Textbook Human Friendly Robotics Fanny Ficuciello Ebook All Chapter PDF
Textbook Human Friendly Robotics Fanny Ficuciello Ebook All Chapter PDF
Textbook Human Friendly Robotics Fanny Ficuciello Ebook All Chapter PDF
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Springer Proceedings in Advanced Robotics 7
Series Editors: Bruno Siciliano · Oussama Khatib
Fanny Ficuciello
Fabio Ruggiero
Alberto Finzi Editors
Human Friendly
Robotics
10th International Workshop
Springer Proceedings in Advanced Robotics 7
Series editors
Prof. Bruno Siciliano Prof. 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 94305-9010
Via Claudio 21, 80125 Napoli USA
Italy E-mail: khatib@cs.stanford.edu
E-mail: siciliano@unina.it
Alberto Finzi
Editors
123
Editors
Fanny Ficuciello Alberto Finzi
Dipartimento di Ingegneria Elettrica Dipartimento di Ingegneria Elettrica
e Tecnologie dell’Informazione e Tecnologie dell’Informazione
Università degli Studi di Napoli Federico II Università degli Studi di Napoli Federico II
Napoli Napoli
Italy Italy
Fabio Ruggiero
Dipartimento di Ingegneria Elettrica
e Tecnologie dell’Informazione
Università degli Studi di Napoli Federico II
Napoli
Italy
This Springer imprint is published by the registered company Springer International Publishing AG
part of Springer Nature
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
Robots! Robots on Mars and in oceans, in hospitals and homes, in factories and
schools; robots fighting fires, making goods and products, saving time and lives.
Robots today are making a considerable impact 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, have 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 brings a peer-reviewed selection of the papers
presented at the 10th International Workshop on Human Friendly Robotics (HFR)
which took place in Naples, Italy, from November 6 to 7, 2017. HFR is an annual
meeting which is organized by young researchers in a rotating fashion around
Europe. The volume edited by Fanny Ficuciello, Fabio Ruggiero, and Alberto Finzi
contains 16 scientific contributions ranging from physical to cognitive human–robot
interaction, from grasping to manipulation, from redundant to cooperative robots,
from bipedal to wearable robots.
v
vi Foreword
From its excellent technical program to its warm social interaction, HFR cul-
minates with this unique reference on the current developments and new advances
in human friendly robotics—a genuine tribute to its contributors and organizers!
The growing need to automate daily tasks, combined with new robot technologies,
is driving the development of a new generation of human friendly robots, i.e., safe
and dependable machines, operating in the close vicinity to humans or directly
interacting with them in a wide range of domains. The technological shift from
classical industrial robots, which are safely kept away from humans in cages to
robots, which are used in close collaboration with humans, is facing major chal-
lenges that need to be overcome. The International Workshop on Human Friendly
Robotics (HFR) is an annual meeting dedicated to these issues and organized by
young researchers in a rotating fashion around Europe. Previous venues were
Naples (Italy), Genova (Italy), Pisa (Italy), Tübingen (Germany), Twente (the
Netherlands), Brussels (Belgium), Rome (Italy), Pontedera (Italy), Munich
(Germany), Genova (Italy). The workshop covers a wide range of topics related to
human–robot interaction, both physical and cognitive, including theories,
methodologies, technologies, empirical and experimental studies. The objective
of the workshop is to bring together academic scientists, researchers, and research
scholars to exchange and share their experiences and research results on all aspects
related to the introduction of robots into everyday life. Senior scientists experts in
the field are invited to the workshop as keynote speakers. Their role is also to guide
students and young researchers during the discussions. The 10th International
Workshop on Human Friendly Robotics (HFR 2017) was held in Naples, Italy,
from November 6 to 7, 2017. The workshop was chaired by Fanny Ficuciello and
co-chaired by Fabio Ruggiero and Alberto Finzi. The meeting consisted of three
keynote talks, a forum with open discussion, and twenty-eight contributed pre-
sentations in a single track. This is the first edition of the workshop with associated
proceedings and thus the first book of the SPAR series dedicated to HFR. The
papers contained in the book have been selected on the basis of a peer-reviewed
process and describe the newest and most original achievements in the field of
human–robot interaction coming from the work and ideas of young researchers.
Each paper presented to the workshop was refereed by at least two members of the
Steering Committee.
vii
viii Preface
Università della Campania Luigi Vanvitelli. We are also indebted to Dr. Chenguang
Yang and Fei Cheng for their evaluable technical contribution and to the staff of
Springer who were responsible for putting the whole book together.
