Maria AliceBaptiste Ba Emmanuelrriga Geirinhas Parente Enes dos Santos Como Eu SouBaptiste Assim Emmanuel, Mapeamento Parente Enes Visual na PrActuationimeira PStrategiesessoa: forDocumento Underactuated e Índice ActuationHands: BetterStrategies Functionality & Better for Anthropomorphism Underactuated Dissertação de Doutoramento em Arte Contemporânea, orientada pelo Professor Doutor António José Olaio Correia de Carvalho e pelo Professor Doutor Carlos Vidal Hands:BetterTenes Oliveira Caseiro e ap resentadaFunctionality ao Colégio das Artes da Universidade de Coimbra& Better Dissertation presented to the University of Coimbra in order to complete the necessary requirements to Anthropomorphismobtain the Master’s degree in Biomedical Engineering Maio de 2013
Dissertation presented to the UniversitySeptember of Coimbra 2014 in order to complete the necessary requirements to obtain the Master’s degree in Biomedical Engineering
September 2014
i
Baptiste Emmanuel Parente Enes
Actuation Strategies for Underactuated Hands: Better Functionality & Better Anthropomorphism
Dissertation presented to the University of Coimbra in order to complete the necessary requirements to obtain the Master’s degree in Biomedical Engineering.
Supervisors:
Dr. Mahmoud Tavakoli (ISR - DEEC)
Prof. Dr. Lino Marques (DEEC)
Coimbra, 2014 ii This work was supported by:
iii iv Esta c´opiada tese ´efornecida na condi¸c˜aode que quem a consulta reconhece que os direitos de autor s˜aoperten¸cado autor da tese e que nenhuma cita¸c˜aoou informa¸c˜aoobtida a partir dela pode ser publicada sem a referˆenciaapropriada.
This copy of the thesis has been supplied on condition that anyone who con- sults it is understood to recognize that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement.
v vi Acknowledgments
First of all, there is a lot thank to everyone in my entourage that made part of all of this during the past 5 years... to COIMBRA, to GRONINGEN... and to all the others who helped me and contributed to make this thesis possible.
I would like to express my sincere gratitude to Prof. Dr. Lino Marques for the availability and advices during the last year, and specially to Dr. Mahmoud Tavakoli for every review, comments, opinion, solutions, problem solving and of course enthusiasm and patience.
THANKS to the guys from the lab, Tifas, Ricardo, Daniel, Bruno and Cabrita for all the breaks, the good mood and advices.
To La Sagrada Familia, Tom´e,Devesa, Ritinha, Mariana, Natas, Varalonga, Margarida & all the others I will just raise my glass and say “Se tudo correr bem, hoje (E SEMPRE) vai...”
Last but not least, to the ones that made everything possible and always believed in me, “Merci Papa, Merci Maman, Merci Doud”!
vii viii Resumo
Esta disserta¸c˜aoestuda as melhores estrat´egiasde atua¸c˜aopara m˜aosrob´oticas sub atuadas, que garantam uma melhor funcionalidade e um melhor antropomor- fismo. Este estudo divide-se em duas partes, a primeira parte foca a capacidade que uma m˜aotem de agarrar diferentes objectos de diferentes formas, enquanto que a segunda se interessa mais na capacidade de uma m˜aomimetizar movimentos de uma m˜aohumana.
Neste estudo pretende-se responder `asduas seguintes quest˜oes: 1) Como ´e que a estrat´egiade atua¸c˜aode uma m˜aoafecta a sua funcionalidade em termos de grasping? 2) Como ´eque a estrat´egiade atua¸c˜aode uma m˜aoafecta o seu antropomorfismo em termos das traject´oriasdefinidas pelos seus dedos?
Para a primeira an´alise foram definidas duas m´etricas: A diversidade das grasps, isto ´e,considerando a maior parte das grasps executadas por uma m˜ao humana; e Funcionalidade das grasps, ou seja, considerando apenas as grasps mais usadas por humanos em tarefas di´arias.A segunda an´alisebaseou-se numa m´etricaj´aexistente, chamada “Grade your hand”, em que ´ecalculado um “´Indice de Antropomorfismo”. Para tal, foram definidas e comparadas 16 estrat´egiasde atua¸c˜aoface as m´etricas definidas. Os resultados destas an´alisespodem ser uma boa orienta¸c˜aopara o design de novas vers˜oesde m˜aossub atuadas de acordo com as suas funcionalidades em termos de grasps execut´aveis e antropomorfismo.
ix Palavras-Chave: M˜aoRob´oticaSub Atuada, Pr´otese Membro Superior, Grasp- ing, Otimiza¸c˜ao,Antropomorfismo.
x Abstract
This work focuses on the best actuation strategies for underactuated robotic hands, for a better functionality and a better anthropomorphism. This study is divided in two parts: the first one focuses on the hands’ capability of grasping, while the second analysis gives more emphasis to the hands’ performance in terms of anthropomorphism.
