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Springer Proceedings in Advanced Robotics 15
Series Editors: Bruno Siciliano · Oussama Khatib
Jadran Lenarčič
Bruno Siciliano Editors
Advances
in Robot
Kinematics
2020
Springer Proceedings in Advanced Robotics 15
Series Editors
Bruno Siciliano Oussama Khatib
Dipartimento di Ingegneria Elettrica Robotics Laboratory
e Tecnologie dell’Informazione Department of Computer Science
Università degli Studi di Napoli Stanford University
Federico II Stanford, CA
Napoli, Napoli USA
Italy
Advisory Editors
Editors
Advances in Robot
Kinematics 2020
123
Editors
Jadran Lenarčič Bruno Siciliano
Jožef Stefan Institute Department of Electrical Engineering
Ljubljana, Slovenia and Information Technology
University of Naples Federico II
Naples, Italy
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
At the dawn of the century’s third decade, robotics is reaching an elevated level of
maturity and continues to benefit from the advances and innovations in its enabling
technologies. These all are contributing to an unprecedented effort to bringing
robots to human environment in hospitals and homes, factories and schools; in the
field for robots fighting fires, making goods and products, picking fruits and
watering the farmland, saving time and lives. Robots today hold the promise for
making a considerable impact in a wide range of real-world applications from
industrial manufacturing to health care, transportation, and exploration of the deep
space and sea. Tomorrow, robots will become pervasive and touch upon many
aspects of modern life.
The Springer Tracts in Advanced Robotics (STAR) was launched in 2002 with
the goal of bringing to the research community the latest advances in the robotics
field based on their significance and quality. During the latest fifteen years, the
STAR series has featured publication of both monographs and edited collections.
Among the latter, the proceedings of thematic symposia devoted to excellence in
robotics research, such as ISRR, ISER, FSR, and WAFR, has been regularly
included in STAR.
The expansion of our field as well as the emergence of new research areas has
motivated us to enlarge the pool of proceedings in the STAR series in the past few
years. This has ultimately led to launching a sister series in parallel to STAR. The
Springer Proceedings in Advanced Robotics (SPAR) is dedicated to the timely
dissemination of the latest research results presented in selected symposia and
workshops.
This volume of the SPAR series is dedicated to the proceedings of a special
edition of ARK on Advances in Robot Kinematics. Returning to Ljubljana,
Slovenia, where it was first founded in September 1988, ARK marks this year an
important milestone in reaching its seventeenth gathering, establishing itself as a
major anchor of research advances in robot kinematics serving the global robotics
community.
v
vi Foreword
The volume edited by Jadran Lenarčič and Bruno Siciliano contains 43 scientific
contributions. This collection spans a wide range of research developments in robot
mechanisms, kinematics, analysis, design, planning, and control.
Rich by topics and authoritative contributors, ARK brings this unique reference
on the current developments and new directions in the field of kinematics. A fine
addition to the SPAR series and a genuine tribute to ARK contributors, organizers,
and founder!
vii
viii Preface
because of them that the conference maintains its high quality. Special thanks go to
Tadej Petrič, Conference Publishing Chair, who provided excellent technical sup-
port, and Aleš Ude, Conference Organizing Committee Chair. We are also grateful
to the Springer staff who have supported our work throughout these years.
We hope that this new ARK book will again attract scholars and researchers
specializing in robot kinematics and will outline the research guidelines for many
years to come.
Conference Chairmen
Honorary Chairman
B. Roth Stanford University, USA
Scientific Committee
J. Angeles McGill University, Montreal, Canada
O. Altuzarra University of the Basque Country, Spain
M. Carricato University of Bologna, Italy
M. Husty University of Innsbruck, Austria
A. Kecskemethy University of Duisburg, Germany
O. Khatib Stanford University, USA
J. M. McCarthy University of California at Irvine, USA
J.-P. Merlet Inria, Sopia-Antipolis, France
V. Parenti-Castelli University of Bologna, Italy
F. Park Seoul National University, Korea
A. Perez Idaho State University, USA
J. Selig London South Bank University, UK
M. M. Stanisic University of Notre Dame, USA
F. Thomas Institute of Industrial Robotics, Spain
P. Wenger Ecole Centrale de Nantes, France
ix
x Organization
Publications Chair
T. Petrič Jožef Stefan Institute, Ljubljana, Slovenia
Contents
xi
xii Contents
Jadran Lenarčič(B)
1 Introduction
same symposium, I also met some other pillars, like Oussama Khatib, Kenneth
Waldron, Bruno Siciliano and David Orin.
