which will govern the relative orientation of each joint. In gravity compensation mode, it is each separate joint can rest in arbitrary position, right?

But the human demonstrator can not ensure the individual joint always in the equilibrium state, there must be some acceleration, in this case, how the extra torque from the Gravity Compensation mechanism is executed? Is there a book about gravity compensation or the mechanics analysis of Kinesthetic Teaching?

Question2: haptic control is advantageous for gripping than simply use a joystick which might break the object or not executing enough force, is there any sources explaining technical details about how that works?

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No, your statement is not entirely correct. During the teaching of the robot the trajectory in geometrical terms (positions velocities, maybe accelerations) are recorded, not torque. The trajectory is then replayed (although in many cases only some way points are recorded not in entire trajectory)

The inverse dynamics is not learned. All parameters of the robot required for a dynamic model and inverse dynamic model are available for robot manufacturers about their robot. However, they do not make these parameters public.

At the "reporoduction phase" as you call it, the inverse dynamics model does not play an important role. It is simply a geometrical path, a trajectory (velocities) is planned for the path and the motion controller executes this motion, by setting the set-point of the position controller, the feed forward signal of the velocity controller and here the inverse dynamics might be used to set the feed forward signal of the torque controller, but this only improves the jerkiness of the motion, it is not essential for obtaining movement.

Your Question 1 is not quite clear. An industrial robot, without power is held in place by many factors. First holding brakes at each joint, used to block the axis mechanically. If the breaks are released, there is still a good probability that the robot will not fall due to friction in many axes (in the gearbox) and due to a hydro pneumatic spring used in the second axis (most subjected to gravitational forces). Robots which have this hydropnenumatic spring set up to a high pressure (exerted force) can lift up instead of falling down on releasing the brakes without power to the motors.

For large industrial robots it is no customary to have a "free-joint" mode.

Haptic feedback is has multiple variants, vibration in a joystick is also a haptic feedback. I assume you refer to force feedback. I do not think force feedback is extensively used in the way you describe. Having the gripper force translate to a joystick force feedback would be beneficial if someone wants to learn to grip with a joystick, but the breaking limit is then learned by the human after many trials intuitively and is not advantageous to make a process dependent on the intuitive knowledge of on human operator. Instead, the breaking force can be determined and the grasping force can be set to a certain upper limit. This would not necessarily work for different grasping positions, but that is also true for a force feedback solution. It is not similar to how a human would feel the force while grasping something, since our fingers feel both force and slippage, such a feedback is not possible with technical systems.

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