This study intends to answer the following two questions for the underactuated anthropomorphic robotic hands: 1) How does the actuation strategy of these hands affects their functionality in terms of grasping? 2) How the actuation strategy of these hands affects their anthropomorphism in terms of finger trajectories?
For the first analysis two metrics were defined based on: Grasp Diversity, i. e., considering almost all the possible grasps by the human hand; and Grasp Functionality, i. e., only considering the highly used grasps by humans in their daily tasks. The second analysis was based on an already existing metric called ‘Grade your hand’, that calculates an “Anthropomorphism Index” for robotic hands.
Then, 16 possible actuation strategies were defined and compared based on the defined metrics. Results of these analysis can be a good guideline for de- signing novel underactuated hands with respect to their functionality in terms of achievable grasps and their anthropomorphism.
xi Keywords: Underactuated Robotic Hand, Upper Limp Prosthesis, Grasping, Optimization, Anthropomorphism.
xii Acronyms
DOF Degrees-of-Freedom
DOA Degrees-of-Actuation
CMC Carpo-Metacarpal joint
MCP Metacarpal joint
IP Interphalangeal joint
PIP Proximal Interphalangeal joint
DIP Distal Interhalangeal joint
DH Denavit-Hartenberg
VF Virtual Finger
AI Anthropomorphic Index
xiii xiv List of Figures
2.1 Forearm Anatomy and Muscles that Actuate the Fingers...... 7
2.2 Bones and Joints of the Human Hand ...... 7
2.3 Range of Motion of the Metacarpal Joint (MCP) ...... 8
2.4 Relation Between PIP and DIP Flexion, Right Index Finger. . . .9
2.5 Range of Motion of the Interphalangeal (IP) Joints...... 9
2.6 Movements and Opposition Capability of the Thumb...... 10
2.7 Degrees-of-Freedom of a Rigid Body in a Plane and Space. . . . . 11
2.8 TUAT hand Structure and DOF Representation...... 12
2.9 Closing Sequence of a 2-DOF Underactuated Finger...... 13
2.10 Denavit - Hartenberg frame assignment...... 14
2.11 Opposition Types ...... 17
2.12 Distinction between Power and Precision Grasp...... 18
2.13 The Taxonomy of Schlesinger...... 19
2.14 The Taxonomy of Cutkosky ...... 20
2.15 The Three First Synergies of the Human Hand...... 22
2.16 Commercial Prosthetic hands ...... 24
2.17 Research Prosthetic hands ...... 26
3.1 Fluxogram for Grasp Categorization...... 36
3.2 Categorization Diagram of the Grasps...... 37
3.3 Number and Symbol Designations...... 39
xv List of Figures
3.4 Fluxogram of the Evolution Idea from a 1 Actuator to a 2 Actua- tors Configuration...... 44 3.5 Fluxogram of the Evolution Idea from a 1 Actuator to a 3 Actua- tors Configuration...... 45 3.6 ISR-Softhand...... 46 3.7 Results from the First Analysis: Grasp Diversity: Total Number of Achievable Grasps for each Configuration...... 56 3.8 Results from the Second Analysis; Grasp Functionality: Frequency of Usage from the TOP10 of each Configuration ...... 56
4.1 Hypothetical Visualization of the High Dimensional Fingertip Space. 64 4.2 System Overview...... 65 4.3 Tested Hands and Respective Projection and Anthropomorphism Index (AI) of the Fingertip Movements to the Latent Space. . . . 68 4.4 Representation of the three different synergies when the hand is closed...... 73 4.5 Projection of the Fingertip Movements onto the Latent Space for the Possible Synergies ...... 76
xvi List of Tables
2.1 Underactuated Hands’ Details and Design Features...... 28
3.1 Detailed List of each Grasp...... 31
3.2 Grasp List based on the Criterias defined in Section 3.1.2 . . . . . 34
3.3 Quantitative Classification, Total Number of Achievable Grasps by the three defined Criterias...... 37
3.4 Quanlitative Classification, Grasps Numbers of the Achievable Grasps by the three defined Criterias...... 38
3.5 Configurations and Actuated Parts...... 41
3.6 Existing Underactuated Hands and Actuated Parts...... 41