I announced the idea of organizing a specialized symposium on robot kine-
matics in 1986 at the Romansy Symposium in Krakow. The interest seemed
sufficiently strong, so I decided to press ahead. The title Advances in Robot
Kinematics turned out very well. Some things in life do not take much time to
think over. One year later, I started organizing the symposium by simply sending
out invitation letters to the people I believed to be the most important in the
field. It was the birth of Advances in Robot Kinematics, whose short title ARK
was surprisingly well accepted by the community.
At the symposium held in Bologna in 2018, I announced that the conference
in Ljubljana in 2020 would be my last in the capacity of chairman. After twenty-
two years, the time has come to step down. This is not a painful or sad moment,
but one full of joy, as this scientific event has certainly left an unforgettable
footprint on robotics and beyond. I would like to thank everyone who contributed
his or her work and enthusiasm.
in the cost of the conference. It was then that I came to the realization that the
social events were at least as important as the technical sessions. It is crucial
for the success of a conference that people come together and feel like they are
important team members.
I organized the oral presentations at the symposium so that everyone had
40 min. The contributions were published in the Proceedings, which was printed
in advance and available at the conference. I edited the proceedings myself and
had it printed by Cankarjev Dom, the agency which was also the technical orga-
nizer of the symposium and all the other events that took place in Slovenia in
the following decades. Most important, however, was the unanimous conclusion
that these symposia should be continued every other year and that the sym-
posium should be organized once in Slovenia and once somewhere else in the
Alps-Adria region. The aim was to emphasize the identity of the symposium by
its geographical characteristic. There was no going back after that decision.
Linz (Austria) 1990 – Sabine Stifter and Jadran Lenarčič
Book: Advances in Robot Kinematics With Enmphasis on Symbolic
Computation, Springer (1991), 53 Contributions
The second symposium moved to Linz by accident. It started with a visit
to Ljubljana from a political delegation of Upper Austria, who were looking for
options to encourage technical and scientific cooperation between the regions.
Shortly thereafter, I received a mail from Linz from Sabine Stifter proposing the
co-organization of the symposium with the University of Johannes Keppler in
Linz. I met her a few months later at the RISC Institute. We invited two commu-
nities to the ARK symposium: a community of kinematicians and a community
of mathematicians specialising in symbolic computation. I was convinced that
significant synergies could be achieved.
The symposium was held in Linz in September. Conference contributions
were collected based on extended abstracts and far more submissions came than
we expected. We accepted about 130 contributions. Although the conference
set important new standards for the future, its focus was, in my opinion, too
diffuse. The Proceedings of the abstracts were published at the conference. Based
on peer reviews of these, we selected full articles that were published one year
later (1991) in an edited book format by Springer. Although this symposium was
quite different from the first and subsequent ones, the group of kinematicians
who attended the conference, became the core of ARK, thus securing its future
and long-term mission.
Ferrara (Italy) 1992 – Vincenzo Parenti-Castelli and Jadran Lenarčič
Book: 3rd International Workshop on Advances in Robot Kinematics,
Antenna Verde & University of Ferrara, 44 Contributions
In 1992, ARK should have been organised in Slovenia. However, the political
situation after Slovenia’s independence process was not the most favourable for
the organization of international events. Although there were no problems and
matters were cleared up in Slovenia much earlier, I decided to make an exception
and organize ARK somewhere else. I was worried about how many participants
would attend an event in Slovenia. Vincenzo Parenti-Castelli solved the problem
4 J. Lenarčič
by proposing to organise ARK in Ferrara, Italy. A more ideal solution could not
have been found.
Ferrara in many ways laid the foundations for today’s ARK. Among other
things, we first agreed with IFToMM to take over the sponsorship that ARK was
awarded for all subsequent years. The link with the Linz mathematicians was
abandoned, and some important new contributors from the field of robot kine-
matics appeared at the symposium, such as Manfred Hiller, Andres Kecskemethy,
Josepf Duffy, Carlo Galletti and Jean-Pierre Merlet. The Proceedings were pub-
lished and printed by the organizer in the form of full papers. New names were
added to the Scientific Committee. The number of oral presentations was signif-
icantly fewer than in Linz. This proved to be appropriate, and in later years this
number never exceeded 58. By doing so, the conference retained its “boutique”
form. Also important was the decision to reposition future symposia to the end
of June or the beginning of July.
