Gains from the control law and the virtual manipulator (Holonomic constraint experiment).
\\n\\n
IntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.
\\n\\nIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society.
\\n\\nLaunching 2021
\\n\\nArtificial Intelligence, ISSN 2633-1403
\\n\\nVeterinary Medicine and Science, ISSN 2632-0517
\\n\\nBiochemistry, ISSN 2632-0983
\\n\\nBiomedical Engineering, ISSN 2631-5343
\\n\\nInfectious Diseases, ISSN 2631-6188
\\n\\nPhysiology (Coming Soon)
\\n\\nDentistry (Coming Soon)
\\n\\nWe invite you to explore our IntechOpen Book Series, find the right publishing program for you and reach your desired audience in record time.
\\n\\nNote: Edited in October 2021
\\n"}]',published:!0,mainMedia:{caption:"",originalUrl:"/media/original/132"}},components:[{type:"htmlEditorComponent",content:'With the desire to make book publishing more relevant for the digital age and offer innovative Open Access publishing options, we are thrilled to announce the launch of our new publishing format: IntechOpen Book Series.
\n\nDesigned to cover fast-moving research fields in rapidly expanding areas, our Book Series feature a Topic structure allowing us to present the most relevant sub-disciplines. Book Series are headed by Series Editors, and a team of Topic Editors supported by international Editorial Board members. Topics are always open for submissions, with an Annual Volume published each calendar year.
\n\nAfter a robust peer-review process, accepted works are published quickly, thanks to Online First, ensuring research is made available to the scientific community without delay.
\n\nOur innovative Book Series format brings you:
\n\nIntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.
\n\nIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society.
\n\nLaunching 2021
\n\nArtificial Intelligence, ISSN 2633-1403
\n\nVeterinary Medicine and Science, ISSN 2632-0517
\n\nBiochemistry, ISSN 2632-0983
\n\nBiomedical Engineering, ISSN 2631-5343
\n\nInfectious Diseases, ISSN 2631-6188
\n\nPhysiology (Coming Soon)
\n\nDentistry (Coming Soon)
\n\nWe invite you to explore our IntechOpen Book Series, find the right publishing program for you and reach your desired audience in record time.
\n\nNote: Edited in October 2021
\n'}],latestNews:[{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"},{slug:"introducing-intechopen-book-series-a-new-publishing-format-for-oa-books-20210915",title:"Introducing IntechOpen Book Series - A New Publishing Format for OA Books"}]},book:{item:{type:"book",id:"438",leadTitle:null,fullTitle:"Etiology and Pathophysiology of Parkinson's Disease",title:"Etiology and Pathophysiology of Parkinson's Disease",subtitle:null,reviewType:"peer-reviewed",abstract:"This book about Parkinson's disease provides a detailed account of etiology and pathophysiology of Parkinson's disease, a complicated neurological condition. Environmental and genetic factors involved in the causation of Parkinson's disease have been discussed in detail. This book can be used by basic scientists as well as researchers. Neuroscience fellows and life science readers can also obtain sufficient information. Beside genetic factors, other pathophysiological aspects of Parkinson's disease have been discussed in detail. Up to date information about the changes in various neurotransmitters, inflammatory responses, oxidative pathways and biomarkers has been described at length. Each section has been written by one or more faculty members of well known academic institutions. Thus, this book brings forth both clinical and basic science aspects of Parkinson's disease.",isbn:null,printIsbn:"978-953-307-462-7",pdfIsbn:"978-953-51-6523-1",doi:"10.5772/956",price:159,priceEur:175,priceUsd:205,slug:"etiology-and-pathophysiology-of-parkinson-s-disease",numberOfPages:554,isOpenForSubmission:!1,isInWos:null,isInBkci:!1,hash:"baad4bf7bcb36df5620d9fea1b92bf07",bookSignature:"Abdul Qayyum Rana",publishedDate:"October 12th 2011",coverURL:"https://cdn.intechopen.com/books/images_new/438.jpg",numberOfDownloads:58771,numberOfWosCitations:31,numberOfCrossrefCitations:14,numberOfCrossrefCitationsByBook:0,numberOfDimensionsCitations:39,numberOfDimensionsCitationsByBook:2,hasAltmetrics:0,numberOfTotalCitations:84,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 14th 2010",dateEndSecondStepPublish:"November 11th 2010",dateEndThirdStepPublish:"March 18th 2011",dateEndFourthStepPublish:"April 17th 2011",dateEndFifthStepPublish:"June 16th 2011",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6",editedByType:"Edited by",kuFlag:!1,featuredMarkup:null,editors:[{id:"32584",title:"Dr.",name:"Abdul Qayyum",middleName:null,surname:"Rana, Md, Frcpc, Frcp (hon)",slug:"abdul-qayyum-rana-md-frcpc-frcp-(hon)",fullName:"Abdul Qayyum Rana, Md, Frcpc, Frcp (hon)",profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:'Dr. Abdul Qayyum Rana is a Canadian neurologist who specializes in the field of Parkinson’s disease and Movement Disorders. He is a fellow of the Royal College of Physicians and Surgeons of Canada. After completing his neurology residency training, Dr. Rana undertook a clinical fellowship in Parkinson’s disease and Movement Disorders at the University of Ottawa, Canada. He is currently the director of the Parkinson’s Clinic of Eastern Toronto and Movement Disorders Centre located in Toronto, Canada. He is also founder of World Parkinson’s Program. He is the author of “Frequently Asked Questions About Parkinson’s Disease”, which is a series of thirteen brochures about Parkinson’s disease, translated in many languages and used in several countries around the world. Dr. Rana has also written the following books: “Neurological Emergencies in Clinical Practice\\", “An Aid to Neuro-ophthalmology “, “An introduction to Essential Tremor”, “50 Ways Parkinson’s Could Affect You”, \\" Differential Diagnosis of Movement Disorders in Clincal Practice\\" ,\\" Neuroradiology in Clinical Practice\\", \\" 99 Faces of Parkinson\\\'s disese\\" and “What is Parkinson’s disease in Arabic?”