en>Yobot: WP:CHECKWIKI error fixes + other fixes using AWB (10065)

2014-03-28T23:25:15Z

WP:CHECKWIKI error fixes + other fixes using AWB (10065)

en>Cydebot: Robot - Moving category Trees (structure) to :Category:Trees (data structures) per CFD at Wikipedia:Categories for discussion/Log/2012 January 12.

2012-01-17T01:05:35Z

Robot - Moving category Trees (structure) to Category:Trees (data structures) per CFD at Wikipedia:Categories for discussion/Log/2012 January 12.

New page

{{Lead rewrite|date=August 2009}}

A '''virtual fixture''' is an overlay of abstract sensory information on a workspace in order to improve the [[telepresence]] of a [[telerobotics|remotely manipulated]] task.

== Concept ==
The concept of virtual fixtures was first introduced in (Rosenberg, 1993) as an overlay of
abstract sensory information on a workspace in order to improve the
[[telepresence]] in a [[telerobotics|telemanipulation]] task. The concept of abstract
sensory overlays is difficult to visualize and talk about, as a
consequence the virtual fixture metaphor was introduced. To understand
what a virtual fixture is an analogy with a real physical fixture such
as a ruler is often used. A simple task such as drawing a straight
line on a piece of paper on free-hand is a task that most humans are
unable to perform with good accuracy and high speed. However, the use
of a simple device such as a ruler allows the task to be carried out
fast and with good accuracy. The use of a ruler helps the user by
guiding the pen along the ruler reducing the tremor and mental load of
the user, thus increasing the quality of the task.

The definition of virtual fixtures in
(Rosenberg, 1993) is much broader than simply providing
guidance of the end-effector. For example, auditory virtual fixtures
are used to increase the user awareness by providing audio clues that
helps the user by providing multi modal cues for localization of the
end-effector. Rosenberg argues that the success of virtual fixtures is
not only because the user is guided by the fixture, but
that the user experiences a greater presence and better localization
in the remote workspace. However, in the context of
human-machine collaborative systems, the term
virtual fixtures is most often used to refer to a task dependent aid
that guides the user's motion along desired directions while
preventing motion in undesired directions or regions of the
workspace. This is the type of virtual fixtures that is described in this article.

Virtual fixtures can be either ''guiding virtual fixtures'' or
''forbidden regions virtual fixtures''. A forbidden regions virtual fixture could be used, for
example, in a [[teleoperation|teleoperated]] setting where the operator has to drive a
vehicle at a remote site to accomplish an objective. If there are pits
at the remote site which would be harmful for the vehicle to fall into
forbidden regions could be defined at the various pits locations, thus
preventing the operator from issuing commands that would result in the
vehicle ending up in such a pit.

[[Image:Forbidden regions virtual fixture.png|frame|center|Example of a forbidden regions virtual fixture]]

Such illegal commands could easily be sent by an operator because of,
for instance, delays in the [[teleoperation]] loop, poor [[telepresence]] or
a number of other reasons.

An example of a guiding virtual fixture could be when the vehicle must
follow a certain trajectory,

[[Image:Guiding virtual fixture.png|frame|center|Example of a guiding virtual fixture]]

The operator is then able to control the progress along the
''preferred direction'' while motion along the
''non-preferred direction'' is constrained.

With both forbidden regions and guiding virtual fixtures the
''stiffness'', or its inverse the ''compliance'', of the fixture can be adjusted. If the
compliance is high (low stiffness) the fixture is ''soft''. On the other hand
when the compliance is zero (maximum stiffness) the fixture is
''hard''.

[[Image: Soft hard virtual fixture.png|frame|center|The stiffness of a virtual fixture can be
soft or hard. A hard fixture completely constrains the motion to thefixture while a softer
fixture allows some deviations from the fixture.]]

== Virtual Fixture Control Law ==
This section describes how a control law that implements virtual
fixtures can be derived. It is assumed that the robot is a purely
kinematic device with end-effector position
<math>\mathbf{p} = \left[ x,y,z \right]</math>
and end-effector orientation <math>\mathbf{r} = \left[ r_\textrm{x}, r_\textrm{y}, r_\textrm{z} \right]</math>
expressed in the robot's base frame <math>F_\textrm{r}</math>.
The input control signal <math>\mathbf{u}</math> to the
robot is assumed to be a desired end-effector velocity
<math>\mathbf{v} = \dot{\mathbf{x}} = \left[ \dot{\mathbf{p}}, \dot{\mathbf{r}} \right]</math>.
In a tele-operated system it is often useful to
scale the input velocity from the operator, <math>\mathbf{v}_\textrm{op}</math> before
feeding it to the robot controller. If the input from the user is of
another form such as a force or position it must first be transformed
to an input velocity, by for example scaling or differentiating.