Ljubljana (Slovenia) 1994 – Jadran Lenarčič and Bahram Ravani
Book: Advances in Robot Kinematics and Computational Geometry,
Kluwer Academic Publishers, 51 Contributions
In 1994 ARK took place again in Ljubljana. In preparation for the event,
my goal was how to ensure high quality and better public visibility of the pro-
ceedings. I decided to try publishing an edited book with the Dutch publishing
house Kluwer Academic Publisher, which impressed me with its professionalism
and expeditiousness. That’s when I met (via mail) Nathalie Jacobs (Kluwer),
first assistant director, later director at Kluwer Academic Publishers, Dordrecht.
Working with her contributed to the creation of the impressive series of books
that we know today. The work had to be conducted as efficiently as possible, as
it was crucial for me to have the book printed and handed over to the conference
participants at the event.
The conference was held in Ljubljana at the Club of Cankarjev dom. The
organizers of the conference strived for an excellent social program in addition
to an excellent scientific program. The motivation was to establish a standard for
ARKs in the coming years. I trust that returning to Ljubljana was an important
contribution to the identity of these symposia.
Piran/Portorož (Slovenia) 1996 – Jadran Lenarčič and Vincenzo
Parenti-Castelli
Book: Recent Advances in Robot Kinematics, Kluwer Academic Pub-
lishers, 45 Contributions
We agreed to organize the ARK again in Slovenia 1996. The reason was to
correct the originally planned order of organizers, which was interrupted due to
the political situation in Slovenia a few years before. Piran was, after Ljubljana,
the second Slovenian location and turned out to be ideal for the style of the ARK
symposia. Certainly, the conference was at an important international level, but
the social events were especially well organized by Cankarjev dom. I remember
this event as perhaps the liveliest and with a full and friendly atmosphere, sug-
gesting that a good conference must first create a community of people who want
to participate and want to share their ideas. I do not know if the environment
Advances in Robot Kinematics Facts and Thoughts 5
3 Conclusion
I decided that my last conference would take place in Ljubljana in 2020, the city
where it all began. I can certainly say that ARK has had a profound impact
on my scientific and personal life. Future conferences are sure to follow, and a
new generation of researchers is here to lead this initiative. The ARK Scientific
Committee has already decided that the conference in 2022 will be held in Spain
and will be organized by Oscar Altuzarra.
Robot kinematics remains an unlimited source of new scientific and practi-
cal challenges. There is scientific material for many more years of research. New
technologies, such as high-performance computing and artificial intelligence, will
further strengthen this research field and allow solving so far unsolvable prob-
lems. In the end, I want to thank all the ARK friends who have contributed with
their professionalism and personal engagement.
Inverse Kinematics Using a Converging
Paths Algorithm
Abstract. This article presents a numerical method for the inverse kine-
matics of serial chains by utilizing dual quaternion formulation of the
robot kinematics within a converging paths algorithm. The method is
inspired by iterative techniques such as FABRIK, however adding infor-
mation on the kinematics of the chain to be solved. The method has been
tested with 2R, planar 4R and spatial 4R robots. Future work includes
optimizing the method to compare with other fast numeric algorithms
for inverse kinematics.
1 Introduction
Inverse kinematics (IK) methods are widely used in robotics and computer
graphics. Analytic and numerical techniques have been develop for solving the
IK problem. Closed-form or analytic methods were among the first to be devel-
oped and are successful for simple chains; however, they are developed in a
case-by-case strategy and they are hard to generalize. See [7] for a review. Some
of the analytic methods use the description of the geometric constraints of the
chain. Others use the matrix formulation to the forward kinematics equations
of the chain to solve the inverse problem when this is equated to the desired
position [4]. Analytic methods have the advantage of avoiding iterative solutions
that in principle are more time consuming; however many times they reduce to
finding the roots of a univariate polynomial [5], which carries its own numerical
problems. New algorithms such as IKFast [3] allow a more systematic approach
combining analytic and numerical solutions.