3.7 Representation of 33 Grasps and imitation by the ISR-Softhand. . 47
3.8 Comparison between the Results of Configuration 3.0M and ISR- Softhand...... 49
3.9 Grasps and Configurations List - PART I ...... 52
3.10 Grasps and Configurations List - PART II ...... 53
3.11 TOP10 Grasps with Valid Configurations and Frequencies of Usage 54
3.12 Hand Gestures and Valid Configurations ...... 55
4.1 Hand Model Specifications...... 69
4.2 Hand Model Details: Segments’ Length, Joints’ Position Coordi- nates and Orientation...... 69
4.3 Configurations and Actuated Parts...... 70
xvii List of Tables
4.4 Representation of 33 Grasps and Imitation by the ISR-Softhand with the Five tested Synergies...... 72 4.5 Configurations and Executable Synergies ...... 74 4.6 Detailed Summary of the Groups presented in Section 4.5 . . . . . 80
5.1 Summary of the Results for the 3 Metrics ...... 84
xviii Contents
Acknowledgments v
Resumo vii
Abstract x
Acronyms xii
List of Figures xiii
List of Tables xvi
1 Introduction 1
1.1 Motivation ...... 1
1.2 Goals ...... 3
1.3 Thesis Outline ...... 3
2 Background 5
2.1 Anatomy of the Human Hand ...... 6
2.1.1 The Muscles & Bones ...... 6
2.1.2 Metacarpal Joint of the Fingers ...... 8
2.1.3 Interphalangeal Joints ...... 8
2.1.4 The Thumb & the Carpo-Metacarpal joint ...... 10
2.2 Robotics and Grasping Terms ...... 11
2.2.1 Degrees-of-Freedom ...... 11
xix Contents
2.2.2 Underactuation ...... 13
2.2.3 Denavit - Hartenberg Formalism ...... 14
2.2.4 Forward Kinematics ...... 15
2.2.5 Workspace ...... 16
2.2.6 Grasp Definition ...... 16
2.2.7 Prehension ...... 16
2.2.8 Oppostion Types ...... 17
2.2.9 Power, Precision & Intermediate Grasp ...... 17
2.2.10 Grasp Taxonomies ...... 18
2.2.11 Synergy ...... 21
2.3 Underactuated Robotic Prosthetic Hands ...... 22
2.3.1 Commercial Prosthetic Hands ...... 22
2.3.2 Research Prosthetic Hands ...... 24
2.3.3 Summary ...... 26
3 Actuation Strategies for Underactuated Hands 29
3.1 Categorization of the Grasps ...... 30
3.1.1 Grasps Details ...... 30
3.1.2 Criteria Definition ...... 31
3.1.3 Categorization of the Grasps according to the Selected Cri- terias ...... 33
3.2 Configurations ...... 38
3.2.1 Configurations Description ...... 38
3.2.2 Evolution of Configurations ...... 42
3.3 Case Study: Validation of the Categorization ...... 46
3.4 Grasp Diversity ...... 49
3.5 Grasp Functionality ...... 50
3.6 Human Gestures ...... 54
3.7 Results ...... 56
xx CONTENTS
3.8 Discussion ...... 56
3.8.1 Grasp Diversity ...... 57
3.8.2 Grasp Functionality ...... 58
3.8.3 Actuation Strategy for performing all 33 grasps ...... 59
4 Evaluation of Anthropomorphic Performances 61
4.1 Anthropomorphism ...... 62
4.2 Methodology ...... 62
4.2.1 System Overview ...... 63
4.2.2 ‘Grade your hand’ Toolbox Description ...... 64
4.2.3 Latent Space ...... 66
4.2.4 Tested Hands ...... 67
4.3 Specifications ...... 68
4.3.1 Hand Model ...... 68
4.3.2 Configurations ...... 69
4.3.3 Synergies ...... 70
4.4 Analysis: Configurations vs. Synergies ...... 73
4.5 Results ...... 74
4.5.1 Group I ...... 75
4.5.2 Group II ...... 75
4.5.3 Group III ...... 77
4.5.4 Group IV ...... 77
4.5.5 Group V ...... 78
4.5.6 Group VI ...... 78
4.6 Discussion ...... 79
4.6.1 3-Actuators Configurations Comparision ...... 80
4.6.2 4-Actuators Configurations Comparision ...... 81
5 Conclusion 83
5.1 Future Work ...... 86
xxi Contents
Appendix Appendices 95
Appendix Publications 97
Appendix MATLAB®Codes 99
xxii Chapter 1
Introduction
1.1 Motivation
Over the years the need to develop new technologies and instrumentation to improve the daily activities of the human kind have arisen. Robotics have shown to have a huge impact in improving people’s life quality either in industrial activities or for physically handicapped people. To do so special machineries were created. However, here the focus is given to robotic hands.