Thus the control signal <math>\mathbf{u}</math> would be computed from the
operator's input velocity <math>\mathbf{v}_\textrm{op}</math> as:
<math>\mathbf{v} = c \cdot \mathbf{v}_\textrm{op}</math>
If <math>c=1</math> there exists a one-to-one mapping between the operator and the slave robot.

If the constant <math>c</math> is replaced by a diagonal matrix <math>\mathbf{C}</math> it is
possible to adjust the compliance independently for different
dimensions of <math>\dot{\mathbf{x}}</math>. For example, setting the first three
elements on the diagonal of <math>\mathbf{C}</math> to <math>c</math> and all other elements to zero
would result in a system that only permits translational motion and not
rotation. This would be an example of a hard virtual fixture that
constrains the motion from <math>\mathbf{x} \in \mathbb{R}^6</math> to
<math>\mathbf{p} \in \mathbb{R}^3</math>. If the rest of the elements on the
diagonal were set to a small value, instead of zero, the fixture
would be soft, allowing some motion in the rotational directions.

To express more general constraints assume a time-varying matrix
<math>\mathbf{D}(t) \in \mathbb{R}^{6 \times n},~ n \in [1..6]</math>
which represents the preferred direction at time <math>t</math>. Thus if <math>n=1</math> the
preferred direction is along a curve in <math>\mathbb{R}^{6}</math>. Likewise,
<math>n=2</math> would give preferred directions that span a surface. From <math>\mathbf{D}</math> two
projection operators can be defined (Marayong ''et al.'', 2003), the
span and kernel of the column space:
<math>
\begin{align}
\textrm{Span}(\mathbf{D}) & \equiv \left[ \mathbf{D} \right] =
\mathbf{D}(\mathbf{D}^T\mathbf{D})^{-1}\mathbf{D}^T \\
\textrm{Kernel}(\mathbf{D}) & \equiv \langle \mathbf{D} \rangle = \mathbf{I} - \left[ \mathbf{D} \right]
\end{align}
</math>

If <math>\mathbf{D}</math> does not have full column rank the span can not be computed,
consequently it is better to compute the span by using the
pseudo-inverse (Marayong ''et al.'', 2003), thus in practice the span is computed as:
<math>
\textrm{Span}(\mathbf{D}) \equiv \left[ \mathbf{D} \right] = \mathbf{D}(\mathbf{D}^T\mathbf{D})^{\dagger}\mathbf{D}^T
</math>
where <math>\mathbf{D}^\dagger</math> denotes the pseudo-inverse of <math>\mathbf{D}</math>.

If the input velocity is split into two components as:
<math>\mathbf{v}_\textrm{D} \equiv \left[ \mathbf{D} \right]
\mathbf{v}_\textrm{op} \textrm{~and~} \mathbf{v}_\tau \equiv
\mathbf{v}_\textrm{op} - \mathbf{v}_\textrm{D} = \langle \mathbf{D} \rangle
\mathbf{v}_\textrm{op}
</math>
it is possible to rewrite the control law as:
<math>\mathbf{v} = c \cdot \mathbf{v}_\textrm{op} = c \left( \mathbf{v}_\textrm{D} +
\mathbf{v}_\tau \right)
</math>

Next introduce a new compliance that affects only the non-preferred
component of the velocity input and write the final control law as:
<math>
\mathbf{v} = c \left( \mathbf{v}_\textrm{D} +
c_\tau \cdot \mathbf{v}_\tau \right) =
c \left( \left[ \mathbf{D} \right] + c_\tau \langle \mathbf{D} \rangle \right)
\mathbf{v}_\textrm{op}
</math>

== References ==
* L. B. Rosenberg. ''Virtual fixtures: Perceptual tools for telerobotic manipulation'', In Proc. of the IEEE Annual Int. Symposium on Virtual Reality, pp. 76–82, 1993.
* P. Marayong, M. Li, A. M. Okamura, and G. D. Hager. ''Spatial Motion Constraints: Theory and Demonstrations for Robot Guidance Using Virtual Fixtures'', In Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 1270–1275, 2003.

{{No footnotes|date=August 2009}}

== See also ==
* [[Telepresence]]

{{DEFAULTSORT:Virtual Fixture}}
[[Category:Perception]]
[[Category:Robotic sensing]]
[[Category:Virtual reality]]
[[Category:Control theory]]
[[Category:Cybernetics]]
[[Category:Robot control]]

Tree homomorphism - Revision history

en>Yobot: WP:CHECKWIKI error fixes + other fixes using AWB (10065)

en>Cydebot: Robot - Moving category Trees (structure) to :Category:Trees (data structures) per CFD at Wikipedia:Categories for discussion/Log/2012 January 12.