A good review for numerical methods, especially those applied to computer
graphics, can be found in [2]. Numerical methods are grouped into those based
on the Jacobian, Newton-based methods and heuristic methods. Jacobian-based
methods [8] are the most popular and a variety of implementations can be found,
see for instance [6]. Heuristic methods are developed as a computationally lean
alternative to other numerical methods. Most of them consist of a simple app-
roach that yields many fast iterations. Among them we highlight Forward And
c The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2021
J. Lenarčič and B. Siciliano (Eds.): ARK 2020, SPAR 15, pp. 7–14, 2021.
https://doi.org/10.1007/978-3-030-50975-0_2
8 O. Heidari and A. P. Gracia
In this section we describe a method to state the inverse kinematics for serial
chains with revolute joints. Let us consider a kinematic serial chain with n
degrees of freedom; let the joint space of the chain be defined by the vector
θ = {θ1 , . . . , θn } and the joint axes be defined by the Plücker coordinates of the
lines Si , i = 1, . . . n.
This can be done using any suitable algebra. In this case, we use Clifford
algebra of dual quaternions which can be seen as 2k products of cosines and sines
of the angles. Select an order, for instance (c1 c2 . . . ck , s1 c2 . . . ck , . . . , s1 s2 . . . sk ).
The forward kinematics can be written as a linear combination of the joint axes
and Clifford products of joint axes by these coefficients,
⎧ ⎫
⎪cos 21 cos 22 . . . cos 2k ⎪
θ θ θ
⎨ ..
⎬
I S1 S2 . . . S1 S2 . . . Sk . = P, (2)
⎪
⎩ ⎪
θk ⎭
sin 2 sin 2 . . . sin 2
θ1 θ2
Inverse Kinematics Using a Converging Paths Algorithm 9
When using this expression to solve the inverse kinematics problem, consider
a desired pose P . In general, for a robot with k revolute joints and a desired
position P we will always have 2k unknowns. The forward kinematics yields 8
linear equations (6 independent). In addition to these, the trigonometric rela-
tions among the unknowns are to be considered which are bilinear and spherical
relations.
The proposed algorithm relies on breaking any serial chain into two lower-degree
ones which is a well-known approach utilized in different kinematics methods.
The end-effectors of these two smaller chains need to get close to each other
at each step along an iterative process and reach perfectly at the final step of
iteration. In this work, apart chains are called left and right leg. Left is the
one having the base of the original robot and right is the one having the ee of
the original manipulator as its stationary base at the given pose for IK input.
Figure 2 shows a 4R serial chain which is divided into two RR chains. To explain
the procedure of the algorithm and different parts of it, this example is illustrated
and followed in the rest of this paper.
The procedure starts with setting the left leg to a random unit dual quater-
nion that satisfies Study’s quadric. Then, this pose is used to calculate the right
leg’s configuration that can be the closest. To this end, a pseudo-inverse matrix
is computed which may result in a solution that does not satisfy the constraints
in Eq. 5. To solve this problem, the algorithm incorporate a method of projection
where solutions out of workspace are projected based on the shortest distance
they can have to the constraint surface. The projected vector in the joint space
is, then, used to compute the Cartesian pose of the right leg and its transforma-
tion is set equal to the left leg equations to see if it is in the workspace of the
left leg.
Equation 1, for a 4R serial chain, can be converted to the following:
θ1 θ2 θ1 θ3
e S1 2 e S2 2 = De−S4 2 e−S3 2 (7)
Separating the left and right transformations of Eq. 7 by setting them to two
different dual quaternion, L = R, results in:
θ1 θ2 θ3 θ4
e S1 2 e S2 2 = L, e S3 2 e S4 2 =T (8)
where hat symbol is the dual quaternion conjugate operator and T = R̂D. As
it was stated in the previous sections, Eq. 8 can be written as a linear combination
of Clifford products of joint axes:
The back and forth procedure explained in the previous section between left and
right leg is shown more in details by Algorithm 1. This iterative process repeats
till the ee of one leg matches the ee of the other leg in its workspace. To make
sure that there is a solution to the inverse kinematics problem, the forward kine-
matics is solved so that we have a D that is in the workspace.
12 O. Heidari and A. P. Gracia
There are some functions used in this algorithm that affect its performance
and speed. Vector() converts a dual quaternion to an 8-element vector and
DualQuaternion() does the opposite. CheckConstraint() verifies if the constraints
in Eq. 5 are satisfied, returning a value for each constraint that can be used to
evaluate the convergence. At last, Project() is the function that finds a solution
with the least distance between the given point and the constraint surface.
There are different approaches to accomplish this. One method uses vector
calculus on the parameterization to compute the normal vector to the surface
and then find the line normal to the surface and passing through the given point.
This is done by finding a line whose moment is equal to the moment of the point
in the direction of the line.
