JMEA Volume 8 Number 2 February 2018 Ser
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Volume 8, Number 2, February 2018 (Serial Number 71)
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DAV ID P UBL ISH IN G
Jour na l of M e cha nic s Engine e ring a nd Aut om at ion
Volume 8, Number 2, February 2018 (Serial Number 71)
Contents
Techniques and Methods
43 Review of Metal AM Simulation Validation Techniques
Aaron Flood and Frank Liou
53 A Brief Tour on Exotic Control Objectives in Robotics
Rafael Kelly and Carmen Monroy
60 Optimizing Hot Forging Process Parameters of Hollow Parts Using Tubular and Cylindrical Workpiece: Numerical Analysis and Experimental Validation
Angela Selau Marques, Luana De Lucca de Costa, Rafael Luciano Dalcin, Alberto Moreira Guerreiro Brito, Lirio Schaeffer and Alexandre da Silva Rocha
Investigation and Analysis
71 Definition of Stationarity Based on Monitoring the Uncertainty at Real Measurement Conditions
Alois Heiss and Woelfel Engineering Group
82 Strengthening Effects of Niobium on High Strength Rebars
Zhang Yongqing, Guo Aimin and Yong Qilong
92 Estimating Emotion for Each Personality by Analyzing BVP
Emi Takemoto, Yusuke Kajiwara and Hiromitsu Shimakawa
Journal of Mechanics Engineering and Automation 8 (2018) 43-52
doi: 10.17265/2159-5275/2018.02.001 DAVID PUBLISHING
Review of Metal AM Simulation Validation Techniques
Aaron Flood and Frank Liou Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla 65409, USA
Abstract: Due to the complexity of metal AM (additive manufacturing), it can require many trial runs to obtain processing parameters which produce a quality build. Because of this trial and error process, the drive for simulations of AM has grown significantly. A simulation only becomes useful to researchers if it can be shown that it is a true representation of the physical process being simulated. Each process being simulated has a different method of validation to show it is an accurate representation of the process. This paper explores the various methodologies for validation of laser-based metal AM simulations, focusing mainly on the modeling of the thermal processes and other characteristics derived from the thermal history. It will identify and explain the various validation techniques used, specifically looking at the frequency of reported use of each technique.
Key words: AM simulation, simulation validation, heat transfer modeling, stress modeling, micro-structure modeling.
1. Introduction To validate the stresses which are induced on the part, qualitative and quantitative approaches have been
AM (additive manufacturing) is a complex process utilized. To qualitatively validate the results, some and many have attempted to generalize the process have looked for the generation of cracks and compared using mathematical models. In order to show the these results to a simulation. This validation can give a validity of each model, researchers have developed gross comparison of the simulation and experiments. A methods to compare the results from these simulations simple method of gathering a quantitative comparison to experiments which can be performed. Each aspect of is to measure the distortion of the final part. This can the AM process which is being simulated will have a either be done using a laser displacement sensor, in situ, different technique for validation. The main or a 3-D scanner after the deposition is complete. These phenomena of AM which have been studied are heat results, though more precise than crack generation, are transfer, induced stress, and microstructure. For each of not extremely precise. To precisely measure the strain, these phenomena, the various validation techniques it is necessary to gather a diffraction pattern, either with which have been used in literature will be investigated X-rays or neutrons, for the part. This allows for the including a brief description of the technique precise locations of the atoms to be known which gives fundamentals. the exact values for the strain in the part. There are two main methods of validation for the Due to the drive for AM from the aerospace industry, modeling of the thermal history, instrumental and many researchers are focusing on Ti-64 (Ti-6Al-4V) as indirect. The instrumental methods utilize a hardware their material of choice. Therefore that will be the focus setup to directly measure the temperature of the of the microstructure section of this paper. Even though process at a specific location. Whereas the indirect the focus is Ti-64, all the methods which are presented methods compare a different physical characteristic, can be generalized to any metal. The first method of such as melt pool depth, which is linked to the comparison is to compare the phase which occurs, temperature, this is then used to validate the usually on a pixel by pixel basis or a voxel by voxel temperature profile. basis for 3-D. This will give a general comparison and
limited quantitative comparison of the experiment and Corresponding author: Aaron Flood, PhD candidate,
research field: metal additive manufacturing simulation. simulation. If a more detailed comparison is desired,
44 Review of Metal AM Simulation Validation Techniques
then in addition to the phase the grain sizes can be
Table 1 Breakdown of validation techniques.
compared. This comparison is usually made by
Physical char. validated comparing the size distribution of the phases.