. He is the editor-in-chief of the Journal of Parkinsonism and RLS. Dr.Rana was Awarded an honorary FRCP by the Royal College of Physicians of U.K. Dr. Rana was also awarded Wayne-Hening Award for his research on Restless Legs Syndrome and Parkinson\\\'s disease. Dr.Rana has published extensively in the field of Neurolgoy, Parkinson\\\'s disease and Movement Disorders.',institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"4",institution:null}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"1057",title:"Neuropsychiatry",slug:"neuropsychiatry"}],chapters:[{id:"21565",title:"Etiology and Pathogenesis of Parkinson’s Disease",doi:"10.5772/20050",slug:"etiology-and-pathogenesis-of-parkinson-s-disease",totalDownloads:3832,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,abstract:null,signatures:"Taku Hatano and Nobutaka Hattori",downloadPdfUrl:"/chapter/pdf-download/21565",previewPdfUrl:"/chapter/pdf-preview/21565",authors:[{id:"37251",title:"Dr.",name:"Taku",surname:"Hatano",slug:"taku-hatano",fullName:"Taku Hatano"},{id:"37257",title:"Prof.",name:"Hattori",surname:"Nobutaka",slug:"hattori-nobutaka",fullName:"Hattori Nobutaka"}],corrections:null},{id:"21566",title:"Genetics of Parkinson Disease",doi:"10.5772/20390",slug:"genetics-of-parkinson-disease",totalDownloads:2742,totalCrossrefCites:0,totalDimensionsCites:2,hasAltmetrics:0,abstract:null,signatures:"Celeste Sassi",downloadPdfUrl:"/chapter/pdf-download/21566",previewPdfUrl:"/chapter/pdf-preview/21566",authors:[{id:"38709",title:"Dr.",name:"Celeste",surname:"Sassi",slug:"celeste-sassi",fullName:"Celeste Sassi"}],corrections:null},{id:"21567",title:"Parkin and Parkinson’s Disease",doi:"10.5772/16990",slug:"parkin-and-parkinson-s-disease",totalDownloads:1715,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,abstract:null,signatures:"Shiam-Peng Tay, Grace G.Y. 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In the first one, these environments are real, while in the second one, we generate them in a computer simulation. However, both types of systems must make the operator perceive, as realistically as possible, the characteristics of the remote or virtual environment. Some variables used to reproduce these characteristics are position and force, which provide visual and haptic feedback, respectively. The biggest difference between them is the procedure of generating the information received by the operator. In the teleoperation case, both signals exist physically and are transmitted via a control algorithm. The algorithm receives both signals from sensors. Both signals do not exist in virtual reality and we must generate computationally them.
Stimulating the senses of sight and touch, as precisely as possible, is essential during the interaction process, since they are the principal channels with which the operator perceives the world around them. For teleoperation, in the visual case, the communication comes directly from the environment or, if the operator is in a remote place, using a camera and a computer screen. The virtual reality system generates the environment through a digital simulation, and the operator receives the visual information through a screen. We need additional devices since the tactile issue is more complex. Those devices must be capable of transmitting the generated forces in the environment. Such a process implies including haptic robots in the systems because of their capability to generate forces and torques that the human operator can perceive in a tactile way. We need for teleoperation systems two physical robots, while in a virtual reality system we only need one robot and the virtual environment as the other.
The medical area has actively seized on both teleoperation and virtual reality systems. In the first case, a specialist can perform surgery procedures over long distances, eliminating the need for the physical presence of either the physicians or patients in the same location [1]. Practically, the specialist can examine or operate on the patient at a different geographic location without having to travel.
In Figure 1, we showed the emblematic
Da Vinci surgical robotic system.
In the second case, someone has widely used virtual reality systems for medical training simulation. With the development of computer graphics, nowadays practically any surgical procedure can be visually simulated. Minimally invasive surgery has been the most beneficial area. It has implemented virtual environments in laparoscopy, neurosurgery, and urology, to name a few [3]. As an example, in Figure 2 we showed
URP Mentor (simulator).
The challenge for researchers in graphic computing and control systems is to design mathematical tools that fit with the object’s physical characteristics to be simulated within the virtual environment. Regarding the visual feedback, the position where such objects are located is essential for the operator to perceive his movements in the Cartesian virtual space. About the force, reproducing rigidity and softness takes special interest when the virtual environment includes penetrable and nonpenetrable objects. Here, the complexity of the mathematical tools increases because their physical laws are not always easy to simulate on a computer. For this reason, it must establish an interchange between visual and haptic realism because of the finite capacity of digital processing.
Teleoperation and virtual reality applications have developed in areas as different as
Goertz presented the first
The idea of force feedback on virtual reality systems began with the fundamental work of Sutherland [11]. He established that the interaction between the human operator and the virtual environment should not only be visual but also tactile. It was not until the 1990s that he adapted the Goertz device to provide force feedback during virtual molecular coupling [12]. Since then, the use of manipulators in virtual reality applications has spread to CAD/CAM assembly [13], aerospace maintenance [14], and especially in medical training through simulators [15] where, unlike systems of master-slave teleoperation, neither the environments nor the contact forces exist. It must transmit the actual forces to the operator with precision. The quality of this transmission depends on the characteristics of the haptic interface and the corresponding force control algorithm [3].