The most frequent causes for upper limb amputation are trauma and cancer, followed by vascular complications of disease [1]. With the technological evolu- tion, the development of upper limb prosthesis and consequently robotic hands became possible. A prosthetic device can be of great benefit to the amputee in the performance of everyday human tasks.
The hand is a masterpiece of the human body as it allows us to interact with the world that surrounds us. Since the early beginning, the first sensations and knowledge are acquired by the usage of the hands. The hand works as a tool, it serves as eyes for the blind, the mute talk with it, and it is used nowadays as a symbol of salutation.
1 Chapter 1. Introduction
Unfortunately, not all the upper limb amputees can receive a prosthetic service. This can be due to the technology price, emerging then the need to develop devices with great functionality while keeping the price low.
Prosthetic devices, in this case robotic hands, have become of great interest in the robotics community. Several hands have been developed over the years that differ in terms of mechanical structure, actuation, design, performance and so on.
Anthropomorphic robotic hands that have been developed so far for industrial and prosthetic purposes can be roughly categorized as fully actuated hands [2], [3], [4], [5] and highly underactuated [6], [7], [8], [9].
The former group has many actuators, placed on the forearm or in the hand itself, by the sacrifice of the weight and the size of the hand and the actuation power. These hands can grasp and manipulate a wide range of objects by apply- ing a complex control strategy. Yet, due to their electromechanical and control architecture complexity, they are not the best option for many applications that demand simplicity, lightness and low cost.
The underactuated hands usually contain 1 to 6 actuators (compared to the 34 muscles that controls human hand). They offer the following advantages [10] over the former group:
• Simpler electro mechanical structure.
• Lower weight, size and price.
• Simpler control architecture.
The human hand has an average weight of 400g [11]. However, prosthetic terminal devices of similar weight have been described as being too heavy by users [12]. With the current technologies it is probably not possible to construct a fully actuated hand lighter than 400g. For this reason fully actuated prosthetic hands are not being commercialized for prosthetic applications.
2 1.2. GOALS
Here, the need for optimization and a step towards simple, lightweight and low cost hands with good functionality and anthropomorphic static and dynamic appearance emerges.
1.2 Goals
This project focuses on the best actuation policy for underactuated robotic hands, for a better functionality and a better anthropomorphism. To do so, two different analyses are proposed: the first one is based on the hands´ capability of grasping where as the second one focuses on the hands’ performance in terms of anthropomorphism.
The goal here is to understand how an underactuated robotic hand should be designed in order to achieve different levels of functionality and anthropomor- phism according to the desired purpose.
At the end of this dissertation, answers to questions like How many actuators are needed for a performant underactuated hand? Where and how should the actuators be placed? Is there the need to take into account any special design feature? will be answered.
1.3 Thesis Outline
This thesis is divided in five chapters. The first chapter presents an introduc- tion to the problem and a brief approach and description of the project itself.
Chapter 2 presents the necessary theoretical concepts in human hand anatomy and defines relevant terms that are used in robotics community, as well as the state of the art, which includes previous works in the area of grasping and un- deractuated robotic hands, and their metrics and optimization.
3 Chapter 1. Introduction
Chapter 3 develops a metric to analyze several actuation strategies proposed against an extensive list of grasps as well as the most used grasps in daily tasks. These analyses define the best actuation strategies for different number of actu- ators that are dedicated to the movement of an anthropomorphic hand.
Chapter 4 presents an evaluation of the anthropomorphism level of the con- figurations that were defined in Chapter 3. Here, a measure to determine the anthropomorphism of artificial hands in a low dimensional space is presented based on a recent method that was developed for grading such hands.
Finally, chapter 5 concludes this thesis and sums up all the results achieved in the thesis and proposes the best way to optimize the design and performance of underactuated hands.
4 Chapter 2
Background
This section is dedicated to background informations and researches that cov- ers the interests of this thesis.
The first section (Section 2.1) is dedicated to the anatomy of the hand in order to understand the biomechanics of the hand, the actuation of the fingers and underactuation of the joints in human hand. A special emphasis is given to the thumb due to its differences from the other fingers.
Section 2.2 is about some robotic and mathematical terms that should be known in order to have a better understanding of this thesis. Also in this section the grasping theory is presented: What is a grasp? What kind of grasps exist? How different are grasps from each other?
The last section (Section 2.3) refers to the already developed commercial and research robotic underactuated hands. They are compared according to their Degrees-of-Freedom (DOF), Degrees-of-Actuation (DOA) and design features. This section is important to understand the actuation strategies that have been used in the developed hands so far.