Instrument validated
IR/CCD camera
[7-10]
Melt pool depth [11-13] Pyrometer [14, 15]
2. Heat Transfer Validation Techniques
Thermal couple
[15-17]
The most fundamental, and first developed, process These papers show that more attempts have been in AM which has been modeled is the flow of heat
made to validate the models using instrumental through the part. This problem was first tackled by
validation as opposed to using another physical researchers focusing on simulating the welding process,
characteristic. This is most likely due to the direct link and much can be derived from their work. A very
between the measured value and the simulated value. extensive review was done by Mackwood and Crafer [1]
When using another physical characteristic, it is from which key elements can be utilized. The first
necessary to know the exact linkage between the trait numerical solutions which can be applied to the
being measured and the one being simulated. For this problem of AM, by Mazumder and Steen [2], created a
reason, there are more opportunities for error and false 3-D finite difference model to simulate a Gaussian
validation, or rejection, of a given model. From the laser on a semi-infinite workpiece. Their model did not
literature reviewed, there are three prominent include temperature dependent material properties,
instruments which have been used to validate the which was later remedied by Chande and Mazumder
models.
[3]. This later iteration also accounted for latent heat of The most common instrument used is an IR or CCD phase change which has recently proven to be an
camera, these cameras are appealing based on several important aspect of AM simulations. The last features. The first key feature is that this is a simulations developed, which are the most applicable
non-contact measurement, this means that it is to AM, are for multi-pass welding by Reed and
applicable to every form of metal AM to date. Cameras Bhadeshia [4], Lindgreen et al. [5], and Frewin and
are also capable of capturing data at a high frame rate, Scott [6]. In these models, the laser is passed over the
Hu and Kovacevic [7] report frame rates as high as 800 same area multiple time to determine the heat flow due
frames/sec. Coupled with this frame rate is the to the multiple passes. These simulations were the first
camera’s resolution, which Kolossov et al. [8] report time that “quiet” elements were utilized. These
using a camera of 256 × 256 pixels where each pixel is elements are considered inactive until the part has been
0.1 × 0.1 mm. A final key feature is its ability to be built up to their location. At that time, they are
used in-situ, which can allow for it to be used as activated and are included in the simulation. This
feedback control if a closed loop system is used. These model has been the foundation that most AM
capabilities allow researchers to quickly and accurately simulations have been built upon.
assess the surface temperature of a build. This method In order to validate these models, thus far in the
of measuring temperature is not without its faults. The literature, there have been two approaches. The first is
first, according to Wegner and Witt [18], is that these to validate the thermal model with an instrument
cameras are very sensitive to the angle and the distance equipped to measure temperature. If this has not been
they are placed from the object begin measured. done, then the researchers will measure another
Additionally, according to Fischer et al. [19], these physical characteristic of the build and use that to show
cameras measure the average temperature of the skin of the model’s validity. A representative set of papers
the object during the time elapsed for 1 frame. This have been presented in Table 1.
problem does not apply to CW lasers, however, when
Review of Metal AM Simulation Validation Techniques
using a pulsed laser, the skin temperature can spike very profile, several thermocouples need to be placed on the rapidly which can result in inaccurate measurements.
working surface. Another downfall with thermocouples is their inability to measure the melt
pool temperature. Since they need to be fixed to the surface, if an attempt is made to measure the melt pool
they will become detached from the substrate and the
1 data will be invalid. For these reasons, current The next instrument most commonly used is a
researchers have only used thermocouples as a pyrometer, which is a non-contact spot measurement
secondary validation technique and utilize another which can be used in-situ. This results in the ability to
technique for the main source of data. measure the average temperature of a specific area.