Articulated robots play a major role in medical training simulation systems with force feedback since this kind of electromechanical device can measure spatial position and generate torques. There has been a large effort to design robot haptic interfaces such as the widely used Phantom serial robot [16], the Delta Haptic parallel robot [17], and the combination of passive elements such as brakes and springs with motors [18]. Such robots are examples of impedance types devices, i.e. they read position and control force in response. There are another robots that read forces and control motion, called
Along with haptic interfaces, there has been an intense development of graphical simulation tools capable of reproducing a wide range of virtual environments. The principal aim is for the operator to perceive, as realistic as possible, objects with a high quality of detail. The applications developed include microscopic exploration [19], aviation [20], and clinical neuropsychology [21], among many others. With medical training simulation, a correct synergy between visual and tactile feedback is essential to heighten the skills of medicine students. However, to increase immersion and consequently the realism of the virtual reality displays, it is necessary to model environments that combine haptic and graphics to the same complexity [22]. This is not always possible since it limited the computational processing and it cannot execute the applications in real-time.
Salisbury et al. [23] presented the basic architecture for a virtual reality application with visual and haptic feedback. They established that the force rendering algorithms must be geometry-dependent. This is a disadvantage in medical training simulation since the virtual objects to be reproduced include bones and organs with irregularities or indentations. There are cases in which the interaction occurs not only on the surfaces of the object, but we must also calculate the penetration forces, as we do in surgery simulators. The alternative is to design algorithms based on physical laws that involve the dynamic and movement of the objects when the operator interacts with them [24]. The perfect scenario would be to render forces by combining physical approaches with the most sophisticated haptic interfaces. However, as mentioned before, doing that is computationally more expensive, not to mention the high costs it would entail.
The more realistic the force transmitted to the operator, the higher the quality of the method used. The factors mentioned above cause a series of compensations between haptic and visual realism, real-time execution, and system costs. Such offsets allowed for establishing two principal methods for rendering forces from virtual environments [25]. The first one is
It is to assume, according to
Using the
The methods mentioned above have been the cornerstone for virtual forces generation both in graphic computing and haptic systems. One of the principal requirements in such areas is that the systems be capable of reproducing the forces that would be present during contact with rigid and soft objects. This is especially important in the development of simulators used in medical training, where the tactile sensations caused by contact between a virtual tool and bones or organs must reproduce [32]. Depending on the goals of the design, we must make a compromise between haptic and visual realism.
In order to implement a virtual reality application, it is important to combine and match both visual and haptic feedback in real-time. Next, we introduce the fundamentals of virtual surface representation, which allow us to show how works the
It is important to distinguish between the different representations of virtual surfaces, both from the point of view of computer graphics and from the point of view of haptic systems. Because the physics of light (with visual representation) differs from the physics of mechanical interactions. It is important to consider that although the graphical and haptic simulation can share the coding of certain properties, such as the shape, they must differ in other aspects, such as models, mathematical techniques, and implementation [32]. It is important to note that haptic rendering in practice avoids the many complex renderings developed by the graphics computing community over the years. However, in this section, the basics of such representations are given to introduce the fundamentals of the proposed haptic representation method, which central idea is to relate holonomic and non-holonomic constraints, which mathematically have a kinematic basis, with the rigid and soft tissues of the body. Surface dynamic complexity is avoided, and instead, from a purely haptic approach, it is classified as nonpenetrable and penetrable. By using the approach of a manipulator in constrained motion, it includes the dynamic of the virtual robot to exemplify that it is possible to model the virtual tool, in a more complex way than that of a single point probe used commonly in computer graphics [34].
In order to represent forces coming from rigid surfaces, it suffices to define algebraically an implicit equation in joint coordinates (task space), or at least two of its geometric characteristics such as normal and tangential vectors, or distance and angle relationships between points, lines, and planes [35]. This simplifies the graphical and haptic implementation since it is possible to define
Convex decomposition by Phys X
In this case, a
Haptic interaction with a sphere. (a) Applied external forces. (b) Collision detection. (c) Collision response. (a) Original mesh. (b) Delaunay triangulation. (c) Mass-spring like system.
The case of deformable surfaces is more complex since, from a biomedical approach, a physically realistic simulation must consider all the nonlinearities of material deformation (e.g. stress, strain, elasticity, and viscoelasticity). One strategy is to combine a finite element discretization of the geometry together with a finite difference discretization of time and an updated Lagrangian iterative scheme [38]. Another very used representations of deformable surfaces in computer graphics are the
Particle model by FLEX (soft tissue). (a) Original mesh. (b) Delaunay triangulation. (c) Mass-spring like system.
Using
More sophisticated graphic tools such as SOFA (Simulation Open Framework Architecture) address the description of the object, typically by using three models: an internal model with independent degrees of freedom, the mass, and the constitutive laws, a collision model with contact geometry, and a visual model with detailed geometry and rendering parameters [39]. During runtime, it synchronizes the models using a generic mechanism called
Let
We map the velocities similarly to
where the Jacobian matrix
Given forces
The kinematic relation (2) allows to rewrite the Eq. (3) as
Since Eq. (4) holds for all velocities
The kinematic mappings (1), (2), and (5) allow to compute displacements and to apply forces. They are also used to connect generalized coordinates, such as joint angles, to task space geometries.
From a robot control approach, we can consider a tool in contact with an object as a robot in constrained motion. The constraints of this system will be well defined if we associate them with physically realizable forces. This occurs, for example, with an industrial robot in contact with a proper surface (a real one) like a car bonnet in a painting or welding task. But with virtual environments, where surfaces do not exist, there are no physical constraint forces associated to them. Thus, the constraints are not well defined, and they are called
Let
where
Constraints that involve not only the generalized coordinates but also their first derivatives in the form
with
where
A kinematic constraint can be integrable, there are
Here, the kinematic constraints are, in fact, geometric constraints. Pfaffian constraints set of
From Eq. (9), we get
where
The set of Pfaffian constraints
where
A vector field
where
Given
where
A distribution assigns a subspace of the tangent space to each point in
where the span over the set of smooth real-valued functions on
A distribution is
We said distribution
The hypersurfaces defined by the level sets
This theorem gives a necessary and sufficient condition for the complete integrability of a distribution. Thus, if
So it is possible to establish when a Pfaffian constraint is non-holonomic by checking if its distribution is not involutive.
