kindyn-doc.sgml

机器人开源项目orocos的源代码

   <para>
These represent the instantaneous velocity of a rigid body. In
geometrical terms, they are 
<ulink url="geometry-doc.html">screws</ulink>
with a physical interpretation of velocity. A correct interpretation
of a
<parameter>Twist</parameter> needs <emphasis>two</emphasis> 
<link linkend="rigid-body-reference-frame">RigidBodyReferenceFrames</link>:
the first frame is the &ldquo;moving frame&rdquo;, whose instantaneous
velocity is represented, and the second frame is the
&ldquo;fixed frame&rdquo; in which the coordinates of the motion
are expressed. 
</para>
   <para>
The two most popular representations are either six-dimensional
coordinate vectors, or four-by-four matrices. There are two
complementary <link linkend="rigid-body-coordinate-type">types</link>
of rigid body velocity, which
defer in their choice of
<link linkend="point-velocity">PointVelocity</link> vector:
<itemizedlist>

<listitem>
<para>
<emphasis role="strong">Euler</emphasis>: the PointVelocity is 
the velocity of the point that instantaneous coincides with the
<emphasis>origin</emphasis> of the &ldquo;fixed frame&rdquo;.
</para>
</listitem>

<listitem>
<para>
<emphasis role="strong">Lagrange</emphasis>: the PointVelocity is 
the velocity of the point that instantaneous coincides with the
<emphasis>origin</emphasis> of the &ldquo;moving frame&rdquo;.
</para>
</listitem>

</itemizedlist>
Both interpretations coincide if both frames coincide.
   </para>
<para>
In summary, a <parameter>Twist</parameter> object is the union
of a coordinate vector (or matrix), two reference frames, a physical
units vector, and a
<link linkend="rigid-body-coordinate-type">coordinate type</link>
indication.
   </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="rigid-body-wrench">
  <parameter> Wrench, RigidBodyForce</parameter>:
 </term>
  <listitem>
   <para>
Similar discussion as for a
<link linkend="rigid-body-twist">Twist</link>,
this time with the physical interpretation of a force acting on a
rigid body.
   </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="rigid-body-acceleration">
  <parameter>AccelerationTwist, RigidBodyAcceleration, FrameAcceleration</parameter>:
 </term>
  <listitem>
   <para>
Similar discussion as for a
<link linkend="rigid-body-twist">Twist</link>,
with a physical interpretation of an acceleration of a rigid body.
   </para>
   <para>
The Euler and Lagrange definitions for the acceleration of a rigid
body result in <emphasis>different</emphasis> accelerations: the Euler
acceleration is the result of the taking the difference of two
subsequent velocities at the <emphasis>same</emphasis> point (the
origin of the &ldquo;fixed frame&rdquo;), while the
Lagrange acceleration is the difference between the velocities at two
<emphasis>different</emphasis> points, (the points where the origin of
the &ldquo;moving frame&rdquo; happens to be at subsequent instants in
time).
</para>
<para>
Hence, in contrast to the velocity case, the Euler and Lagrange
accelerations are different (in general), even if the
&ldquo;fixed&rdquo; and &ldquo;moving&rdquo; reference frames
coincide.
   </para>
   <para>
Note also that the <parameter>RigidBodyAcceleration</parameter> in
itself is not sufficient to find the acceleration of every possible
point that moves together with the body: for this purpose, one also
need to know the <parameter>RigidBodyVelocity</parameter>.
   </para>
  </listitem>
 </varlistentry>

</variablelist>

<variablelist>
<title>Symbolic properties:</title>

 <varlistentry>
 <term>
  <anchor id="rigid-body-reference-frame">
  <parameter>RigidBodyReferenceFrame</parameter>:
 </term>
  <listitem>
   <para>
  a reference frame on the rigid body, with respect to which the
coordinate representations of the rigid body's physical properties are
to be interpreted.
   </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="rigid-body-dimension">
  <parameter>dimension</parameter>:
 </term>
  <listitem>
   <para>
  1D, 2D, 3D.
   </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="rigid-body-coordinate-type">
  <parameter>CoordinateType</parameter>:
 </term>
  <listitem>
   <para>
  Matrix, VectorAngularLinear, VectorLinearAngular,
VectorXYZFixedLinear, VectorLinearXYZFixed,
VectorXYZMovingLinear, VectorLinearXYZMoving,
VectorXYXFixedLinear, VectorLinearXYXFixed,
VectorXYXMovingLinear, VectorLinearXYXMoving,
&hellip;
   </para>
   <para>
Rigid body pose and motion properties contain, respectively, 1, 3 or 6
independent parameters, depending on whether the rigid body is 1D, 2D
or 3D. In the 1D case, the properties of a
<link linkend="point-mass">Point</link> and a
<link linkend="rigid-body-frame">RigidBody</link> (and 
<parameter>Frame</parameter>) coincide, and their
coordinate is a scalar, with a symbolic physical unit indication
attached to it. The 2D and 3D cases for rigid bodies can have a
variety of coordinate types:
<itemizedlist>