Besides these direct methods of validating the This is not as useful as cameras previously presented
thermal modeling, some researchers have taken the due to the lack of resolution. However, because of their
approach of measuring a more easily attained data set simplicity, it is possible to create a mathematical model
and compared that to the simulation, namely the melt to predict the pyrometer output. This can be done by
pool size and the shape of the build. In this method a knowing the power of the thermal radiation which
simple surface laser heating simulation and experiment returns to the pyrometers and is shown in Eq. (1) [20],
are performed, where the laser is simply used to melt a where I( λ, T), is the spectral distribution of the
track on the surface of the substrate. In the experiments, blackbody emissive power given Planck’s radiation law.
a slice is taken perpendicular to the laser path which is It is possible to then integrate Eq. (1), assuming that the
then analyzed, typically with an optical microscope. laser is a Gaussian heat source and that the pyrometer is
This allows for the width and depth of the melted sampling a 1 mm radius, it is possible to solve for the
region to be measured, as seen on the left image in Fig. effective temperature that the pyrometer reads, Eq. (2),
1. In the simulation, since the temperature is tracked for where h is Planck’s constant, c is the speed of light, λ is
each element, it is possible to flag elements which have the wavelength of the emitted radiation, σ is
melted, this is done in the right image in Fig. 1 by Stefan-Boltzmann constant, n is the number of small
changing their color to red. In addition to the use of the sampling areas within the pyrometer viewing area, and
surface laser heating, some have simulated a single T i is surface temperature within the small n areas.
track build, which can be seen in Fig. 2. This has allowed for Dia et al. [14] to create a
simulation which includes a pyrometer to control the laser power. This simulation can predict the changes that the pyrometer will make to the laser power, for a closed loop system, to keep a constant melt pool size.
Fig. 1 Validation of thermal analysis by comparing melt pool
The last method found in the literature to measure
dimensions of experiment (left) and simulation (right) [12].
the temperature directly utilizes thermocouples, which are contact spot measurements. The fact that they must
be fixed, welded in most cases, to the surface makes them impractical for some applications, such as powder bed process. In addition, they will only record the
Fig. 2 Validation of thermal analysis by comparing single
average temperature of a specific location. Therefore,
track build dimensions of experiment (left) and simulation
to obtain an accurate representation of the temperature
(right) [13].
46 Review of Metal AM Simulation Validation Techniques
Table 2 Applicability of validation techniques to basic AM
location of interest on the part. This stress is
processes.
compressive since the volume under the heat source is Powder bed DED expanding. This compressive stress is elastically IR/CCD camera
Pyrometer X X compensated for by the material until the compressive Thermal couple
X yield stress limit is surpassed. When the compressive Melt pool depth
X X yield limit is surpassed, stage B takes place. In this
stage, plastic flow of material occurs and the techniques to basic AM processes .
Table 3 Highest accuracy reported of validation
compressive stress is reduced. Stage C has begun when Response Time Resolution the material begins to cool which results in tensile
stress. These stresses are caused by the contraction of Pyrometer
IR/CCD camera 800 fps [7]
10.9 um 2 [8]
the surrounding material. They remain elastic until the Thermal couple
3 mm 2 [14]
0.2 mm 2 [15]
tensile yield stress is surpassed. The final stage of *Values not reported are left blank.
stress is stage D, which occurs when the tensile yield This indirect method of validation can typically be
limit is surpassed and plastic flow begins. These done without specialty equipment. However, this
stresses can all be derived from the thermal history of a method of validation introduces new complications
specific location and its neighbors. Due to the difficulty which can hide, or skew, the results. Since the material
of measuring the stress, only a few methods have been is melted, the flow of the molten material dictates the
used throughout literature as displayed in Table 4. shape of the melt pool. For that reason, this validation
One of the simplest, though not accurate method, is technique requires that both the thermal and fluid
to observe the creation of cracks within the part and models are correct. Therefore, the direct methods are
compare that to simulation results. This method, used simpler to implement than the indirect methods.
by Zhu et al. [9], is simple and can be done without any In general, these methods all have different specialty equipment. This method, however, due to its
applicability to the various metal AM processes. As lack of precision, can only be used to qualitatively can be seen in Table 2, all the methods of validation are
verify that a simulation is giving results which applicable to DED (directed energy deposition) metal
generally agree with the experiment. This method AM. When working with a powder bed process, on the
cannot be used to quantitatively validate a contrary, it is impossible to use a thermocouple as
mathematical model.
previously stated. For this method of metal AM, it is If a more refined approach is needed Liu et al. [22] necessary to use one of the non-contact methods. When
have looked at build plate deformation as a link looking at the accuracy of the methods, displayed in
between the simulation and the experiment. Thus far in Table 3, the camera system will usually have the
the literature, this has been implemented by using a highest resolution and response time, but will also be
laser displacement sensor or a 3-D scanner to measure the most expensive. Therefore, it is necessary to
the distortion which occurs in the final part. To use a balance the cost and the accuracy needed.
laser displacement sensor, as shown in Fig. 3, one edge
3. Stress Validation Techniques
Table 4 Frequency of stress analysis techniques.
