Full and Partial Pose Measurements in Robotic Applications
Zaviša Gordić1*, Kosta Jovanović2 and Veljko Potkonjak3
School of Electrical Engineering, University of Belgrade, Serbia
Submission: September 20, 2017; Published: January 16, 2018
*Corresponding author: Zaviša Gordić, School of Electrical Engineering, University of Belgrade, Serbia, Tel: +381113218318 Email: zavisa@.etf.rs
How to cite this article: Zaviša G, Kosta J, Veljko P. Full and Partial Pose Measurements in Robotic Applications. Robot Autom Eng J. 2018; 2(1): 555576. DOI: 10.19080/RAEJ.2018.02.555576
Abstract
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
Introduction
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.
Full 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
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.
Discussion
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.
Acknowledgment
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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