5 Chapter 2. Background
2.1 Anatomy of the Human Hand
This section briefly describes some details about the human hand anatomy. Special focus is given to the joints of the fingers and the thumb itself due to its uniques features.
2.1.1 The Muscles & Bones
The major part of the hand and wrist muscles lie in the forearm and, nar- rowing into tendons, traverse the wrist reaching insertions in the hand’s bones or ligaments. Due to its high levels of complexity and dexterity the human hand needs a lot of different muscles in order to achieve its great level of independence between its joints [13], [14].
The muscles located in the forearm, extensor (Fig. 2.1a) and flexor (Fig. 2.1b) 1, are the ones that drive the fingers movements. Controlled movements involve at least a pair of muscles: agonist and antagonist muscles. The agonist causes the movement whereas the antagonist produces the opposite action [15].
Generally the bones of the hand are grouped into the carpus (carpals bones), eight bones that form the wrist and the root of the hand, and the digits, each composed by metacarpals and phalangeal bones. In each digit, except from the thumb (described later in Section 2.1.4) due to its unique features, the anatomical design is the same: one metacarpal bone and three phalanges as shown in Fig. 2.2. The metacarpals are capable of doing some flexion and extension, however for some of them the independent flexion is limited. The axes of the metacarpals are arched which gives the form to the palm [16].
1These images show the large number of muscles that drive the fingers (the name of the muscles are not of interest for this thesis).
6 2.1. ANATOMY OF THE HUMAN HAND
(a) Extensor Muscles on the Forearm.
(b) Flexor Muscles on the Forearm.
Figure 2.1: Forearm Anatomy and Muscles that Actuate the Fingers [13].
Figure 2.2: Bones and Joints of the Human Hand (Left hand dorsal view) [17]; CMC-Carpo-Metacarpal, MCP-Metacarpal, IP-Interphalangeal, PIP-Proximal Inter- phalangeal, DIP-Distal Interhalangeal joints.
7 Chapter 2. Background
2.1.2 Metacarpal Joint of the Fingers
The metacarpal joint (MCP) is a two DOF joint. It enables movement about two axes: flexion/extension and adduction/abduction [18]. The MCP joint has a:
• Maximum flexion of about 90o that increases from the index to the little finger (Fig. 2.3a).
• Variable active flexion that can reach up to 30o to 40o (Fig. 2.3b).
• Passive extension that can reach up to 90o (Fig 2.3c).
• Side-to-side movement (abduction/adduction) of 30o for the index (Fig. 2.3d, (A)Abduction and (B)Adduction).
(a) (b) (c) (d)
Figure 2.3: Range of Motion of the Metacarpal Joint (MCP) [18].
2.1.3 Interphalangeal Joints
All the fingers, except from the thumb (that will be discussed in Section 2.1.4), have two Interphalangeal (IP) joints: the Proximal interphalangeal (PIP) and the Distal interphalangeal (DIP) joint. These joints are hinge joints, i.e., they have one Degree-of-Freedom (DOF) only which are used for flexion and extension of the fingers.
8 2.1. ANATOMY OF THE HUMAN HAND
Figure 2.4: Relation Between PIP and DIP Flexion, Right Index Finger [19]
The capability for flexion in these joints is much greater than extension. The motion of these two joints are coupled together, as shown in Fig. 2.4, with flexion at the PIP joint being more extensive than at the DIP joint of the same digit [19].
According to [18] about the PIP and DIP joint, it is stated that:
• The range of flexion in the PIP joints is greater than 90o and the DIP joints slightly less than 90o (Fig. 2.5a).
• The range increases from the second to fifth finger to reach a maximum of 135o with the latter (Fig. 2.5b).
• The range for PIP extension is zero and for active DIP extension zero or trivial (Fig. 2.5c, (D) DIP and (P) PIP joints).
(a) (b) (c)
Figure 2.5: Range of Motion of the Interphalangeal (IP) Joints [18].
9 Chapter 2. Background
2.1.4 The Thumb & the Carpo-Metacarpal joint
The thumb differs from the other digits first in that the second phalanx is miss- ing and, second, in that there is greater mobility in the Carpo-Metacarpal(CMC) joint. It plays a unique role in the function of the hand. Its movements include extension (position of reference, Fig. 2.6a), flexion (Fig. 2.6b), adduction and abduction (Fig. 2.6c). The opposition capability of the thumb is also shown in Fig. 2.6d [18]. The human thumb’s opposability and strength is fundamental to the hand’s interaction with and manipulation of objects [20]. Thus, without the thumb, the hand loses most of its capabilities.