A common practice in the computer graphics community is to associate the position and orientation of virtual tools directly with that of the haptic interface. However, this assumption is because some real tools have negligible dynamics, such as a scalpel. From a teleoperation approach, we assumed that even the simplest tool has some dynamic properties to consider in the virtual environment. This section presents a description of this proposal, both mathematical and intuitive.
In order to describe the operation of the haptic system, two independent sets of task space coordinates are considered as shown in Figure 6.
Haptic system.
The operator manipulates the haptic interface, i.e., the master robot in the real environment and we denote whose Cartesian coordinates as
In a similar approach, Faurlin et al. clarify in [44] that the virtual environment can be represented by a set of generalized coordinates
which is a mapping between the real and virtual environment, similar to that of Eq. (1) but where the former acts as a master model.
The set of coordinates
Consider a
while the virtual slave dynamics is modeled by
where the subscripts m and v denote the real master and the virtual slave manipulators, respectively. For
where
External torques are acting in both robots, either the real torque
where
where
Whit of holonomic constraints we assume that, in virtual task space coordinates, the virtual robot is subject to
where a suitable normalization is done for the gradient of this constraint,
to be unitary.
The representation of constraint (25) in generalized virtual coordinates is
where
These two gradients are related by
where
where
According to
With non-holonomic constraints, something well known is that we cannot express them as a function of only the generalized coordinates as in (25) or (27). Instead, they are commonly expressed as Pfaffian constraints. In the present case, these constraints are written more intuitively in terms of the virtual end-effector velocities
where
Assuming that the virtual robot is subject to
the torque because of the contact with the virtual environment in (21) can be expressed as
where
The non-holonomic constraints reduce the number of virtual robot available degrees of freedom to an
In this section, the theoretical and practical aspects of implementing a virtual reality system with virtual restrictions are presented. The principal aspect concerned is the design of a controller capable to perform accurate haptic feedback that makes to feel the operator to be in contact with either a penetrable or nonpenetrable virtual surface. The method for visually reproducing the
As mentioned in Section 2, the important aspect to get realistic haptic feedback from a surface embedded into a virtual environment comprises defining its geometry. In Figure 7, we show an idealized representation of a virtual point probe in contact with either an nonpenetrable or penetrable virtual surface.
(
In the first case, we assume that the contact arises at a single point over the surface from where the virtual probe cannot move forward, i.e., its velocity is equal to zero. Therefore, a normal force vector, which magnitude increases depending on the force applied by the operator, avoids motion. In robot control, if we are supposed to connect the probe to the end effector of a manipulator, according to
The best way to find the place of the contact point (which belongs to a set of points defining each surface) is by establishing an implicit equation
which coincides with the holonomic constraint of Eq. (25) in Cartesian coordinates or Eq. (27) in generalized coordinates. From those expressions, it can establish a collision detection algorithm by defining the following conditions:
If
If
If
For the virtual reality system, it is important to remember that the vector
Motion in 2D of the virtual tool inside a virtual object.
For easy visualization, it showed the motion in 2D but during the simulation, we must reproduce it in 3D with the aim of increase the realism of the application by improving the operator’s dexterity. The contact begins in
The trajectories of the virtual tool shown in Figure 8 are common in noninvasive surgical procedures. For example, in the simulator of
The contribution of this approach is, in contrast to common single point haptic feedback methods, that we produce forces that prevent lateral movement of the virtual tool. However, the major disadvantage is that the environment’s elastic properties are not considered. As a result, the reaction of the force that limits the movement of the operator, depending on such properties, is not reproduced and can move the
In Figure 9, we show a scheme in 2D of the contact between a virtual tool and a virtual surface to illustrate the use of the model given by Eq. (21).
Virtual robot in interaction with a penetrable surface.
We attach the tool to the virtual robot’s last DOF, acting as its end-effector. It is important to note that the manipulator dynamic model is used to reproduce a classic bilateral teleoperation system and assuming that, since it is simulated digitally, it can be exchanged by a simpler or more complex model, including those of medical instruments such as forceps endoscopes, gripers, and retractors. This assumption leads to the proposition that, if we use the model of a surgical tool during the simulation, the realism of the contact with the surface would increase. The principal difference between defining a holonomic and a non-holonomic constraint is a need for an expression of
for which each column represents a vector of the end-effector coordinate frame, described in the base frame. This allows defining
We claim that a set of non-holonomic constraints can be defined if the manipulator degrees of freedom are greater than those necessary to control the end-effector position, i.e.,
where
If the robot may not move in the
By choosing the distribution
where
as a basis for the null-space of the
can be constructed, representing the directions of allowed motion, [42].
It is easy to verify that the Lie bracket is
which shows the non-involutivity of the distribution and thus establishes the non-holonomic nature of the constraints according to
Notice also that if the degrees of freedom were 2, the null-space would be of dimension 1, which is necessarily involutive, and the constraints would be holonomic.
A correct haptic rendering largely depends on the force control algorithm. In classic haptic systems, the common solution is to define indirect impedance or compliance control schemes. In contrast, in this section, we present two hybrid control algorithms for haptic interaction with virtual constrained systems. As mentioned in Section 2, the usual practice is to associate the position of the haptic interface directly with that of the virtual avatar. Therefore, a position control scheme is unnecessary, as the operator’s movements are reflected in the graphical application accurately. However, in the proposed approach, the task space coordinates of the virtual environment depend on the correct tracking between the position of the haptic robot and that of the virtual one, i.e., the control algorithm generates the virtual environment itself. This is due to including the virtual robot dynamics and the fact that the operator should feel the virtual tool because of the masking effect. In order to address this, we explored a control scheme used in teleoperation to achieve both position and force tracking. Next, we show a block diagram of this scheme in Figure 10.
Block diagram of the proposed scheme.