<listitem>
<para>
Matrix: the angular motion component is expressed with a 2-by-2 (2D)
or a 3-by-3 (3D) matrix; the linear component is a 2-by-1 (2D) or a
3-by-1 vector.
</para>
</listitem>

<listitem>
<para>
VectorLinearAngular: the total motion is a 3-by-1 (2D) or a 6-by-1
(3D) vector, of which the first 2 (2D) or 3 (3D) numbers represent the
linear component, and the last 1 (2D) or 3 (3D) numbers represent the
angular component.
</para>
</listitem>

<listitem>
<para>
VectorAngularLinear: as above, but with angular and linear components
interchanged.
</para>
</listitem>

<listitem>
<para>
VectorLinearXYZFixed: the first components of the numeric
representation are the linear components; the last components
represent the angular motion, expressed with
<emphasis>Euler angles</emphasis> defined by subsequent rotations
about the <parameter>X</parameter>, <parameter>Y</parameter> and
<parameter>Z</parameter> axes of a <emphasis>fixed</emphasis>
reference frame. (This convention is also often called 
<emphasis role="strong">Roll, Pitch, Yaw</emphasis>.)
</para>
<para>
There are twelve combinations of rotations about frame axes that are
physically meaningful, because subsequent rotations about twice the
same axis are not independent, and hence insufficient to represent the
three angular degrees of freedom.
</para>
<para>
Note that each of these possibilities has a
<emphasis role="strong">representational singularity</emphasis>
somwhere in its domain. A representational singularity gives problems
in inverting a mapping, and is only due to the
<emphasis>choice</emphasis> of representation, and not to a physical
singularity problem.
</para>
</listitem>

<listitem>
<para>
VectorXYZFixedLinear: same as above, but the order of linear
and angular components is interchanged.
</para>
</listitem>

<listitem>
<para>
VectorLinearXYZMoving, &hellip;: same as above, but the rotations are
about the axes of subsequent <emphasis>moving</emphasis> reference
frames.
</para>
<para>
Again, there are twelve possible alternatives.
</para>
</listitem>

</itemizedlist>
   </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="rigid-body-mass-units">
  <parameter>RigidBodyMassUnits</parameter>,
  <anchor id="rigid-body-motion-units">
  <parameter>RigidBodyMotionUnits</parameter>,
  <anchor id="rigid-body-force-units">
  <parameter>RigidBodyForceUnits</parameter>,
  <anchor id="rigid-body-impedance-units">
  <parameter>RigidBodyImpedanceUnits</parameter>:
 </term>
  <listitem>
   <para>
  gram, kilogram, meters/seconds, Newton, etc., depending on the type
of coordinate vectors or coordinate matrices.
   </para>
  </listitem>
 </varlistentry>
</variablelist>
</para>

</section>

<section id="impedance">
<title> Impedance </title>
<para>
&ldquo;Impedance&rdquo; is the collective name of all (physical or
virtual) 
<emphasis role="strong">relationships between, on the one hand, the
forces that two rigid bodies impose on each other, and, on the other
hand, their relative motion.</emphasis>. 
That is, a relationship of the following kind:
force = inertia &times; acceleration +
damping &times; velocity + stiffness &times; displacement.
</para>
<para>
<variablelist>
<title>Symbolic properties</title>
 <varlistentry>
 <term>
  <anchor id="impedance-dimension">
  <parameter>dimension</parameter>:
 </term>
  <listitem>
  <para>
  1D, 2D, 3D.
  </para>
  </listitem>
 </varlistentry>

 <varlistentry>
 <term>
  <anchor id="impedance-units">
  <parameter>units</parameter>:
 </term>
  <listitem>
  <para>
  physical units of each impedance element.
  </para>
  </listitem>
 </varlistentry>

</variablelist>

<variablelist>
<title>Physical properties</title>
 <varlistentry>
 <term><parameter></parameter></term>
  <listitem>
   <para>
   add, scale
   </para>
  </listitem>
 </varlistentry>
</variablelist>
<variablelist>