[9, 23] Inherent in AM processes, is a cyclic heating which
Presence of cracks
[17, 22, 24] leads to stresses being induced. The stressing process
Final part distortion
[25, 26] has been divided into four stages by Ding et al. [21].
DIC (digital image correlation)
[16, 21] Stage A occurs when the heat source approaches the
Neutron diffraction
X-ray diffraction
Review of Metal AM Simulation Validation Techniques
Fig. 3 Experimental setup using laser displacement sensor to measure distortion [23].
of the build plate is clamped creating a cantilever, and the sensor is used to monitor the free end. This edge of the build plate is monitored in real time to determine the fluctuations that occur during the build. These fluctuations are then correlated to the distortions which are seen in the simulation. When done correctly, the stress which occurs in the part can be correlated to the simulation to show the accuracy of the simulation. This method, in addition to measuring the stresses as they occur, has the added capability to measure the residual stresses which build up throughout the entire process. One problem with this setup is that the depositions location on the substrate is critical for accurate results. This is simple in the simulation, however, in the experimental setup, this can prove challenging. The other method of measuring the induced stresses is to build the part and upon removal from the machine, to use a 3-D scanner to measure distortions. This will give the final dimensions of the part and a more complete picture can be gained using this approach.
Each of these approaches has its advantages. If a full picture of the part is needed, then a 3-D scanner should
be utilized. This is because the scanner inspects the whole part, or at least a larger section of the part, compared to the laser displacement sensor which only monitors a single point.
However, if more accurate results are needed, then a laser displacement sensor should be used. The laser sensor used by Heigel et al. [17] reports an accuracy of ±1 µm, whereas the 3-D scanner used by Denlinger et al. [24] reported an accuracy of ±500 µm.
Another method of obtaining the distortion, or the surface stresses induced, of the part is DIC. The process of DIC uses a camera to observe the part and sense any motion which is induced on the part. Pan et al. [29] describe how this method tracks points which are placed on the part to determine their relative motion to calculate the stresses and distortion a part endures. An example of how the points move can be seen in Fig. 4. This method will inherently give the distortion of the part. However, Wu et al. [25] showed that it is possible to precisely determine the surface level stresses which are induced on the part. This is done by selectively stress relieving the part through sectioning, hole drilling, or slitting. These methods allow for the distortion that occurs to be related back to the stress which the part is experiencing. The main drawback to this method of validation is that it is a destructive method. However, one of the main advantages of this method is that the resolution is limited by the camera which is being used. The motion of the material is measured in pixels on the camera. That results in the ability to have a fine resolution if a high-resolution camera is used. The resolution of the camera can also
be supplemented by attaching the camera to a microscope. This technique can greatly increase the detail which can be observed with the DIC method.
Validation of the simulation with extreme precision requires the exact stress, or strain, values from the experimental work. This is done, according to Fitzpatrick et al. [30], using Bragg’s law and the scattering of either X-rays or neutrons. To obtain the spacing, the part is placed in the apparatus and the diffraction patterns are recorded from various angles. This allows for a baseline pattern set which gives the starting spacing for all the atoms. The part is then put through the thermal process being investigated which
48 Review of Metal AM Simulation Validation Techniques
Fig. 4 Schematic showing displacement of tracking points in DIC [29].
will move the atoms. The difference in the diffraction models to determine the microstructure of an AM patterns directly correlates to the distance that the
build.
atoms shifted. This motion of atoms is known as the To understand the modeling of the microstructure of strain which can then be converted to stress using
Ti-64, it is necessary to study the microstructures that Hooke’s law.