Organizers
Workshop Chair
Fanny Ficuciello, Università di Napoli Federico II
Workshop Co-chairs
Alberto Finzi, Università di Napoli Federico II
Fabio Ruggiero, Università di Napoli Federico II
Special Session Chairs
Fei Chen, IIT, Italy
Chenguang Yang, Swansea University, UK
Local Arrangement Chairs
Jonathan Cacace, Università di Napoli Federico II
Mario Selvaggio, Università di Napoli Federico II
Program Committee
xi
xii Organization
Sponsoring Institutions
xiii
xiv Contents
1 Introduction
While elastic actuators exhibit many advantages, the complexity of the drive
train can lead to an increased fault-sensitivity and reduced reliability. According to
an expert study, faults have a high practical relevance for the utilization of elastic
actuators [6]. Faults occur thereby frequently in kinematic components, sensors and
software. However, elastic elements are rated with increased probability ratings,
which supports their practical relevance [6]. Especially in close contact between
human and robot, faults of the elastic robotic system can compromise safety, hence,
a fault management system appears crucial to ensure a safe and reliable pHRI [7].
A fault is generally defined as an inadmissible deviation of a property from the
desired condition [8], which leads to a system that does not fulfill its function properly
[9]. Fault diagnosis is required to detect deviations, identify the malfunctioning com-
ponent, and perform countermeasures, e.g. transfer the system into a safe operational
state or enable specific modes of operation by means of fault-tolerant control [9].
This paper focuses on the detection, identification, and compensation of faults
occurring in the elastic element, which is an unique component of elastic actuators
and has a significant influence on pHRI. Therefore, a fault-tolerant control strategy is
designed and applied to a series elastic actuator in Sect. 2. The model-based detection
of a stiffness fault and corresponding compensation strategy is developed in Sect. 3.
Simulation results in Sect. 4 show the feasibility of the proposed method. At last, a
conclusion is given in Sect. 5.
In this section, an actuator with Variable Torsional Stiffness (VTS) [10, 11] is pre-
sented. It serves as an exemplary SEA to develop and evaluate the dependability
of pHRI in presence of a stiffness fault and develop appropriate countermeasures.
Further, an introduction to impedance control is given since it forms the basis of the
proposed stiffness-fault-tolerant control strategy.
(a) (b)
Il 0 ϕ̈l ks −ks ϕl τ
+ = ext (1)
0 Ia ϕ̈a −ks ks ϕa τa
For VTS, the external loads consist of the gravitational torque of the pendulum,
determined by the mass m, the distance to the center of rotation l and the gravitational
acceleration g as well as the an external disturbance τdis :
In the following, all loads due to pHRI are considered as external disturbance and
described by τdis . The parameters of the VTS-actuator according to the identification
in [12] are given in Table 1.
The control input u is determined to achieve passivity of the system [13], yielding:
To track a motion, the control input considers the desired position of the link
ϕl,d and the corresponding gravitational torque mlg sin (ϕl,d ) to calculate the desired
actuator angle ϕa,d via inverse dynamics from Eq. (1). For the VTs-actuator, this
yields:
1
ϕa,d = ϕl,d + mlg sin (ϕl,d ) + Il ϕ̈l,d (5)
ks
The first two terms of Eq. (4) represent compensation of loads for the desired motion
of link and actuator. The last two terms in Eq. (4) represent PD-control of the actu-
ator and define the reaction to external, unknown disturbances. The PD-controller
implements a virtual stiffness kc and viscous damping dc with respect to the actuator,
yielding the characteristic structure of the impedance-controlled SEA presented in
Fig. 3. This leads to the following system dynamics with respect to the position error
ϕ̃:
Il 0 ϕ̃¨ l 0 0 ϕ̃˙ l ks −ks ϕ̃l τ
+ + = dis (6)
0 Ia,d ϕ̃¨ a 0 dc ϕ̃˙ a −ks ks + kc ϕ̃a 0
Hence, the interaction stiffness ki as the relation between the disturbance τdis and
position error at the link ϕ̃l is a series configuration of virtual and physical stiffness:
ks kc
ki = (7)
ks + kc
Modeling the pHRI as external disturbance, the impedance control allows to set
the interaction stiffness ki between actuator and human via the control parameter
kc . Configuring kc generates the possibility to create a situational or user-specific
characteristic of the pHRI.
However, to achieve a specific stiffness of the interaction, detailed knowledge
about the value of the physical stiffness ks is required. Furthermore, ks is required
as input to determine the desired motion of the actuator with Eq. (5) as well as the
impedance control law given by Eqs. (3) and (4). Hence, the occurrence of a fault,
A Stiffness-Fault-Tolerant Control Strategy … 7
which causes a change of the physical stiffness, would reduce control performance
and influence pHRI characteristics.
This section presents the detection of a stiffness fault and an adaptation of the control
strategy in order to compensate for the malfunction and to maintain specified pHIR
characteristics.
