Technology

> Haptic devices - force feedback
       > Does the haptic device simulate the user, or the environment?
       > Common model block diagram

> Impedance control vs. admittance control
       > Impedance control
       > Admittance control
       > Simulating added mass
       > The duality between impedance and admittance control

Haptic devices  -  force feedback

A haptic device is a small robot, designed to present to a human user the feeling of actually touching a virtual or remote world. It is, in fact a display for force sensations from a virtual or remote world, in the same way that a TV or a computer screen is a display for visual images from a virtual or remote world.

The main limitation of current haptic devices is that they present only  point-based contact, usually only in the three XYZ directions, sometimes also in rotational torques. Tactile displays which also render to the skin of the fingertips the detailed local shapes of ridges, sliding motion etc. will also become important in the future. 

Current haptic devices give such skin sensations only by the shape of the handle or end effector. End effectors may take a variety of shapes, ranging from a simple ball or pen, to real world tool handles or complete physical objects like a welding torch, fire fighting equipment or other objects to handle or move.

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Does the haptic device simulate the user, or the environment?
Haptic devices act as a display for virtual or remote worlds. The device should be able to mimic the properties of the virtual or remote  environment. The device must be able to simulate "free air", i.e. not put up resistance to motion, in a range of speeds and workspace similar to that of the human user, but the device does not simulate the user's hand. For instance, unlike the user's hand, the device should be able to simulate a hard stop, as in touching a hard object or a wall. A haptic device must have high stiffness and low (apparent) mass in order to be able to achieve this.

The haptic device is the interface between the user and the virtual world.  The device inevitably has some mass of its own, but in every other respect it should provide a "transparent" interface between the user and the virtual world. Users will feel like they are touching the virtual world with some small mass attached to their hands.

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Common model block diagram

 

 

 

 

 

The diagram above shows the basic physics in terms of Newton's law for the device's end effector mass. Both the user and the virtual environment exert forces on the end effector, and it will move accordingly. If the virtual world contains a rigid object like a wall, reaction forces from this wall will stop the end effector regardless how much the user pushes it. If the virtual world exerts no forces, the end effector will follow the forces applied by the user according to Newton's law of  "acceleration equals force divided by mass", and the user will be free to move it around accordingly.

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Impedance control vs. admittance control

There are two major ways in which a haptic device can be controlled, the so-called impedance control and admittance control paradigms. Both algorithms are discussed below.

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Impedance control
In impedance control, the paradigm is: the user moves the device, and the device will react with a force if needed. This is the basic interaction between the user and the control loop. Viewed from the control loop, the paradigm is: "displacement in - force out". 

 

 

 

 

 

 

 

 

In simulated free air, the user is free to move the device, and the motor does not not have to do anything. In control terms: the gain from changes in position to changes in motor force is zero. This will hold even if the device is in contact with a hard physical surface. There is no special stability problem there, since the object can stop the end effector without any special reaction being required of the motor.

In contact with a simulated hard surface however, there is a stability problem. Any small change in position will cause  a very high rise in motor reaction force while the device is in contact with the virtual wall. This implies a very high control gain from measured device position to motor force. For stability, control gains cannot become infinitely high. Therefore, in an impedance controller there is a limit to the "hardness" or stiffness of a virtual surface that can be rendered stably. 

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Admittance control

In admittance control, the paradigm is: the device measures the forces that the user exerts on it, and reacts with motion (acceleration, velocity, position). Viewed from the control loop, the paradigm is: "force in - displacement out". 

 

 

 

 

 

 

 

 

 

To simulate free air, the device needs to accelerate very quickly at the lightest touch. This means a very high control gain from force input to acceleration output. A very low simulated mass means a very high control gain. So, admittance controlled devices have a potential stability problem in free air, when the mass needs to be low. The same holds on a physical hard surface. A small movement of the machine will give a strong rise in contact fore from the physical surface. It is the physical environment which closes the admittance control loop with a very high gain from position to force this time, creating contact instability. On a simulated virtual surface however, a very high force will command only a very small motion. In fact,  on for an infinitely stiff simulated surface, the control gain from force to position is zero.

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Simulating added mass
Adding simulated mass to the end effector is in the same class as rendering a stiff virtual wall. It is very easy for an admittance controller,  and very difficult for an impedance controller. In an admittance controller,  increasing the virtual mass amounts to changing the control gain from force input to acceleration. There is a limit however to how far the apparent mass can be  reduced. It can be reduced by maybe a factor of 10 from that of the actual machine. But the apparent mass can be increased indefinitely to very high values. Increasing the apparent mass reduces the control gain in the direction of zero, and makes the machine only more stable. In an impedance controller, increasing the virtual mass would require a direct force response to an acceleration of the user's input. This is a simultaneous, algebraic loop and very difficult to achieve in practice.  Increasing the apparent mass of an impedance controlled device is usually only possible if the mass is added via a relatively soft virtual spring, to avoid contact stability problems between the end effector and the added virtual mass.

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The duality between impedance and admittance control
So, admittance control and impedance control are dual. What is difficult for the one is easy for the other, and vice versa, as shown in the following table:

	Impedance	Admittance
Low mass	+
Stable on physical surface	+
Low costs	+
Low friction		+
Stable on virtual surface		+
Can simulate added mass		+
Crisp master-slave control		+
Robust device		+

Admittance control is the paradigm of choice in the following cases:
- simulated contact with stiff objects.
- simulated contact with heavy objects.
- total elimination of friction.
- robust devices (stiff, strong or large machines, large workspaces).
- moving larger physical masses.
- detailed measurement of forces.

Impedance control comes into its own in the following cases :
- safe, light and passive movements.
- contacts with hard physical surfaces.
- very low simulated mass, but with some friction allowed.
- small, low-cost devices.

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