Considering once again
as the desired position trajectories, and
as the desired velocity trajectories, i.e., if
We define the corresponding tracking error as
Based on [48], we proposed
and
where
with
Now, by considering the velocity reference as
where
We define also the auxiliary variable
By supposing that both robots are in free movement, for that case, the control laws for the master and the virtual robots are proposed as
respectively, where
Making an approximation of what happens during the tactile interaction of a point probe with a rigid surface, we considered the one-dimensional case (
where
we use a PID-like controller for the virtual reality system. Consider that
By defining
as the desired force trajectory where if
The force tracking errors are
and the corresponding integral, the momenta tracking error, is
Note that we use the standard notation for momenta
respectively, where
In contrast with the holonomic case, when the constraints are non-holonomic, we cannot define them as a function of a set of generalized coordinates, as stated by the Frobenius theorem. As a result, we cannot compute the Lagrange multipliers as in (58). We define these constraints in the form (31) or equivalently (34). One problem arising from these constraints is how to compute the Lagrangian multipliers to satisfy (36). These multipliers represent the forces required to maintain such constraints. Unfortunately, most of the methods used to calculate the lagrange multipliers are designed for systems with holonomic constraints [30, 49, 50] and, therefore, these methods require a position-level definition of the Pfaffian constraints as in (25) or (27). As stated in (45), the calculation presented in [42] can be used for this case. However, it is well known that this solution is unstable since its underlying mechanism is a second-order integrator with zero input. In this work, a modification of the approach used in [50] is proposed as follows. For simplicity, we define
Then, the Lagrange multipliers can be computed as
where the constraints are forced to satisfy
with
Note that the constraint function
Therefore, the initial condition of the integral term on the left-hand side of (72) can be set to zero. Each element
By substituting (71) in the motion Eq. (72), a complete description of the dynamics of the system is gotten. Regarding force, sensor measurements
By defining
as the desired force trajectory in joint space. The corresponding integral is
Finally, instead of (56) and (57), for the master and virtual robot the proposed position-force control for a virtual dynamic system subject to non-holonomic constraints is
Note that the novelty of the approach is not the control scheme because very well-known techniques are employed, but the novelty lies in the effective use of non-holonomic constraints to describe penetrable virtual surfaces. Therefore, a technical stability proof is not provided, but it shows a set of reliable experiments in the next section with the aim of validating the proposed approach.
A fundamental part of the developed virtual reality system is visual feedback. In dynamic systems and control research, there is no interest in including such elements but in real-world applications, as surgery simulators, it is essential. Nowadays, in those developments, we compose the virtual environments by merging several numeric techniques that, combined with the fast velocity of today’s processors, give the virtual objects and surfaces a realism that before would seem impossible to reach., since the goal of this dissertation is to show how a teleoperation control scheme can be used in a virtual reality system, we design the environment by using the fundamentals of graphic computing. The tool used to design the virtual environment was the graphic standard OpenGL 2.0 which is an API, which is a software library for accessing features in graphics hardware. It contains different commands that are used to specify objects, images, and operations needed to produce interactive three-dimensional graphic applications, [51]. Among those operations, the possibility to give texture1 and lighting to the virtual objects is possible, besides proportioning position and orientation changes to the scene’s camera, i.e., the way the operator sees the images on the computer screen regarding height, deep, viewing angles as pitch, roll, and yaw, etc. As we can see in Figure 11, the environment of the developed application comprises a motionless floating sphere and the virtual avatar of the system.
Virtual environment developed in OpenGL 2.0.
For simplicity’s sake, there are no changes in the camera’s position and orientation, but we gave lighting and texture to the scene. We appreciate a notable difference in Figure 12, where the avatar has no lighting, the quality of its texture is less and the background color changes.
Virtual avatar of the system.
Here, a set of aligned cylinders becomes the avatar, which directly related position and orientation to those of the end-effector of the haptic interface. Since OpenGL has the instructions to create elements from primitives, the generation of such cylinders and the floating sphere was straightforward.
It is important to remember that, from a haptic rendering approach, we established the classification of nonpenetrable and penetrable objects for rigid and deformable objects, respectively. With the rigid object, the Open GL instruction
Sectors and stacks of a solid sphere.
We give the effect of rigidity because that vertex’s position is not changed when contact with the virtual avatar occurs. However, giving the haptic effect of highly rigid objects to the operator was difficult since an impedance device was used. For such reason, it is important to establish the control scheme (63) and (64) that compensates, as possible, the limitations of hardware and make feel it produced contact with a rigid object.
The real challenge comes when the
Surface mesh generated using different values for
As mentioned before, the more the resolution of the sphere, the more the realism of the application. However, the computational processing when using the resolution of the last case did not allow a correct performance of the graphic or haptic part. For this reason, a resolution
where
Every vertex
where
Algorithm 1 shows the part of the pseudocode where the modification of the adjacent planes takes place. This does not occur at the same time as the modification of the contact plane, since the code has not yet created these. Figure 15 shows the visual effect that the motion, both of the contact plane and adjacent planes produce. It is important to note that the code implemented needs to be optimized and, above all, to be adapted to the force rendering algorithm through non-holonomic constraints.
Deformation effect of the sphere. (a) Contact. (b) Deformation effect.
The experimental platform comprises a Geomagic Touch haptic robot with six revolute joints, having only the first three of them actuated. An ATI Nano–17 six-axis force sensor is adapted at the last link, as shown in Figure 16. A PC executes the control loop with a sample time of
Experimental platform.
As mentioned in Section 3, the virtual environment comprises a sphere developed using the graphic standard OpenGL 2.0. We should note that both the control algorithm and the graphic simulation run in the same application developed in Visual Studio/C++.
A practical limitation of the Geomagic Touch robot is that it actuated only the first three joints. Therefore, a projection of both the force reflection and the controller torques is necessary, i.e., the contribution of the last two joint torques is neglected. The virtual robot does not have this limitation, and therefore is considered to be fully actuated. The master robot limitation is not so restrictive, since the virtual environment considers only force but not end-effector torque feedback, avoiding the problem of sensor/actuators asymmetry haptic interfaces [53]. The contribution of the last two joints to the force reflection is much less in magnitude when compared with the contribution of the first three joints.