The control strategy presented in Fig. 4 adapts the stiffness parameter kc of the
impedance control algorithm to compensate for deviations of the physical stiffness ks .
Therefore, kc is set according to an estimation of the physical stiffness k̄s to retain the
desired pHRI characteristics. The upper part of Fig. 4 shows the presented impedance
control, composed of inverse dynamics (Eq. 5), the impedance control law (Eqs. 3
and 4) and the plant (Eq. 1). An estimation of the physical stiffness k̄s (τa , ϕa , ϕ˙a , ϕl )
is determined based on the approaches given in [14–16], fed back to the inverse
dynamics and impedance control, and used to determine kc .
Fig. 4 Block diagram of the fault-tolerant control strategy for dependable pHRI
(RLS) algorithm with fixed directional forgetting [17] to dynamically compute the
estimated physical stiffness k̄s . To estimate and filter the spring torque, an equivalent
residual re is generated from the part of the model that represents the actuator, i.e., the
lower line of Eq. (1). With a positive design parameter K , the residual is calculated
from: ⎛ t
⎞
1
τa ( j) + τa ( j − 1)
J ( j) = J ( j − 1) + T (9)
2
r ( j) = K (Ia ϕ̇a ( j) + Dϕa ( j) − J ( j)) (10)
2−TK 2(r ( j) − r ( j − 1))
re ( j) = re ( j − 1) + (11)
2+TK 2+TK
For estimation of the physical stiffness, an RLS algorithm with directional forgetting
is proposed that uses a linear parameterization of the unknown stiffness parameters
αh based on a parametric model f (φ, α ):
n
f (Δϕ, α ) = f h (Δϕ)αh . (12)
h=1
A Stiffness-Fault-Tolerant Control Strategy … 9
Based on the recursive calculation of the residual re in Eqs. (9) to (11) and the linear
model for elasticity from Eq. 13 an on-line estimation of k̄s is performed with a
discrete-time recursive least squares algorithm with directional forgetting. Hereby,
the input signals are φ as regressor and re as response.
1−λ
ε( j − 1) = λ − (14)
φ( j)C( j − 1)φ( j)
C( j − 1)φ( j)φ( j)C( j − 1)
C( j) = C( j − 1) − (15)
ε( j − 1)−1 + φ( j)C( j − 1)φ( j)
C( j − 1)φ( j)
L( j) = (16)
1 + (φ( j) · C( j − 1) · φ( j)
k̄s ( j) = k̄s ( j − 1) + L( j) (17)
Inserting the estimated physical stiffness k̄s into Eq. 7 and rearranging to determine
the virtual stiffness kc to achieve a given, desired interaction stiffness ki yields the
adaptation law:
k̄s ki
kc = (18)
k̄s − ki
ki < ks . (20)
10 F. Stuhlenmiller et al.
This condition for stability limits the range of adaptation of ki , as the pHRI can only
be softer than the physical stiffness. Additionally, the selection of high gains due to
high desired values of kc can practically limit control performance.
4 Simulation Results
The reaction of the system to faults occurring in the physical stiffness as well as the
feasibility of the proposed method is evaluated in simulation. To evaluate stiffness
estimation and control adaptation, dynamic behavior of the VTS-actuator in interac-
tion with the human during fault occurrence is considered. A fault of the stiffness is
modeled as a sigmoid progression of k f ault , characterized by a decrease of pdecr in
% of ks at time t f ault according to:
−1
−a (t−t f ault )
k f ault (t) = ks 1 − pdecr 1 + e (21)
Thereby, a affects the gradient of transition of the sigmoid function and is set to
a = 20 s −1 .
As a simple case of pHRI, a contact with a human is considered. It is represented
by a spring-damper system with the stiffness kh = 500 N m rad−1 and the damping
coefficient dh = 20 N m rad−1 as depicted in Fig. 5. The disturbance is activated for
positive angles:
0 for ϕl < 0
τdis = (22)
kh (ϕl − ϕdis ) + dh ϕ̇l for ϕl ≥ 0
Hence, in this case, the interaction stiffness ki determines the contact force and
how far the point of contact is pushed to negative ϕdis values by the pendulum. While
in general, compliance and damping of the human are non-linear and comprised with
uncertainties, the simplified model is deemed sufficient to show that the presented
fault-tolerant control strategy achieves the desired interaction stiffness.
A simulation is performed for a sinusoidal motion of the link with an amplitude of
10◦ , a frequency of 0.5 Hz, and a desired interaction stiffness of ki = 50 N m rad−1 .