can occur. Ti-64, according to Kelly [31], has a This method of determining the stress locally allows
microstructure which is a combination of a BCC for a direct correlation between the experiment and
(body-centered cubic), which is denoted as a β phase, simulation. The choice of neutron or X-ray is based
and an HCP (hexagonally closed packet), which is mainly on availability to the researchers. The use of
denoted as an α phase. These phases will coexist within XRD (X-ray diffraction) is much more widely
the Ti-64 part and the quantities and sizes will depend available to researchers and therefore generally a more
on the maximum temperature and cooling rate at a cost-effective method, whereas the use of neutrons is
specific location. At room temperature, the typical only done in specific facilities. One of the downfalls of
micro-structure is α + β. If the material’s temperature is these strain measurements is their inability to be used
raised higher than the beta transus temperature the in-situ. Therefore the measurements are only of the
material will transition into pure beta phase. As the final stresses. In addition to the localized strain, Ding et
material cools, the alpha phase will reappear and the al. [16] have used the aforementioned 3-D scanners to
cooling rate will dictate which alpha phases occur. This further verify the simulations results.
is shown graphically in Fig. 5. If the cooling rate is fast then the resulting alpha phase will be Martensitic ( α 0 )
or Massive ( α m ). These phases will appear Due to its many desirable characteristics, namely its
4. Microstructure Validation Techniques
intra-granularly and on the grain boundaries high strength to weight ratio and corrosion resistance,
respectively. On the contrary, if the cooling rate is slow Ti-64 has been the focus of many researchers and
then the resulting micro-structure will start with leaders in industry. Because of this previous body of
Allotriomorphic ( α GB ) on the grain boundaries knowledge, this section will focus on Ti-64. However,
followed by primary-alpha ( α P ), which is simply any these techniques can be applied to most metals. In
alpha phase that appears from cooling above the beta many metals, and in particular Ti-64, the transus temperature, which is shown in the BSE microstructure is critical to obtain optimal strength.
(back-scattered electron) graph in Fig. 6. Lastly, when Because of this, many researchers have developed
the material containing α P + β is heated, but not past the
Review of Metal AM Simulation Validation Techniques
beta transus temperature, some of the α P will convert to from the layer by layer manufacturing strategy. Based β. When this material then cools, the new phase created
on this understanding of the micro-structure evolution is called secondary-alpha ( α S ). This secondary phase
there are a few methods of quantifying, and therefore becomes critical in AM due to the constant reheating
validating, a simulation which are outlined in Table 5.
Fig. 5 Phase transformations which occur in Ti-64 [31].
Fig. 6 Phases of Ti-64 [31].
50 Review of Metal AM Simulation Validation Techniques
Table 5 Frequency of micro-structure analysis techniques.
Another method of validating the micro-structure is by Element Wise Comparison
comparing the size distribution of the alpha phase, Phase Volume Comparison
which was done by Charles [35]. To compare the size Grain Size Distribution
distribution of the alpha phase, the average width of the In the first simulation method, by Kelly et al. [32],
alpha phases can be calculated and this can be used to the elements are only allowed to be one of the various
compare the simulation to the experimental data. In phases. Based on the elements thermal history, it is
order to be more rigorous Katzarov et al. [33] created a denoted as either beta or one of the alpha phases. This
histogram of the sizes of the alpha phase in addition to allows for a very general comparison with the use of the volume percent of the phases. All in all, if experimental results. When a thin wall is built, it can be
a more detailed and rigorous validation technique is sliced perpendicular to the laser scanning direction.
used the simulation can be more trusted. This slice can then be observed with the SEM (scanning electron microscope). These images will
then produce distinct regions, as shown in Fig. 7, of each phase which can be compared to simulations.
This simplified method is a fundamental start but is very lacking. Metallurgy has shown that the grain size, morphology, and distribution of fine particles are just as important to the mechanical properties as the phase itself. Therefore, Murgau et al. [34] have attempted to model the grain size along with the phase. The simplest of these validations use the volume percent of each of the phases. To ensure that their solution is robust, several cooling rates were modeled and compared to experimental results. When several cooling rates simulated matched experimental results, the simulation
Fig. 7 Phase layers of Ti-64 produced via thin wall
was considered correct, which is illustrated in Fig. 8.
deposition [32].