A detailed description of the interaction process between the virtual tool and the virtual environment is presented, simulating separately a rigid and a penetrable sphere. Since the goal of this research was to extend the use of the control scheme to medical training applications, we adopted the shape of the avatar as a
While on a rigid surface, the force does not let the needle penetrate the tissue, in a penetrable surface this is possible. The force behaviors are different, as in the first case, there is a major contribution in the normal direction, which would allow the operator to move the needle laterally over the surface. In the second case, the normal force contribution is smaller and the surrounding tissue would not allow moving the needle in the lateral directions.
In the approach presented, we assume we attach the virtual tool to the end-effector of a five degrees-of-freedom manipulator, which is not visible in the graphic simulation. It may seem counterintuitive because, evidently in real life, a needle does not have such dynamics. We use the robot model as a demonstrative example of other medical tools such as an endoscope, resectoscope, forceps. Attached to teleoperated surgical robot arm have such complex dynamics that must be modeled. The graphic simulations in those cases include pulling, gripping, clamping, and cutting, and therefore it is convenient to have a complete description of both the kinematics and the dynamics of the tool-tissue interaction, [3]. The task starts with the Geomagic Touch robot in its home position. The operator grasps the master robot stylus using the force sensor adapter tip to later gently bring it closer to the virtual surface. We imposed the desired trajectory in free motion in this way. The virtual robot moves following such a trajectory in the virtual environment, with no scaling between the virtual and the real workspaces. It perceived visually both the avatar movement and the virtual surface through a computer screen. When the collision-detection algorithm detects contact with the surface, the force-response algorithm generates a virtual force trajectory by computing the corresponding Lagrangian multipliers, either by employing (58) or (70). The operator perceives an interaction force exerted by the master robot and registered by the Nano-17 force sensor until the contact is over. Finally, the operator returns the sensor adapter to its initial position, thus completing the task.
For simplicity’s sake, the surface used to test the validity of the proposed approach is a sphere described by
where
Variable (control law) | Value | Variable (virtual manipulator) | Value |
---|---|---|---|
0.0550 | 0.20 | ||
0.0055 | |||
10.050 | 0.20 | ||
0.2500 | 20.0 | ||
0.0100 | 1.00 | ||
0.0150 | 0.20 |
Gains from the control law and the virtual manipulator (Holonomic constraint experiment).
Finally, by using the Generic Penalty Method, the surface parameters are
As mentioned before, we cannot express a deformable surface implicitly, even when the operator perceives it as a sphere both visually and haptically. We use a discrete representation similar to that presented in [52], where we assume the surface to comprise many neighboring planes defined by shared nodes. We propose a technique that comprises iteratively choosing a small neighborhood of planes where the contact will occur, depending on the position of the virtual tool. Subsequently, we associate the Lagrange multipliers in Eq. (70) with a pair of planes using the impulse-based technique for multiple rigid body simulations, [55]. The micro-collisions with this technique occur only in the chosen vicinity of the sphere and Lagrange multipliers replace the impulses preventing body interpenetration. In the collision’s case detection algorithm, the implicit surface representation replaces the convex polyhedra decomposition, [56], using the Eq. (84). We did this for ease and to reduce the computational cost of the application, otherwise, the control algorithm sample time would increase. Considering the case where the needle is inside the sphere, but it may not move laterally. However, it may pivot to change orientation.
We adequately describe this kind of scenario by employing non-holonomic constraints. As mentioned in Section 1, non-holonomic constraints have been little exploited to represent the interaction with penetrable surfaces. For example, in [57] it is claimed that to model a surgeon’s scalpel both holonomic and non-holonomic constraints could be employed by limiting the depth of its incision and the direction of its motion, respectively. However, there is not any analysis or modeling of this process in such work.
The most representative proposal is the derivation of the non-holonomic generalized unicycle model presented in [58], where a coordinate-free representation is used to model the insertion of a flexible needle into soft tissue. We employed a similar approach by using the homogeneous matrix representation, but taking into consideration both the kinematic and the dynamic model of the virtual robot and the fact that non-holonomic constraints are more intuitively got if we define them in task space coordinates. The computation of the Lagrangian multipliers for non-holonomic constraints, which is proposed in (71), is an important improvement regarding the cited works. The experiment comprised five degrees of freedom virtual manipulator interacting with a deformable sphere. Once in contact, the end-effector may not move laterally, i.e., along the
The experiment has four steps, as shown in Figure 17. First, the virtual robot is in free motion and only the teleoperation part of the controller (77) is active. In the second part, we insert the needle into the sphere. Next, in the third part, approximately 45 degrees rotate the needle without changing its position. Finally, we insert the needle deeper into the sphere with a new orientation.
Interaction sequence between the avatar and the non-holonomic virtual surface. (a) Free motion. (b) Insertion. (c) Pivoting. (d) Insertion.
The force of the human operator in the lateral directions of the needle is difficult to measure directly with the force sensor. Instead, we take advantage of the projection of such forces on the torque of the master manipulator joint, we calculate
The gains of the master manipulator, described in (76), and the virtual manipulator, are shown in Table 2.
Variable (control law) | Value | Variable (virtual manipulator) | Value |
---|---|---|---|
0.0550 | 0.20 | ||
0.0550 | |||
0.010 | 2.00 | ||
0.2500 | 20.0 | ||
0.0150 | 1.00 | ||
0.0150 | 0.20 |
Gains from the control law and the virtual manipulator (Non-holonomic constraint experiment).
We present a proposal on chaptic interaction with holonomic and non-holonomic virtual constraints. Since extensive research on haptic interaction with rigid surfaces has been presented in the literature, the principal aim was to reproduce the forces generated by the interaction with soft surfaces from a force feedback approach.