The pHRI takes place between t = 10 and 18 s to provide sufficient time for reach-
ing steady-state behavior. Considering the interval 10 s < t < 15 s allows to assess
the estimation and control performance in nominal operation, while the effects due
to fault occurrence are analyzed for t ≥ 15 s. The control parameter kc is directly
determined from Eq. 18, dc is set to 20 N m rad−1 . The desired actuator inertia is not
changed from the original value, i.e., Ia,d = Ia . In the residual generator, K τa is iter-
atively tuned to a value of 500. For the stiffness estimation, an exponential forgetting
factor of 0.999 is selected. The stiffness and the covariance matrix are initialized by
0.8ks and with a unity matrix scaled with the factor 10, respectively.
The physical stiffness is set to ks = 100 N m rad−1 and reduced by pdecr = 30%
to 70 N m rad−1 at t f ault = 15 s as presented in Fig. 6. During steady-state operation
before fault occurrence, the estimated stiffness coincides with the real one. After the
stiffness fault occurs, a period of approximately 2 s is required until the estimation
converges to the new stiffness value, which is deemed fast enough to compensate
for a stiffness fault after one oscillation. The mean squared error between estimated
stiffness and true value is 0.35 N m rad−1 , thus, the estimation is sufficiently accurate
for fault-compensation.
A simulation without compensation of the fault is presented in Fig. 7. The dis-
turbance τdis shown in the upper plot results from pHRI. The compliant behavior
of the system can be observed in the middle and lower plots which show the devi-
ation of the link position. The desired system behavior (red) is shown as reference
and is determined from τdis via Eq. 6. After the occurrence of the stiffness fault,
which is indicated by the dashed black line, the compliance of the system is higher
Fig. 6 Progression of the real stiffness (blue) and the estimated stiffness (red) with t f ault = 15 s
(dashed-black)
12 F. Stuhlenmiller et al.
Fig. 7 Simulation without compensation of the stiffness fault with t f ault = 15 s (dashed-black);
top: interaction torque (black), middle: position link (blue), desired position link (red); bottom:
magnification of the plot in the middle
Fig. 8 Simulation with compensation of the stiffness fault with t f ault = 15 s (dashed-black); top:
interaction torque (black), middle: position link (blue), desired position link (red); bottom: magni-
fication of the plot in the middle
than desired, and the link position deviates from the desired trajectory. This also
results in lower interaction force. Furthermore, the control performance decreases
even without disturbance.
Figure 8 shows the results obtained with activated stiffness estimation and corre-
sponding control parameter adaptation. The link tracks the desired trajectory with
A Stiffness-Fault-Tolerant Control Strategy … 13
negligible position error and the system exhibits the specified interaction behavior as
red and blue curve are overlapping throughout the simulation. Hence, the stiffness-
fault is compensated and a fault-tolerant pHRI is achieved.
5 Conclusion
This paper presents a method to detect a stiffness fault of SEAs via online estimation
of the physical stiffness to provide reliable pHRI by impedance control adaptation.
Stiffness estimations are determined via a model-based calculation of the spring
torque and a recursive least squares algorithm. An observation of variations in the
estimation allows to detect stiffness faults. In order to compensate for a change in
the compliance and maintain the desired interaction stiffness, the estimated physical
stiffness is used to adapt the virtual stiffness of the impedance control. Simulations
considering a stiffness fault in an actuator with variable torsion stiffness point out
that the accuracy, convergence, and robustness of the stiffness estimation are suit-
able. With the presented fault-tolerant control approach, a reliable behavior during
faulty operating states and a preservation of the desired interaction characteristics is
ensured. By enabling fault-tolerant pHRI, the proposed control strategy contributes
to safe system behavior, which should to be investigated experimentally in future
work.
References
1. Vasic, M., Billard, A.: Safety issues in human-robot interactions. In: 2013 IEEE International
Conference on Robotics and Automation (ICRA), pp. 197–204. IEEE (2013)
2. Haddadin, S., Albu-Schffer, A., Hirzinger, G.: Safe physical human-robot interaction: mea-
surements, analysis and new insights. In: ISRR, vol. 66, pp. 395–407. Springer (2007)
3. de Santis, A., Siciliano, B., de Luca, A., Bicchi, A.: An atlas of physical human robot interaction.
Mechan Mach Theory 43(3), 253–270 (2008)
4. Bicchi, A., Bavaro, M., Boccadamo, G., De Carli, D., Filippini, R., Grioli, G., Piccigallo,
M., Rosi, A., Schiavi, R., Sen, S.: Others, physical human-robot interaction: dependability,
safety, and performance. In: 10th IEEE International Workshop on Advanced Motion Control:
AMC’08, vol. 2008, pp. 9–14. IEEE (2008)
5. Verstraten, T., Beckerle, P., Furnmont, R., Mathijssen, G., Vanderborght, B., Lefeber, D.: Series
and parallel elastic actuation: impact of natural dynamics on power and energy consumption.