The kinematic structure of the thumb is much more complex than the other fingers as the thumb has more than only one DOF. The IP joint is described as having only one rotational Degree-of-Freedom whereas the same does not happen for the MCP and CMC joints. According to their motion, the MCP and CMC joints (Fig. 2.2) are considered to be universal joints, which have two perpen- dicular and intersecting axes allowing flexion/extension and abduction/adduc- tion [21]. To sum up, five DOF are necessary and adequate to achieve the overall functionality of the thumb.
(a) Extension (b) Flexion (c) Abduction (d) Opposition
Figure 2.6: Movements and Opposition Capability of the Thumb [22].
10 2.2. ROBOTICS AND GRASPING TERMS
2.2 Robotics and Grasping Terms
In this Section some of the terms that are used in the robotics and grasping community are defined and briefly described.
2.2.1 Degrees-of-Freedom
Several definitions for the number of Degrees-of-Freedom (DOF) of a system were defined according to the area that it belongs to (e.g.: robotics, mechanics, grasping community and so on).
Generally speaking, “the Degrees-of-Freedom of a rigid body is defined as the number of independent movements it has” [23]. Fig. 2.7a shows a rigid body in a plane. In a 2D plane there are 3 DOF. The number of DOF is given by the distinct ways the bar can be moved, i. e., the bar can be translated along the x axis, along y axis, and rotated about its centroid. However, a rigid body in space has six degrees of freedom: three translating motions along the x, y and z axes and three rotary motions around the x, y and z axes respectively.
(a) In Plane (b) In Space.
Figure 2.7: Degrees-of-Freedom of a Rigid Body in(a )a Plane and (b) Space [23].
Nevertheless, in the grasp community there is no consensus in the definition of DOF. In [24] another definition is proposed: “the number of joints of a ma- nipulator determines also its number of Degrees-of-Freedom (DOF)”. The same
11 Chapter 2. Background definition is used for instance in the TUAT hand [25] (presented in Section 2.3). This robotic hand is considered as a 21 DOF driven by only one actuator. The high number of DOF is justified by the number and types of joints used in its design: there are six 2-DOF ball joints and nine 1-DOF joints (one for the thumb and two for each of the other fingers) (Fig. 2.8).
Figure 2.8: TUAT hand Structure and DOF Representation [25].
Nonetheless, when two joints of a kinematic chain are coupled, the DOF are reduced by one. This happen when the rotation of one joint is influenced by the rotation of another joint. This feature and designation of DOF can be found in all the commercial underactuated hand presented in Section 2.3.1. In other words, the definition of DOF presented in these many research works is that the number of DOF of a system is the number of independent variables necessary to define completely the condition of the system. To sum up, the TUAT hand presented in [25] is actuated with only one actuator, and therefore, one can consider that due to its underactuated mechanism, all links are related to each other, becoming then 1 DOF mechanism.
12 2.2. ROBOTICS AND GRASPING TERMS
2.2.2 Underactuation
An underactuated mechanism is one which has fewer number of actuators than DOFs. When applied to mechanical fingers, the concept of underactuation leads to selfadaptability, i e., with some adaptive mechanisms underactuated fingers can envelope the objects to be grasped and automatically adapt to their shape with only one actuator and without complex control strategies. In order to obtain a determined system, elastic elements and mechanical limits can be introduced in underactuated mechanisms. While a finger is closing on an object, the configuration of the finger is determined by the external constraints associated with the object. When the object is fully grasped, the force applied at the actuator is distributed among the phalanges [26], [27].
Figure 2.9: Closing Sequence of a 2-DOF Underactuated Finger [6].
An example of an underactuated 2-DOF finger is shown in Fig. 2.9 [6]. The finger is actuated through the lower link, as can be seen by the arrow in the figure, and a spring is used to maintain the finger fully extended. A mechanical limit is set so the phalanges are aligned under the action of this spring when no external forces are applied on them. In the first two steps of the figure, the finger behaves as a single rigid body in rotation around a fixed pivot. When the proximal phalanx makes contact with the object, the second phalanx is rotated away from the mechanical limit, and the finger close on the object since the
13 Chapter 2. Background proximal phalanx is constrained. During this phase, the actuator produces the force required to extend the spring and both phalanges are in contact with the object, completing the shape adaptation phase.
2.2.3 Denavit - Hartenberg Formalism
Denavit–Hartenberg developed four parameters (also called DH parameters) that are associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain [28].
