Juniper Publishers- Journal of Robotic Engineering
Partial Pose MeasurementsDiscussionAcknowledgment
This paper offers a brief review of full and partial
pose measurements with application in robotics. Each type is presented
with its main inherent advantages and disadvantages. Typical measuring
devices, their complexity, technical properties and requirements are
also presented for both types of measurement. Differences and
similarities are discussed as well as one technique that can be used to
obtain full pose information from a set of partial pose measurement.
Keywords: Full pose measurement; Cartial pose measurement; Calibration; Trajectory tracking
Robotics related fields are inherently dependent on
various measurements. This review focuses on measurement of position and
orientation of certain points in space. Information about these points
of interest can be used for robot's positioning, calibration, trajectory
tracking, motion capture and many other applications.
In general, position and orientation of a point or a
set of points in space is determined by their coordinates in Cartesian
space. Usually, full information can be obtained from three coordinates
describing position of a point, and three more coordinates describing
its orientation [1]. Measurements that provide both position and orientation information, are called full pose measurements.
However, for some applications, it is sufficient to
measure only position of a point, which means it can be described using
only three position coordinates. Since this type of measurement does not
contain any information about orientation, it is usually referred to as
partial pose measurement.
This paper will describe advantages and disadvantages
of both types of pose measurements. Second and third sections
respectively present full and partial pose measurements, their typical
fields of application, devices used to perform them, as well as some
typical examples. Fourth section offers a brief discussion about both
types of measurements and explains a method to obtain full pose
information from partial pose measurements.
Measurements that provide both coordinates
determining position as well as those determining orientation of a point
or sets of points are called full pose measurements. Therefore, full
pose measurements are used in all applications where it is needed to
know distance to an object, as well as its posture. These applications
include assembly, welding, milling, and various other tasks that require
posture control. Robot calibration, calibration of its workspace and
other equipment in its working environment are also some of the
applications where full pose measurements are used, since most
calibration procedures require information about position and
orientation of points of interest.
Coordinates are predominantly given in Cartesian
space, and in that case positions are offsets of point from the origin
of coordinate system along its x, y and z axis directions. Rotations
around x, y and z axes are called yaw, pitch and roll, respectively, and
are commonly referred to as the Euler angles. Using Euler angles, any
orientation can be achieved using three elemental rotations i.e.
rotations about the axes of a coordinate system. Depending on whether
these rotations are performed about axes of original, stationary
coordinate system, or about rotating coordinate system which is coupled
with moving object, these rotations are called extrinsic or intrinsic.
Regardless of whether the rotations are extrinsic or intrinsic, in order
to properly interpret these angles, it is necessary to know which order
of rotations was used. There is a total of twelve possible different
sequences of rotation. Proper or classic Euler angles are for sequences
while there are also angles for sequences which are sometimes referred
to as Tait-Bryan angles.
Devices that provide full pose measurements usually
do so by following multiple points attached on a frame or a jig
resembling Cartesian coordinate frame. One point is placed in the origin
of that frame, and three more on each axis of the coordinate system. By
measuring positions of points on the frame, and knowing their location,
the orientation of the frame can be calculated. There are other types
of frames, like the one shown on Figure 1, which use known position of points to calculate orientation [2,3].
Therefore, full pose measurement is actually formed from a set of
partial pose measurements. However, since outcome of measurements of
these points is a single six coordinate vector, rather than set of
individual positions, they can be considered to be a single measurement.
The described measuring frame can be attached to an object whose
coordinates need to be measured. Devices that provide full pose
measurements can be roughly divided into two main types.
First type consists of devices that need to establish
a physical contact with their probe, or other sensing element, with the
object in order t perform measurement. One of typical representatives
is the CMM- Coordinate Measuring Machine, shown on Figure 2.
CMMs are precisely machined devices that can move in a cuboidal space,
along three mutually orthogonal axis. Precision of CMMs is usually
measured in micrometres, which is their main asset. Measuring arms are
one more representative of contact based measuring devices. These
articulated devices can be powered, or manually guided. While they tend
to be very flexible and easy to use, their accuracy is significantly
lower than those of CMMs', and it depends onarm's proper calibration and
resolution of sensors it uses. Using a precisely made jig and ballbars,
shown on Figure 3, it is possible to perform highly accurate full pose measurements [4]. However, this method is highly restrictive in terms of measuring volume.