Mechan Mach Theory 102, 232–246 (2016)
6. Beckerle, P.: Practical relevance of faults, diagnosis methods, and tolerance measures in elas-
tically actuated robots. Control Eng. Pract 50, 95–100 (2016)
7. Filippini, R., Sen, S., Bicchi, A.: Toward soft robots you can depend on. IEEE Robot. Autom.
Mag. 15(3), 31–41 (2008)
8. Isermann, R.: Fault-Diagnosis Systems: an Introduction from Fault Detection to Fault Toler-
ance. Springer (2006)
14 F. Stuhlenmiller et al.
9. Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M.: Diagnosis and Fault-Tolerant Control:
with 218 Figures, 129 Examples, and 43 Exercises, 3rd edn. Springer (2016)
10. Beckerle, P., Wojtusch, J., Schuy, J., Strah, B., Rinderknecht, S., von Stryk, O.: Power-optimized
stiffness and nonlinear position control of an actuator with variable torsion stiffness. In:
IEEE/ASME International Conference on Advanced Intelligent Mechatronics (2013)
11. Lendermann, M., Singh, B.R.P., Stuhlenmiller, F., Beckerle, P., Rinderknecht, S., Manivan-
nan, P.V.: Comparison of passivity based impedance controllers without torque-feedback for
variable stiffness actuators. In: IEEE/ASME International Conference on Advanced Intelligent
Mechatronics (2015)
12. Lendermann, M., Stuhlenmiller, F., Erler, P., Beckerle, P., Rinderknecht, S.: A systematic
approach to experimental modeling of elastic actuators by component-wise parameter identi-
fication. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct. 2015
13. Ott, C.: Cartesian Impedance Control of Redundant and Flexible-Joint Robots. Springer (2008)
14. Perner, G., Yousif, L., Rinderknecht, S., Beckerle, P.: Feature extraction for fault diagnosis in
series elastic actuators. In: Conference on Control and Fault-Tolerant Systems (2016)
15. Flacco, F., de Luca, A., Sardellitti, I., Tsagarakis, N.G.: On-line estimation of variable stiffness
in flexible robot joints. Int. J. Robot. Res. 31(13), 1556–1577 (2012)
16. Flacco, F., de Luca, A.: Residual-based stiffness estimation in robots with flexible transmis-
sions. In: 2011 IEEE International Conference on Robotics and Automation (ICRA), pp. 5541–
5547. IEEE (2011)
17. Navrtil, P., Ivanka, J.: Recursive estimation algorithms in matlab & simulink development
environment. WSEAS Trans. Comput. 13, 691–702 (2014)
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stiffness actuation. In: IFAC World Congress, pp. 6872–6879 (2011)
Tracking Control of Redundant
Manipulators with Singularity-Free
Orientation Representation and
Null-Space Compliant Behaviour
Abstract This paper presents a suitable solution to control the pose of the end-
effector of a redundant robot along a pre-planned trajectory, while addressing an
active compliant behaviour in the null-space. The orientation of the robot is expressed
through a singularity-free representation form. To accomplish the task, no extero-
ceptive sensor is needed. While a rigorous stability proof confirms the developed
theory, experimental results bolster the performance of the proposed approach.
1 Introduction
Over the last years, robotic systems are started to be used in those application areas
where human-robot physical interaction becomes unavoidable and necessary. A new
term, Socially Assistive Robotics (SAR), is defined in [6] for service robots working
with humans. In certain cases, it might also be useful to measure, or at least estimate,
the exchanged forces and to figure out whether the contact with the human operator
has been unintentional or intentional (i.e., required for collaborative tasks). The need
of safety and dependability measures is discussed in [8] based on impact tests of a
lightweight robot with a crash-test dummy for possible injuries that can happen in a
SAR system, and on the severity of these injuries.
Hence, for safety reasons, a compliant behaviour is often requested to a robot.
Such compliance can be in principle achieved through either a mechanical device or
a suitable control law. In the former case, an elastic decoupling is placed between
the actuators and the link, obtaining a fixed or a variable joint stiffness [1]. In the
latter case, the compliant behaviour is obtained via software, like implementing an
impedance control [7, 9, 19].
In the research project PHRIDOM, see [5], the components of a robotic application
are discussed based on safety and dependability in physical human robot interaction.
The mentioned components are mechanics, actuation control techniques and real-
time planning for safety measures.
In the event of using a redundant robot, the compliant behaviour can be obtained
both at the main task level [15, 17] and in the null-space [18]. This last is helpful
when the interaction control cannot interfere with the execution of the main task. In
principle, the resulting external wrench affecting the main task should be properly
measured or estimated: in this way, it is possible to design an impedance behaviour
in the null-space without seizing the main one.
Using a redundant robot to minimize the injury possibilities prior to detect the
contact is proposed in [13]. To this aim, a posture optimization technique is employed
to make a redundant robot arm able to change its posture to minimize the impact
forces along a given direction while carrying out the main task.