Fig. 8 Volume fraction of alpha phase comparison [34].
Review of Metal AM Simulation Validation Techniques
Review.” Optics & Laser Technology 37: 99-115. [2] Mazumder, J., and Steen, W. 1980. “Heat Transfer Model This paper presents the main validation techniques
5. Conclusions
for CW Laser Material Processing.” Journal of Applied in literature for the validation of thermal modeling of Physics
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[4] Reed, R., and Bhadeshia, H. 1994. “A Simple-Model for direct means include the use of cameras, pyrometers,
Multi-pass Steel Welds.” Acta Metall Mater 42: 3663-78. [5] Lindgren, L., Runnemalm, H., and Nasstrom, M. 1999.
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This method relies heavily on the fluid model being [7] Hu, D., and Kovacevic, R. 2003. “Sensing, Modeling and
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International Journal of Machine Tools and Manufacture method of measuring the heat flow.
43: 51-60. [8] Kolossov, S., Boillat, E., Glardon, R., Fischer, P., and
Closely linked to the thermal history are the stresses Locher, M. 2004. “3D FE Simulation for Temperature
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International Journal of Machine Tools and Manufacture of cracks. This is only a rough correlation and to be
44: 117-23.
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build, can be analyzed, along with distortions which Laser Direct Metal Deposition.” The International Journal occur after selective sectioning to reveal the induced
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[11] Contuzzi, N., Campanelli, S. L., and Ludovico, A. D. 2011. validation of this simulation can take a crude form of “3D Finite Element Analysis in the Selective Laser Melting Process.” International Journal of Simulation
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“A Three Dimensional Transient Model for Heat Transfer and sometimes an overlooked step. The selection of a
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Journal of Mechanics Engineering and Automation 8 (2018) 53-59
doi: 10.17265/2159-5275/2018.02.002 DAVID PUBLISHING
A Brief Tour on Exotic Control Objectives in Robotics
Rafael Kelly 1 and Carmen Monroy 2
1. DET-DFA, Division de Fisica Aplicada, CICESE, Carretera Ensenada-Tijuana No. 3918, Zona Playitas, Ensenada, B.C., 22860, Mexico 2. ISEP–Sistema Educativo Estatal, Zona 01, Ensenada, B.C., 22800, Mexico
Abstract: Formulation of control objectives is a key issue in automatic control systems design. Although at first sight the desired goal (control objective) of a control system seems to be a trivial and obvious matter, for effectiveness of some high level robotic tasks, unusual exotic control objectives may be required. This paper presents a review of some exotic control objectives useful in robotics, such as velocity field control objective and range control objective. The paper also proposes a novel confinement control objective. The
usefulness of these exotic control objectives may appear in safe robot-human interaction and self-protection of robots against collisions.
Keywords: Control objective, robot, robot-human, confinement, range, velocity field, TEFDA (total energy function with damping assignment), exotic.
1. Introduction to Elements of Automatic
powerful high task-level control system is still open in Control of Robots robotics sheltered under the so-called in this paper as
exotic control objectives. This paper is an enhanced Robots as a kind of amazing autonomous machines version of an early one presented in Ref. [4]. are equipped with digital computer implemented This paper adopts the following definition of robot. automatic control system (the “robots brain”). So, the
Definition 1—Robot
effectiveness, applicability and accuracy of robots depend strongly on features of the underlying control
“A robot is a reprogrammable, multifunctional, system.
and autonomous amazing animate machine”. It is recognized that many standard robot manipulator
♦ Remark 1: This definition 1 includes both mobile
positioning/handling, painting, and pick-and-place can robots as well as robot manipulators.
be well accomplished by standard well-established Remark 2: Although some engineers use the word
control systems such as PID control or compute-torque “autonomous” to refer robots where the computational
control [1-3]. Notwithstanding, some other new and hardware is close—on board—to them, in this paper more challenging robotic tasks such as safe the word “autonomous” is more related to a decision robot-human
interaction,
multi-robot
making meaning: without neither human intervention cooperation/competition, robot self-protection against
nor human assistance during motion or during task auto-collisions, tasks under multi-sensor fusion, and
execution. Thus, machines under remote control/handling robot tasks under embedded dynamic and unstructured
via wireless or umbilical cable communication by a environments are unable to be done by using such
human operator such as drones, telemanipulators, or standard textbook control systems, hence this paper ROVs (remotely operated underwater vehicles), are not claims that a broad spectrum for innovation in novel
really robots. Exoskeletons and prosthesis are not
Corresponding author: Rafael Kelly, Ph.D., professor, either considered robots because they are “on-board”
research fields: automatic control, robotics,
human-pilot-operated.