<title>Numeric coordinate representation:</title>
 <varlistentry>
 <term>
  <anchor id="impedance-coordinates">
  <parameter>Damping</parameter>,
  <parameter>InverseDamping</parameter>,
  <parameter>Stiffness</parameter>,
  <parameter>Compliance</parameter>.
  <parameter>Inertia</parameter>,
  <parameter>InverseInertia</parameter>,
  <parameter>Mobility</parameter> (which is a synonym for
<parameter>InverseInertia</parameter>):
 </term>
  <listitem>
   <para>
   floating point numbers, representing the impedance elements,
   with a number of values that is consistent with the 
   dimension and the
   <link linkend="impedance-units">physical units</link>.
   </para>
  </listitem>
 </varlistentry>
</variablelist>
</para>

</section>

</section>


<section id="kinematic-chain-interface">
<title>
 Kinematic chains
</title>
<para>
This Section describes programming interfaces that are common to all
kinematic chains (such as robots and machine tools). The interfaces
represent the
<emphasis role="strong">transformation relationships</emphasis>
between the properties of the chain's joints and the properties of the
chain's &ldquo;externally visible&rdquo; Ports. These Ports are most
often the &ldquo;Tool Centre Point&rdquo; or
&ldquo;End-Effector&rdquo;
reference frames of the kinematic chain, i.e., those parts of the
chain that the designers destined to be used to interact with the
environment, with tools, or with other kinematic chains. 
A kinematic chain can have more than one of these reference
frames.
</para>
<para>
The motion properties of the Ports as &ldquo;rigid bodies&rdquo; or
&ldquo;reference frames&rdquo; are called the
<emphasis role="strong">Cartesian</emphasis> properties of the
kinematic chain the Ports belong to; those related to the joint forces
and motions are <emphasis role="strong">joint space</emphasis>
properties. The interface described in this Section works with
any <link linkend="architectures">kinematic family</link>. They
are independent of the dimensions of both the Cartesian work space and
the joint configuration space; and of the choices of mathematical
representations or physical units. 
</para>
<para>
<ulink url="motion-api.html">Another document</ulink>
describes the <emphasis>Cartesian</emphasis> interface of a kinematic
chain, <emphasis>i.e.</emphasis> the motion properties of the
above-mentioned externally visible Ports, (mostly) irrespective of the
structure of the chain that drives the Ports. The Cartesian motion
interface is the same as the motion properties of one single rigid
body. 
</para>


<section id="kinematic-chain-connectivity">
<title>Kinematic chain connectivity</title>

<para>
An object of the <parameter>KinematicChain</parameter> type contains
as sub-classes many of the classes described in the previous sections:
rigid bodies, reference frames, joints, motors, transmissions,
impedances, etc. The specific contents of a
<parameter>KinematicChain</parameter> object 
<emphasis role="strong">depends on the application context</emphasis>;
in other words, it is not useful to define <emphasis>the</emphasis>
content of the  <parameter>KinematicChain</parameter> class.
There will be such a class for every application, and hence, each of
these <parameter>KinematicChain</parameter> classes should carry a
&ldquo;namespace&rdquo; indication of that particular application.
<xref linkend="architectures"> gives examples of such particular
kinematic chains.
</para>
<para>
One important information that an object of the
<parameter>KinematicChain</parameter> class must contain (and which is
not further discussed in this document, but in 
<ulink url="general-dynamics-doc.html">another document</ulink>)
is the <emphasis role="strong">connectivity</emphasis> within the chain;
i.e., how are the links in the chain constrained with respect to each
other, through kinematic and/or dynamic constraints. 
This document makes use of the
<ulink url="decoupling.html">Object-Port-Connector</ulink>
pattern, to encode this <emphasis>connectivity</emphasis> information of
<emphasis>general</emphasis> kinematic chains. (For families with
efficient kinematic <link
linkend="architectures">architectures</link>, the connectivity
information is trivially encoded in the sequence of joint values in
the joint coordinate vectors.)
For example, in the case of an ideal revolute joint that constrains
the relative motion of two connected rigid bodies, the
&ldquo;Port&rdquo; on each of the connected bodies contains the
symbolic information about the fact that this constraint is a revolute
joint, the physical units of the relative motion parameters, and the
numerical coordinates of the joint axis with respect to the 
rigid body of the link. The connector
contains the numerical information about the instantaneous relative
motion, i.e., position, velocity, torque, etc.

<figure id="fig-opc-link-joint" float="1" pgwide="0">
<title>
 The Object-Port-Connector pattern applied to a simple kinematic chain.
</title>
<mediaobject>
<imageobject>
<imagedata fileref="../pictures/opc-link-joint.png" format="PNG">
</imageobject>
<imageobject>