Another method that is used in the algorithm is through Lagrange Mul-
tipliers. The objective function to minimize is the squared Euclidean distance
between the given point and points lying on the constraint surface.
The proposed algorithm is in the early stage and the authors are exploring dif-
ferent approaches to do the projection. However, the Lagrangian method seems
to have a faster response at the current stage. Numerical results suggest con-
vergence by iteratively approaching each leg to the other using Moore–Penrose
pseudo inverse method, however convergence needs to be formally proved. At
each step the pose of one leg’s end effector is set equal to the other one to see if
it is in its workspace or not. If not, the corresponding vector in joint space gets
projected to the constraint surface to make sure that the ee is in the workspace.
Inverse Kinematics Using a Converging Paths Algorithm 13
⎡ ⎤ ⎡ ⎤
0 −0.639867 0.0305296 0.732783 0 −0.0689129 0.84182 0.263595
⎢0 0.512895 −0.510064 0.567498 ⎥ ⎢0 −0.994039 0.491349 −0.0865131⎥
⎢ ⎥ ⎢ ⎥
⎢0 0.572284 0.859595 0.310715 ⎥ ⎢0 −0.0844797 −0.223418 0.802942 ⎥
⎢ ⎥ ⎢ ⎥
⎢1 0 0 −0.210788⎥⎥ ⎢1 0 0. 0.527558 ⎥
L=⎢
⎢0 R = ⎢ ⎥
⎢ −0.13248 1.10913 −0.322849⎥⎥
⎢0
⎢ −1.12461 0.562694 −0.792586 ⎥⎥
⎢0 −0.912657 −0.523315 0.545166 ⎥ ⎢0 0.040865 −0.732085 0.10385 ⎥
⎢ ⎥ ⎢ ⎥
⎣0 0.66982 −0.349916 −0.138578 ⎦ ⎣0 0.43654 0.510156 0.0228117 ⎦
0 0 0 0.14111 0 0 0 0.378327
(10)
The convergence of the right and left leg to the The convergence of the left (black) and right
solution in joint space in terms of x1 , x2 and x3 . (green) leg to the solution in Cartesian space.
Green: u pro jected and v pro jected , Blue: u and v,
Red: expected solution.
The computation time is relatively high in its current version, as the steps
have not been optimized for spped yet. The interest of the method is going to
depend on finding efficient processes for each of the steps of the algorithm.
14 O. Heidari and A. P. Gracia
4 Conclusion
This work presents an inverse kinematics method based on dividing the chain
and iteratively projecting the closest point on the workspace. The equations are
derived from the forward kinematics and hence it can be applied systematically
to serial chains. The method is tested on serial chains with 2, 3 and 4 degrees
of freedom and revolute joints. In these examples, the algorithm exhibits fast
convergence. Future work will include optimizing the calculations, applying the
method to increasingly complex chains and comparing it to the current state of
the art as well as examining its behavior at non-regular points.
References
1. Aristidou, A., Lasenby, J.: Fabrik: a fast, iterative solver for the inverse kinemat-
ics problem. Graph. Models 73(5), 243–260 (2011). http://dblp.uni-trier.de/db/
journals/cvgip/cvgip73.html
2. Aristidou, A., Lasenby, J., Chrysanthou, J., Shamir, A.: Inverse kinematics tech-
niques in computer graphics: a survey. Comput. Graph. Forum 37(6), 35–58 (2017)
3. Diankov, R.: Automated construction of robotic manipulation programs. Ph.D. the-
sis, Carnegie Mellon University (2010)
4. Manocha, D., Canny, J.F.: Efficient inverse kinematics for general 6R manipulators.
IEEE Trans. Robot. Autom. 10(5), 648–657 (1994). https://doi.org/10.1109/70.
326569
5. Raghavan, M., Roth, B.: Inverse kinematics of the general 6R manipulator and
related linkages. J. Mech. Des. 115(3), 502–508 (1993). https://doi.org/10.1115/1.
2919218
6. Siciliano, B., Khatib, O.: Springer Handbook of Robotics. Springer, Heidelberg
(2007). https://doi.org/10.1007/978-3-540-30301-5
7. Tsai, L.W.: Robot Analysis and Design: The Mechanics of Serial and Parallel Manip-
ulators, 1st edn. Wiley, Hoboken (1999)
8. Wampler, C.: Manipulator inverse kinematic solutions based on vector formulations
and damped least-squares methods. Proc. IEEE Trans. Syst. Man Cybern. 16(1),
93–101 (1986)
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