54 A Brief Tour on Exotic Control Objectives in Robotics
(2) Plant output 𝑦𝑦 of all sensors; (3) Plant variable to be controlled 𝑧𝑧. Typically,
controlled variable is also a measured one, so 𝑦𝑦 = 𝑧𝑧; (4) Environmental disturbances 𝜔𝜔. Disturbances can be seen as no manipulable/controlled inputs. However, in some cases they may be measured.
1.2 Plant In this paper a plant (physical real world system like
a robot, see Fig. 2, or intangible abstract mathematical system to be controlled) is characterized in an abstract way by a 3-tuple 𝛴𝛴 𝑃𝑃 ( 𝒞𝒞, 𝒰𝒰 , 𝒴𝒴) by means of an Input/Output description through the map/operator 𝛴𝛴 𝑃𝑃 :
Fig. 1 Sketch of the 2 DOF ℛℛ Planar “Pelican robot” [1]. (1)
Through the paper, for 𝐴𝐴 ⊂ ℝ 𝑛𝑛 and 𝑝𝑝 ∈ ℝ 𝑛𝑛 , the
where
distance from a point 𝑝𝑝 to a set 𝐴𝐴 denoted by 𝒞𝒞 is the configuration space (dimension 𝑛𝑛); domain 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑝𝑝, 𝐴𝐴) is defined as the smallest distance from
of internal variables, e.g., generalized positions or state point 𝑝𝑝 to any point in 𝐴𝐴; more precisely [5]:
variables;
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑝𝑝, 𝐴𝐴) ≜ 𝑑𝑛𝑖 𝑥𝑥∈𝐴𝐴 ∥ 𝑝𝑝 – 𝑥𝑥 ∥ 𝒰𝒰 is the input space (dimension 𝑝𝑝); where ∥∙∥ stands for the Euclidean norm.
𝒴𝒴 is the output space (dimension 𝑚𝑚). For illustration purpose in this paper the 2 DOF ℛℛ
This definition of a plant can include a number of “Pelican robot” [1] shown in Fig. 1 shall be evoked.
standard robot models (mobile robots as well as robot manipulators) such as [7]:
1.1 Control System
geometric models;
In few colloquial words a control system is an
kinematic models;
interconnection of components forming a system differential kinematic models; configuration that will provide a desired behavior.
dynamic models.
Beyond physical matters, the main conceptual In the control issue so-called “control of ingredients of a control system are:
torque-driven robot manipulators in joint space” the Plant;
robot plant 𝛴𝛴 𝑃𝑃 is the joint space dynamic model Actuators and sensors;
where 𝒴𝒴 = 𝒞𝒞 , and output 𝑦𝑦 corresponds to the Control objective;
generalized joint positions 𝑞𝑞 ∈ 𝒞𝒞 , and the input Controller.
𝑢𝑢 ∈ 𝒰𝒰 is the torque/forces 𝜏𝜏 applied at the robot Among them the main sine qua non element is the
joints.
control object or plant defined roughly by:
1.3 Control Objectives
Plant: The device, physical process, or system to be controlled. Interaction is defined in terms of
Generally speaking, the objective in a control variables—“Signals” in engineering jargon; usually
system is:
𝑦𝑦 = 𝑧𝑧— [6]: (1) to make a plant behaves in a desired way; (1) Plant controlled/manipulable input 𝑢𝑢;
(2) by manipulating its input u [6].
A Brief Tour on Exotic Control Objectives in Robotics
Fig. 2 Plant: Input/Output variables.