A link may be considered as a rigid body defining the relationship between two neighbours joint axes and can be specified by two numbers, the link length
(ai) and link twist (αi), which define the relative location of the two axes in space. The joints may be described by two parameters. The joint offset (di) is the distance from one link to the next along the axis of the joint and the joint angle (θi) is the rotation of one link with respect to the next about the joint axis.
Figure 2.10: Denavit - Hartenberg frame assignment [29].
To facilitate describing the location of each link a coordinate frame is affixed to it — frame i is attached to link i (Fig. 2.10). Denavit and Hartenberg proposed a matrix method of systematically assigning coordinate systems to each link of an articulated chain [29]. The link and joint parameters can be summarized as:
14 2.2. ROBOTICS AND GRASPING TERMS
ai = distance along xi from oi to the intersection of the xi and zi−1 axes.
di = distance along zi−1 from oi−1 to the intersection of the xi and zi−1 axes. di is variable if joint i is prismatic.
αi = the angle between zi−1 and zi about xi.
θi = the angle between xi−1 and xi about zi−1. θi is variable if joint i is revolute.
The transformation matrix Ai corresponding to link i is given by the following relation:
Ai = Rotz,θi T ransz,di T ransx,ai Rotx,αi = (2.1)
cosθi −sinθicosαi sinθisinαi aicosθi sinθi cosθicosαi −cosθisinαi aisinθi = 0 sinα cosα d i i i 0 0 0 1
Finally, the full transformation from the base frame to the end effector frame is given by multiplying all the transformation matrices corresponding to the links li.
0 H = Tn = A1(l1)...An(ln) (2.2)
The Denavit Hartenberg (DH) formalism is used to define the hand models in Section 4
2.2.4 Forward Kinematics
The forward kinematics goal is to find the positions and orientation of the end-effector relative to the base given the positions of all joints and the values of all the geometric link parameters [27]. In most cases, the DH parameters are used to calculate the forward kinematics.
15 Chapter 2. Background
2.2.5 Workspace
The workspace of a robotic manipulator is the total volume swept out by the end-effector as the manipulator executes all possible motions. The workspace is determined by the geometry of the manipulator and the limits of the joint motions [27].
2.2.6 Grasp Definition
In order to manipulate objects they first need to grasped. Depending on the desirable task to be executed different configurations can be adopted by the human hand, emerging then the need to define this called term grasps. Although there is no consensus in the literature on how the human grasp is defined, here the definiton of grasp is based on the one defined by Feix et al. [30]:
“A grasp is every static hand posture with which an object can be held securely with one hand, irrespective of the hand orientation.”
2.2.7 Prehension
The motions of the hand are divided into two main groups [31]:
Prehensile Movements or movements in which an object is seized and held partly or wholly within the compass of the hand.
Non-Prehensile Movements or movements in which no grasping or seizing is involved but by which objects can be manipulated by pushing or lifting motions of the hand as a whole or a of the digits individually.
16 2.2. ROBOTICS AND GRASPING TERMS
2.2.8 Oppostion Types
Basically, there are three kinds of opposition types in which the hand can grasp an object and hold it securely [32], [33]. Those oppositions are:
Pad Opposition It is the opposition between the pads of one or more fingers and the thumb pad along a direction parallel to the palm (Fig. 2.11a).
Palm Opposition It is the opposition between the digits and the palm. The object is fixed in hand coordinates along an axis normal to the palm of the hand (Fig. 2.11b). Greater stability is achieved in this opposition type.
Side Opposition It is the opposition between the thumb pad and the side of the index finger, or between the sides of the fingers (Fig. 2.11c).
(a) Pad Opposition (b) Palm Opposition (c) Side Opposition
Figure 2.11: Opposition Types [32].
2.2.9 Power, Precision & Intermediate Grasp
A grasp is considered as a:
Power Grasp when the object is held in a clamp formed by the fingers and the palm (Fig. 2.12a). Used when the required task needs stability and security.
17 Chapter 2. Background
Precision Grasp when the object is pinched between the fingers and the opposing thumb (Fig. 2.12b). Used when the required task needs sensitivity and dexterity.
Later, Kamakura et al. [34] introduced a third classification, the Intermediate Grasp. Here, the power and precision are equally needed and the palm is not included as contact area.
(a) Power Grasp (b) Precision Grasp
Figure 2.12: Distinction between Power and Precision Grasp [31].
2.2.10 Grasp Taxonomies
A lot of studies have been performed for categorization of the grasps. Different approaches have been taken resulting then in several categorizations. Here some of the most relevant taxonomies will be presented.