This paper extends what presented in [18, 20] by explicitly addressing the tracking
case and employing a singularity-free representation for the orientation of the robot’s
end-effector, e.g., axis-angle or unit quaternion. Notice that using one of these two
orientation representations, the theoretical framework in [18] fails.1 The sought aim is
to control the robot arm while the end-effector has to follow a pre-planned trajectory
in terms of both position and orientation, and the manipulator has to exhibit an active
compliant behaviour in the null-space. A rigorous stability analysis is carried out
thanks to the presence of a dynamic term in the controller, filtering both the effects
of the velocity and of the external wrench, while no exteroceptive sensors are needed
to fulfil the given task.
2 Mathematical Framework
2.1 Notation
A redundant robot manipulator (n > 6) is considered in this paper, with n the number
of joints. The vector q ∈ Rn denotes the joint positions, while q̇ ∈ Rn and q̈ ∈ Rn
the joint velocities and accelerations, respectively.
1 In
detail, the proof of Proposition 3 within [18] cannot be applied whether the orientation error is
chosen as it will be defined in this paper.
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a really first-class highly certificated magician from Cairo, or some
big town, and get him to come out and do the job. In the meantime,
as Qwaytin had told me that there were some mounds in the
Kairowin hattia, that we should go there through the eastern part of
the Farafra depression and see if they did not contain treasure.
Qwaytin had heard that they contained buildings, and so thought that
it would be a likely place for buried riches, though, as he said
lugubriously, he did not expect that we should find anything like what
we might have done if we had discovered the treasure of those three
Sultans. The following morning a rather crestfallen caravan set out
for the eastern side of Farafra.
CHAPTER XXIII
O N leaving the hill we took a road that led us towards the north.
We first rounded the western end of the scarp of the detached
plateau parallel to which we had marched on coming from Bu
Gerara, and, about two hours after our start, ascended a steepish
bank on to the top of the plateau, which here was only about fifty feet
high.
From the summit of a small hill close by, a huge cliff stretching to
the north and south, as far as it was possible to see, was visible, far
off in the east; this was evidently the eastern boundary of the Farafra
depression, and, as I afterwards discovered, the continuation of the
cliff to the north of Bu Gerara.
The scarp was too far for me to be able to see any details of its
surface, with the light behind it, and as the top of it showed as only a
straight line, there were no points on it to which I could take a
bearing.
In these circumstances it was impossible either to fix its position
or to estimate the direction in which it ran. I several times met with
this difficulty, but found that, when a cliff faced towards the south, it
was only necessary for me to wait till the sun came round far enough
to begin to light up its surface, and then a rough estimate of the
direction in which it ran could be obtained by taking a bearing on to
the sun itself. This dodge was especially useful when it was
necessary to map the continuation of a cliff, part of which had
already been surveyed and the remainder of it could only be seen
from one point, such as the top of a high hill.
The part of the Farafra depression in which we found ourselves
was an absolutely featureless plain, of hard level sand, that sloped
slightly towards the foot of the scarp on our east. Here and there we
came across patches of greenish clay, with white lines running
through it, showing above the surface of the sand.
The Persian King, Cambyses, during his occupation of Egypt,
sent a great army across the desert to destroy the oracle of Jupiter
Ammon in Siwa Oasis. The army never reached Siwa; but was lost
in the desert. Its last resting-place is unknown, but, according to
native reports, the whole host perished of thirst in this huge
depression in which the oasis of Farafra lies.
I happened to mention to Qwaytin the subject of singing sands,
and asked him if he had ever heard any. He told me that somewhere
in the north of the Farafra depression there was a rock that was
supposed to be the “church” of the spirits of the lost Persian army. It
was called the “infidel rock,” because it “sang on Sunday.” It
appeared to be some form of musical sands.
It was not until the third day after our start from the treasure hill
that we sighted in the west the field of dunes that occupies the
centre of the Farafra wady. They appeared to be almost white in
colour, and lay a long way off.
Qwaytin told me that we should reach the Kairowin hattia on our
third day after leaving his hill. It will give some idea of his utter
incompetence as a guide when I say that we did not actually get
there until two days later.
He came into my tent on the first evening and began yarning in an
aimless sort of way, as he generally did as a preliminary to serious
business, and I endeavoured to extract some information from him
as to the topography of the Bedayat country, with which he was well
acquainted.
But he at once got impatient and changed the subject to that of
his confounded hill. He ended by asking—almost demanding—that
we should go back there to have another look at it, and to make
certain that there was not another hill in the neighbourhood which
might be the one indicated in his book. On my refusing to do so, he
flounced out of the tent—he was certainly a queer customer to deal
with.