Throughout the document, we introduced the theory to establish an optimal relationship between the visual and haptic interaction for the virtual reality system developed. The key lies in adapting the mathematical properties of the holonomic and non-holonomic constraints to the tool’s kinematics in contact with a nonpenetrable and penetrable virtual surface, respectively. However, it is important to note that we made this adaptation to achieve haptic feedback purposes only and consider the basic contact properties of simulated rigid and soft tissues.
Adapting a teleoperation control scheme to a virtual reality system was the strategy to follow since it allowed embedding a robot’s dynamic model into the virtual environment. By doing this, we addressed the teleoperated slave system as a problem of a virtual robot in constrained motion and either holonomic or non-holonomic constraints gave whose contact force.
We studied the differences between one or another representation, both mathematically and intuitively, and the particularities of each one. Among them, there is the fact that they could render forces using the
The principal use detected is that such a method can render similar forces to those arising from contact between a tool and a penetrable surface. We can see, non-holonomic constraints have been used to reproduce the operator’s tactile sensations with practical meaning. We can eventually use this approach in virtual reality medical simulators, and it presented the fundamentals to do that throughout this document. However, adapting the developed method to complex virtual environments, such as those found in the medical field, requires more research both in control and computer graphics. In the first case, adapting more accurately the teleoperation controller presented is necessary and makes it fit with the current methods of graphic computing. Finding more optimal ways to model force using non-holonomic constraints is essential to heighten the realism of the applications. Regarding graphic computing, it is necessary to design numerical methods that adapt more efficiently to the control algorithms designed and that are capable of running with continuum mechanics models.
Naturally, this will increase computational processing and require more analysis to establish the compensation between real-time processing and control performance, without sacrificing application realism. All this requires a wide range of knowledge that does not belong to control or computer graphics.
The authors are grateful for the support provided by PRODEP-BUAP ID90934 and the DGAPA-UNAM under grant IN117820.
1:
2:
3:
4:
5: Calculate the vertices of the upper hemisphere using (81)-(83).
6:
7: Move the contact plane through the auxiliary normal force
8: Store data of the contact plane (based on
9:
10: Compute vertices of the lower hemisphere
11:
12: Move the contact plane using (81)-(83) and the negative numbers on the
13: Store data of the contact plane (based on
14:
15:
16:
17:
18: Reordering adjacent planes
19:
20:
21:
22: Draw plane
23:
24:
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His studies in robotics lead him not only to a PhD degree but also inspired him to co-found and build the International Journal of Advanced Robotic Systems - world's first Open Access journal in the field of robotics.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"441",title:"Ph.D.",name:"Jaekyu",middleName:null,surname:"Park",slug:"jaekyu-park",fullName:"Jaekyu Park",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/441/images/1881_n.jpg",biography:null,institutionString:null,institution:{name:"LG Corporation (South Korea)",country:{name:"Korea, South"}}},{id:"465",title:"Dr.",name:"Christian",middleName:null,surname:"Martens",slug:"christian-martens",fullName:"Christian Martens",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Rheinmetall (Germany)",country:{name:"Germany"}}},{id:"479",title:"Dr.",name:"Valentina",middleName:null,surname:"Colla",slug:"valentina-colla",fullName:"Valentina Colla",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/479/images/358_n.jpg",biography:null,institutionString:null,institution:{name:"Sant'Anna School of Advanced Studies",country:{name:"Italy"}}},{id:"494",title:"PhD",name:"Loris",middleName:null,surname:"Nanni",slug:"loris-nanni",fullName:"Loris Nanni",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/494/images/system/494.jpg",biography:"Loris Nanni received his Master Degree cum laude on June-2002 from the University of Bologna, and the April 26th 2006 he received his Ph.D. in Computer Engineering at DEIS, University of Bologna. On September, 29th 2006 he has won a post PhD fellowship from the university of Bologna (from October 2006 to October 2008), at the competitive examination he was ranked first in the industrial engineering area. He extensively served as referee for several international journals. He is author/coauthor of more than 100 research papers. He has been involved in some projects supported by MURST and European Community. His research interests include pattern recognition, bioinformatics, and biometric systems (fingerprint classification and recognition, signature verification, face recognition).",institutionString:null,institution:null},{id:"496",title:"Dr.",name:"Carlos",middleName:null,surname:"Leon",slug:"carlos-leon",fullName:"Carlos Leon",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Seville",country:{name:"Spain"}}},{id:"512",title:"Dr.",name:"Dayang",middleName:null,surname:"Jawawi",slug:"dayang-jawawi",fullName:"Dayang Jawawi",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Technology Malaysia",country:{name:"Malaysia"}}},{id:"528",title:"Dr.",name:"Kresimir",middleName:null,surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/528/images/system/528.jpg",biography:"K. Delac received his B.Sc.E.E. degree in 2003 and is currentlypursuing a Ph.D. degree at the University of Zagreb, Faculty of Electrical Engineering andComputing. His current research interests are digital image analysis, pattern recognition andbiometrics.",institutionString:null,institution:{name:"University of Zagreb",country:{name:"Croatia"}}},{id:"557",title:"Dr.",name:"Andon",middleName:"Venelinov",surname:"Topalov",slug:"andon-topalov",fullName:"Andon Topalov",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/557/images/1927_n.jpg",biography:"Dr. Andon V. Topalov received the MSc degree in Control Engineering from the Faculty of Information Systems, Technologies, and Automation at Moscow State University of Civil Engineering (MGGU) in 1979. He then received his PhD degree in Control Engineering from the Department of Automation and Remote Control at Moscow State Mining University (MGSU), Moscow, in 1984. From 1985 to 1986, he was a Research Fellow in the Research Institute for Electronic Equipment, ZZU AD, Plovdiv, Bulgaria. In 1986, he joined the Department of Control