Notice that for “plant behavior in a desired way” no some engineering applications may be vague and explicit allusion to the plant measured output 𝑦𝑦 has
sometimes unclear and ambiguous. This may also been performed, notwithstanding this is usually the
occur in control engineering and robotics [4]. case, i.e., to make the plant measured output 𝑦𝑦 or
Classifications of control objectives may include unmeasured variable to be controlled 𝑧𝑧 behaves in a
features as: locally or globally; asymptotic-time or desired way (typically in an asymptotic fashion). But
finite-time; e.g., rare but practical control objectives this paper emphasizes that this is not mandatory. In
like: finite-time global tracking is also possible. some application such a “plant desired behavior” may
This paper classifies the control objectives in two
be captured by unmeasured plant variables (to be
groups: standard and exotic.
controlled!), say 𝑧𝑧 in the control jargon [6]. (1) Standard Control Objectives: Something surprising, it is allowed in automatic
Regulation: keep controlled variable 𝑧𝑧 close to a control to
constant target value—setpoint, say 𝑟𝑟—; behavior—of unmeasured plant variables 𝑧𝑧 with
intend control—force a desired
Tracking: keep measured variable 𝑦𝑦 = 𝑧𝑧 close to feedback (closed–loop) or
a time-varying target value 𝑦𝑦 𝑑𝑑 ( 𝑑𝑑), see Fig. 3. (open-loop) of measured output ones 𝑦𝑦.
without feedback
(2) Exotic Control Objectives: Intuitively, the meaning of the control objective
Velocity field;
should be fairly obvious to people with some
Range;
knowledge of automatic control. Nevertheless,
Immobilization;
intuition has its limitations.
Reach;
Roughly speaking:
Confinement;
A control objective is a goal, reason or purpose for which an automatic control system should be
implemented. A control objective provides a specific target against which is to evaluate the effectiveness of an automatic control system. A control system is said to
be effective provided that its control objective is achieved. Many control systems may exist which are able to achieve a given common control objective.
Most of engineering challenges must begin by a clear, precise and unambiguous problem specification
Fig. 3 Standard “Position Tracking” control objective in together with a wish or objective to be achieved. But,
output space (Cartesian space).
in contrast with standard common sense, the wishes in Desired output trajectory: 𝒚𝒚 𝒅𝒅 ( 𝒕𝒕) ∈ 𝓨𝓨.
56 A Brief Tour on Exotic Control Objectives in Robotics
flow lines in the velocity field represented by arrows in the output space 𝒴𝒴.
3. Range Control Objective
Generally speaking, the regulation control objective in a control system is to make some output, say 𝑦𝑦, to be exactly a desired constant setpoint, say 𝑟𝑟. Although this may be an acceptable (theoretical, academic, classroom or textbook) wish, due to the following arguments,
such a wish may be unrealistic or unrealizable:
Fig. 4 Velocity field control objective concept [9, 10].
Instead of a constant exact value 𝑟𝑟, real control Path;
system desired goal may require to keep the output 𝑦𝑦 TEFDA [12];
within a prescribed interval; For example [14]: (Ride) Comfort [15, 16].
In papermaking the moisture content must be Some of these exotic control objectives shall be
kept between prescribed values. re-called/introduced below.
Sensors and measurement instruments have always uncertainties in some degree, so it may be
unrealizable to wish the output 𝑦𝑦 to get exact precise Although an original velocity field controller but
2. Velocity Field Control Objective
values; instead, it is more realistic to maintain the under a passive approach was first introduced in 1999
output 𝑦𝑦 within a desired range according to sensors by Li and Horowitz [8], this paper borrows the
and measurement devices accuracy. velocity field control objective definition stated later
Let borrow the following two clever paragraphs in Refs. [9, 10] without regard of neither passive
from the Janert’s book [14]:
requirement nor passive formulation. More precisely: (1) “A standard feedback loop is not suitable for Definition 2—Velocity Field Control Objective
maintaining a metric within a range of values; instead, Given an user defined smooth desired vector field
it will try to drive the output metric to the precise 𝑣𝑣(𝑦𝑦) ∶ 𝒴𝒴 ⟶ 𝒯𝒴 , where 𝒯𝒴 denotes the tangent
value defined by the setpoint 𝑟𝑟.” bundle of 𝒴𝒴 [8, 11]. The velocity field control
But in some real world control engineering objective is defined by:
applications:
(2) “We do not care about tracking a setpoint lim � 𝑣𝑣 � 𝑦𝑦 ( 𝑑𝑑 ) � − 𝑦𝑦 ( 𝑑𝑑 ) �=0