Whenever I spoke to him the next day he began gassing about his
wretched hill, and saying that he wanted to go back to it; but towards
evening he rather recovered himself, and when he came to my tent I
again threw out feelers about the country of the Bedayat, though he
declined to tell me anything about the district, he started giving me a
lot of information about the Bedayat themselves, which, as they are
an almost unknown race, proved extremely interesting.
They claim to be descended from an afrit, whom, for some crime,
either David or Solomon shut up in a box, till he grew to such an
enormous size that he burst it open. There still exists apparently a
mongrel Bedayat—Tibbu tribe, known as the M’Khiat er Rih, that
possess the miraculous power of being able to walk over sand
without leaving any tracks behind them—a most useful
accomplishment in the desert for a race of born freebooters. This
peculiarity they owe to the fact that wherever they go they are
followed by a wind that immediately obliterates their footprints!
On our fourth day after leaving the treasure hill, our road
converged towards the dunes lying on our west, and, as Qwaytin
seemed to be hopelessly lost, I climbed one of the biggest of them
with him to try and make out our position.
From the top, the east and west scarp, with a break in it leading
up to Baharia Oasis, that lies on the north of Farafra, could be seen
in the far distance, but no sign of the hattia Kairowin was visible. In
front of us, however, was a high three-headed sif, or longitudinal
sand dune, that Qwaytin declared to be the landmark for the hattia
from the south.
As we were getting very short of water, the news that the hattia
was not in sight caused something like consternation among my
men. They all started grumbling at Qwaytin’s ignorance of the road,
and Ibrahim went so far as to ask him point-blank why he called
himself a guide, if he knew so little about the desert.
This coming from a young Sudani, hardly out of his ’teens, to an
elderly Arab guide, who, moreover, was a sheykh of his tribe, was a
great ayb, and Qwaytin was intensely put out. Qway, under the
circumstances, would have retaliated with some stinging remarks on
the inferiority of “slaves” and the respect that was due from a boy to
his elders and superiors in rank; but Qwaytin lacked his ready
powers of vituperation. He was a slow-witted old curmudgeon, and
failed entirely to put Ibrahim in his place. His own men stood up for
him in a feeble sort of way. But they were no match for Ibrahim, and
eventually gave up any attempt to defend their sheykh, probably
feeling themselves that there was not much to be said in his
defence. As I rather wanted to encourage a certain amount of friction
between my men and Qwaytin’s, I left them to settle their differences
as best they could, with the result that Qwaytin and his men got
much the worst of the wrangle.
Kairowin hattia measures some eighteen miles from north to
south, by seven from east to west. It consists of a level scrub-
covered area, in which, here and there, are to be seen a few
neglected-looking palms. A number of wells have been sunk here at
various times; one on the extreme eastern edge of the hattia, where
the road coming from Assiut first enters the scrub, is known as Bir
Murr. This well, which I did not visit, is said to be sanded up. Another
well somewhere to the north, I believe, is known as Bir Abd el Qadr.
There are also several others, all of which seem to be impartially
named Bir Kairowin. Probably water can be found under all the lower
lying parts of the hattia by digging for a few feet into the ground,
which throughout this district consists of chalk.
The wells in every case apparently give water so thick with chalk
particles that when first drawn from them it is almost as milky as
whitewash. Attempts to clear the water by passing it through a
Berkefeld filter failed, as the chalk clogged the filter after a few
strokes. But when it had been allowed to stand for a few hours, most
of the chalk settled down to the bottom, and the water that was
poured off passed quite easily through the filter, after which it proved
to be of quite good quality.
I, unfortunately, forgot to wind my watches the first night in the
hattia, and so allowed the half chronometer I had been using in
taking my observations to run down. As I was depending on it for my
longitudes, this necessitated a stay of two or three days in the camp
in order to ascertain its new rate after it had been rewound.
These watches are for some reason only made so as to run for
one day. As oversights of this kind must be of common occurrence
with travellers, it would seem to be preferable that they should be
made so as to run for two days, and be furnished with an up and
down indicator to show how long an interval has elapsed since they
were last wound.
I spent a considerable part of the time while in the hattia in trying,
without success, to get a shot at gazelle. There appeared to be very
few in the district, though a considerable number of old tracks were
to be seen where they had been feeding on the scrub.
This scarcity of game may perhaps have been due to the fact that
a few bedawin were at that time living there in charge of some
camels belonging to the Senussi zawia at Qasr Farafra. These men
kept away from the camp, but I saw them and their camels several
times wandering about in the scrub, and twice found small hovels
constructed of brushwood, in which they had been living—they had,
so far as I could see, no tents.
My men spent most of their time in grubbing about in some large
mounds. On the top of one of these, about thirty feet high, Ibrahim
found some burnt bricks. The whole mound was covered by a thick
growth of terfa bushes, among which the sand had collected,
completely hiding any building there might have been beneath it.