Systems, Technical University of Sofia at the Plovdiv campus, where he is presently a Full Professor. He has held long-term visiting Professor/Scholar positions at various institutions in South Korea, Turkey, Mexico, Greece, Belgium, UK, and Germany. And he has coauthored one book and authored or coauthored more than 80 research papers in conference proceedings and journals. His current research interests are in the fields of intelligent control and robotics.",institutionString:null,institution:{name:"Technical University of Sofia",country:{name:"Bulgaria"}}},{id:"585",title:"Prof.",name:"Munir",middleName:null,surname:"Merdan",slug:"munir-merdan",fullName:"Munir Merdan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/585/images/system/585.jpg",biography:"Munir Merdan received the M.Sc. degree in mechanical engineering from the Technical University of Sarajevo, Bosnia and Herzegovina, in 2001, and the Ph.D. degree in electrical engineering from the Vienna University of Technology, Vienna, Austria, in 2009.Since 2005, he has been at the Automation and Control Institute, Vienna University of Technology, where he is currently a Senior Researcher. His research interests include the application of agent technology for achieving agile control in the manufacturing environment.",institutionString:null,institution:null},{id:"605",title:"Prof",name:"Dil",middleName:null,surname:"Hussain",slug:"dil-hussain",fullName:"Dil Hussain",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/605/images/system/605.jpg",biography:"Dr. Dil Muhammad Akbar Hussain is a professor of Electronics Engineering & Computer Science at the Department of Energy Technology, Aalborg University Denmark. Professor Akbar has a Master degree in Digital Electronics from Govt. College University, Lahore Pakistan and a P-hD degree in Control Engineering from the School of Engineering and Applied Sciences, University of Sussex United Kingdom. Aalborg University has Two Satellite Campuses, one in Copenhagen (Aalborg University Copenhagen) and the other in Esbjerg (Aalborg University Esbjerg).\n· He is a member of prestigious IEEE (Institute of Electrical and Electronics Engineers), and IAENG (International Association of Engineers) organizations. \n· He is the chief Editor of the Journal of Software Engineering.\n· He is the member of the Editorial Board of International Journal of Computer Science and Software Technology (IJCSST) and International Journal of Computer Engineering and Information Technology. \n· He is also the Editor of Communication in Computer and Information Science CCIS-20 by Springer.\n· Reviewer For Many Conferences\nHe is the lead person in making collaboration agreements between Aalborg University and many universities of Pakistan, for which the MOU’s (Memorandum of Understanding) have been signed.\nProfessor Akbar is working in Academia since 1990, he started his career as a Lab demonstrator/TA at the University of Sussex. After finishing his P. hD degree in 1992, he served in the Industry as a Scientific Officer and continued his academic career as a visiting scholar for a number of educational institutions. In 1996 he joined National University of Science & Technology Pakistan (NUST) as an Associate Professor; NUST is one of the top few universities in Pakistan. In 1999 he joined an International Company Lineo Inc, Canada as Manager Compiler Group, where he headed the group for developing Compiler Tool Chain and Porting of Operating Systems for the BLACKfin processor. The processor development was a joint venture by Intel and Analog Devices. In 2002 Lineo Inc., was taken over by another company, so he joined Aalborg University Denmark as an Assistant Professor.\nProfessor Akbar has truly a multi-disciplined career and he continued his legacy and making progress in many areas of his interests both in teaching and research. He has contributed in stochastic estimation of control area especially, in the Multiple Target Tracking and Interactive Multiple Model (IMM) research, Ball & Beam Control Problem, Robotics, Levitation Control. He has contributed in developing Algorithms for Fingerprint Matching, Computer Vision and Face Recognition. He has been supervising Pattern Recognition, Formal Languages and Distributed Processing projects for several years. He has reviewed many books on Management, Computer Science. Currently, he is an active and permanent reviewer for many international conferences and symposia and the program committee member for many international conferences.\nIn teaching he has taught the core computer science subjects like, Digital Design, Real Time Embedded System Programming, Operating Systems, Software Engineering, Data Structures, Databases, Compiler Construction. 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The toxic and allergic reactions of synthetic dyes are compelling the people to think about natural dyes. Natural dyes are renewable source of colouring materials. Besides textiles it has application in colouration of foods, medicine and in handicraft items. Though natural dyes are ecofriendly, protective to skin and pleasing colour to eyes, they are having very poor bonding with textile fibre materials, which necessitate mordanting with metallic mordants, some of which are not eco friendly, for fixation of natural dyes on textile fibres. So the supremacy of natural dyes is somewhat subdued. This necessitates newer research on application of natural dyes on different natural fibres for completely eco friendly textiles. The fundamentals of natural dyes chemistry and some of the important research work are therefore discussed in this review article.",book:{id:"9203",slug:"chemistry-and-technology-of-natural-and-synthetic-dyes-and-pigments",title:"Chemistry and Technology of Natural and Synthetic Dyes and Pigments",fullTitle:"Chemistry and Technology of Natural and Synthetic Dyes and Pigments"},signatures:"Virendra Kumar Gupta",authors:[{id:"305259",title:"Dr.",name:"Virendra",middleName:null,surname:"Kumar Gupta",slug:"virendra-kumar-gupta",fullName:"Virendra Kumar Gupta"}]},{id:"49647",title:"Fiber Selection for the Production of Nonwovens",slug:"fiber-selection-for-the-production-of-nonwovens",totalDownloads:10512,totalCrossrefCites:9,totalDimensionsCites:17,abstract:"The most significant feature of nonwoven fabric is made directly from fibers in a continuous production line. While manufacturing nonwovens, some conventional textile operations, such as carding, drawing, roving, spinning, weaving or knitting, are partially or completely eliminated. For this reason the choice of fiber is very important for nonwoven manufacturers. The commonly used fibers include natural fibers (cotton, jute, flax, wool), synthetic fibers (polyester (PES), polypropylene (PP), polyamide, rayon), special fibers (glass, carbon, nanofiber, bi-component, superabsorbent fibers). 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