Second type of full pose measuring devices is
contactless, as they do not require physical contact with measured
object. These devices typically use laser, light or ultrasonic beams,
which track certain points on a frame attached onto the measured object.
By using concepts of trilateration or triangulation, devices can
precisely determine position of each tracked point, and by using
information from a set of points on a frame, as shown on Figure 1, they can provide also the orientation [2,3].
Compared to contact based measuring devices, contactless measuring
devices generally have lower accuracy, which mainly depends on the
measuring volume and technology they use. Main advantage of the
contactless type of devices is that they can perform measurements while
the observed object is moving, meaning they can be used for trajectory
tracking, motion capture and similar applications.
One of the devices that use these principles are
theodolites, and they have an extraordinary ratio of measuring volume
and accuracy. Ultrasonic solutions, such as Nexonar's [5] cannot reach the accuracy of theodolite, but their volume, shown on Figure 4,
can be increased by receiving measurements from several devices
combining them in the processing unit. This makes them an interesting
and affordable solution for applications with lower accuracy
requirements. Creaform is another brand that offers contactless
measuring solutions for various fields of application, such as quality
inspection, 3D scanning, dynamic tracking etc. 3D scanning device
attached to a robot mounted CMM is shown on Figure 5 [6].
Their solutions use optical C-tracker devices based on stereo cameras
to acquire position of points mounted onto frames, measuring probes, and
scanners.
Partial pose measurements provide position
information of a point in space. For a great number of applications,
partial pose measurements are sufficient and even desirable. Main
advantages of this type of measurements, is that they are less complex
to obtain and require cheaper equipment. Since cost is an ever relevant
factor both in research and industry and production in general, partial
pose measuring devices always have a competitive advantage over full
pose measurement devices.
Although at first glance partial pose measurements
may seem incomplete, it is important to understand that most
applications in field of robotics suffice with them. Due to their
availability, a number of papers have been published [2-4,7,8], where
partial pose measurements were used. Besides calibration, robot's
positioning, trajectory tracking, TCP parameter identification all can
be achieved using only position information.
Similar to full pose measuring devices, partial pose
measuring devices can be divided into those who require physical contact
with the object, and those who not. Coordinate measuring machines can
also be used for partial pose measurements. Since they do not require
complex mechanical construction for measuring orientation, they cost
significantly less than their full pose counterparts.
As mentioned before, many of devices that provide
orientation information do so by performing multiple partial pose
measurements. Therefore, in many ways they should be considered as
partial pose measurement devices. Various ultrasonic,
laser-interferometry and stereo optics based devices output position
measurements if they track only a single point.
The intention of this article was to offer a short
overview of advantages and disadvantages of various methods for full and
partial pose measurements in fields related to robotics. Depending on
the field of use, both types of pose measuring can find their
application.
Full pose measurements are necessary for the more
complex tasks which require orientation measurement, such as
calibration, assembly, motion capture etc. Due to challenges posed by
orientation measurement, they require either more complex construction
of devices, or more complex algorithms for processing obtained data.
Although partial pose measurements provide only
position information, orientation information can be obtained by
combining multiple measurements. An interesting, yet simple, method was
proposed in [7] and with some modifications successfully used in [8].
The method is primarily applicable in field of robotic calibration. The
idea is to attach a point onto a joint of a robot, in a position that
is not located on the axis of the rotation of the joint. When joint is
rotated, the point moves in a circular path, enabling formation of a
coordinate system, and therefore full pose measurement. In [7],
line connecting center of the circle with current point position is
declared to be x axis, current point position represents the origin of a
coordinate system, vector parallel with axis of the rotation is
considered to be z axis, and finally, y axis is chosen in a way that it
forms a right-handed Cartesian coordinate system. In presented way, it
is possible to perform full pose measurements of robot's end effectors
by measuring only position of a single point located on it.
The common conclusion is that for both types of
measurement, higher precision is achieved by using devices that require
contact with the measured object. Contactless methods offer greater
measuring volume and enable applications requiring tracking and dynamic
measurement. Although their accuracy may vary, it is safe to conclude
that newer generations of contactless measuring devices offer
significant improvements in both measuring volume and accuracy.
The work on this article was partly supported by the
Ministry of education, science, and technological development, Republic
of Serbia, grant No. TR35003.
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