It must have been originally a building of some size and of
considerable height, and was perhaps a tower. The men unearthed
part of a small room at the base of the mound. It had been well built,
of the same burnt bricks, and the interior was covered with plaster. A
few pieces of broken pottery were found, one of them covered with a
green glaze. There were four or five other mounds of a similar nature
in the neighbourhood; but we had neither time nor implements
thoroughly to examine them.
As the total result of their treasure hunt in Kairowin the men only
unearthed one corpse and a few bits of broken pottery, without
finding even a single copper coin to gratify their cupidity. They were
consequently considerably disillusioned with their occupation, and I
experienced no difficulty in getting them to start for Qasr Farafra.
I made first for the main well, that is known as the Bir Kairowin, in
order to close my traverse. The water lay about eight feet below the
surface; access being gained to it by the usual sloping path, cut out
of one of its sides. By the top of the well was a mud-built trough for
watering camels, with an empty paraffin tin lying beside it for use as
a bucket.
Immediately on leaving the hattia we got into the dunes, which
cover a large area in the centre of the Farafra depression. The first
two or three dunes gave a little difficulty, but we found the rest of
them quite easy to cross. They were all, so far as I could see, of a
very elongated whalebacked type, which ran roughly from north to
south, in the direction of the prevailing wind.
Qasr Farafra lay almost due west from our camp. Soon after we
got into the sand it became clear that Qwaytin was again hopelessly
lost, as I found we were marching almost due south. I was obliged to
put it to my guide, as inoffensively as I could, that if he would change
the direction in which he was leading us by a mere right angle, we
might perhaps reach our destination, instead of going on to Dakhla
Oasis as we seemed to be doing. Qwaytin was so hopelessly lost
that he accepted my suggestion without the slightest argument.
Soon after this we got out of the sand on to level desert, where a
large number of black nodules of iron pyrites were to be seen lying
on the surface. Further on some fine specimens of sand erosion
were met with in the shape of chalk “mushrooms” and table rocks.
Otherwise this part of the desert was quite featureless. The road lay
entirely over white chalk, which caused a rather trying glare in the
blazing sunlight.
We sighted Qasr Farafra on the evening of the second day after
leaving Kairowin hattia; but as night fell before we could reach it, we
camped a few miles away from the village. Two hours’ march on the
following morning brought us into the oasis. On the outskirts we
passed a patch of ground on which the sand was encroaching, some
palms lying on the north of it being almost entirely submerged.
We camped on the northern side of the village. A large crowd of
natives came out and stood watching us while the tent was being
pitched. Among them was a sulky-looking fellow whom I was told
was the ’omda; so, as soon as the tent was pitched, I invited him and
some of the other men standing by to come in.
We had foolishly camped too close to the village, with the result
that throughout the greater part of the day the camp was surrounded
by a crowd of men and children watching all our actions, peering into
the tent, thronging round the theodolite, when I began to take
observations, and generally showing an ill-mannerly curiosity that
was in great contrast to the conduct of the natives of the other oases
in which we stayed. Farafra being the least known of the Egyptian
oases, the advent of a European was an event of such rare
occurrence that the natives had evidently decided to make the most
of it.
The natives of Farafra Oasis, who are known as the Farfaroni, or
sometimes as the Farafaroni, are a far more vigorous lot than those
of Kharga and Dakhla. They were a surly unpleasant-looking crowd.
The day after our arrival, I went out with the ’omda and Qwaytin to
see the village and plantations. With the exception of an ezba at ’Ain
Sheykh Murzuk, where there are a few houses, a Senussi zawia and
a family or two continuously resident to tend the cultivation near the
well, Qasr Farafra is the only permanently inhabited spot in the
whole Farafra depression. It is a poor little place with a total
population of about five hundred and fifty inhabitants. The houses
are of the usual mud-built type, and in most cases little better than
huts; almost the only exception being that of a square tower,
showing in places the remains of battlements, attributed, perhaps
rightly, by the natives to the Romans, who are said to have erected it
as a keep to protect the village.
This proved to be rather an interesting place. It is not inhabited,
but the door is kept locked with a watchman perpetually on guard
over it. The building is used solely as a storehouse, each family in
the village having the right to the use of one of the rooms that it
contains—there were said to be no less than one hundred and
twenty-five chambers in the building.
The ’omda showed us over the tower. The entrance lay through a
strong wooden door, at the top of a flight of steps, in a passage
entered in the middle of one of the outer walls, the walls on either
side of which were pierced with apertures, apparently intended for
use as loop-holes. The passage extended the whole height of the
building and was unroofed, in order that stones might be dropped
from above on to any assailant attempting to attack the door.
BOY WITH CROSS-BOW, FARAFRA.