Schlesinger (1919) This was the first grasp categorization in which six human grasps types were defined: cylindrical, tip, hook, spherical and lateral, as shown in Fig. 2.13 [35].
Kapandji et al. (1982) Kapandji [18] classified grasps into several categories: Static Grasps, Grav- ity Dependent and Dynamic Grasps. However, for the purpose of this thesis and according to the chosen definition of grasp (Section 2.2.6), only one of them is of interest: the Stratic Grasps. The grasps were classified by the
18 2.2. ROBOTICS AND GRASPING TERMS
hand parts which are in contact with the object. This can be either the fingers, the palm or Symmetrical Grasps. Within these categories there are additional properties which focus on the number of fingers in use.
Figure 2.13: The Taxonomy of Schlesinger [36].
Elliot and Conolly (1984) They described three general classes of within-hand (intrinsic) manipulation movements: simple synergies, reciprocal synergies, and sequential patterns. Here intrinsic movements are defined as coordinated movements of the digits to manipulate an object within the hand. Simple synergies are defined as those in which all digits involved move as one unit (e.g., pinching or squeezing). In reciprocal synergies, by contrast, the fingers move together, but the thumb moves independently. In sequential patterns, the digits move independently in a repeatable sequence [37].
Cutkosky (1989) From this taxonomy 16 different grasp patterns were generated. It was de- fined based on surveys on professional machinists and the previous works of Schlesinger and Napier (presented in Section 2.2.9). The Cutkosky tax- onomy tree, shown in Fig. 2.14, is first divided into power and precision
19 Chapter 2. Background
Figure 2.14: The Taxonomy of Cutkosky [38].
grasps from left to right, and by shape and function down the tree [38].
Feix et al. (2011) This comprehensive taxonomy [39] [40] is the most recent one and reaches a total of 33 different grasps that are distinguished by their: type, opposition type, thumb position and the concept of virtual fingers 2, where:
• The grasp type category can be defined as in Section 2.2.9: power, precision or intermediate.
• The opposition types are the one mentioned in 2.2.8: pad, palm or side opposition.
2Virtual Finger (VF): when more than one finger work together as a functional unit.
20 2.2. ROBOTICS AND GRASPING TERMS
• The position of the thumb that can be either abducted or adducted.
• Virtual Fingers that can be: VF1, the first Virtual Finger (VF); VF2, the second virtual finger, which acts against VF1; VF3, some grasp types also use a third virtual finger.
From the taxonomies mentioned in this section, the last one (Feix et al. [39]) is considered as the most complete one with the largest number of grasps. Here 33 grasps are listed whereas there are only 6 and 16 different grasps presented in the Schlesinger [35] and Cutkosky [38] taxonomies respectively. Till then, from the mentioned taxonomies, the one from Kapandji et al. [18] was the largest taxonomy with 24 grasp types.
2.2.11 Synergy
A keypoint for the grasps’ achievement is the way a hand moves till it grasps the object. The coordination phase in which the hand shapes itself before con- tacting with the grasped object is called synergy. A synergy can also be defined as the relation between the joints’ movements [41].
Special focus is given to synergies while talking about underactuation. This coordination facilitates the interaction between the multiple elements present in a robotic hand as it simplifies the selection of control inputs for a given behavioral goal. Fig. 2.15 shows the three first defined synergies of the human hand [42].
A different approach of synergy can be done: Muscle Synergy. Muscle synergy is defined as “the coordinated recruitment of a group of muscles with specific activation balances or specific activation waveforms. Recent experiments have indicated that many motor behaviors are controlled through the flexible combi- nation of a small number of muscle synergies. This mechanism is believed to simplify the selection of the appropriate muscle commands for a given behavioral goal” [43].
21 Chapter 2. Background
(a) (b) (c)
Figure 2.15: The Three First Synergies of the Human Hand: (a) First, (b) Second and (c) Third synergy. Rows (top to bottom) correspond to negative, null (average) and positive intensities [42].
2.3 Underactuated Robotic Prosthetic Hands
This section presents a review of several underactuated hands, which are either a prototype in a reasearch center or a commercialized product as well as their design specifications. The presented hands are then categorized based on their number of actuators.
2.3.1 Commercial Prosthetic Hands
Note that here, DOF does not imply independent movements, and presents only the number of single axis joints, whether they are independent, or coupled with another joint with an external mechanism.
One Actuator Sensorhand (Fig. 2.16a) is a 1-DOF, 1-DOA commercial prosthetic hand. It includes only 1 actuator that actuates the thumb, index and middle finger. The other two fingers have only an aesthetic purpose [44].
Two Actuators Michelangelo (Fig. 2.16b) is a 2-DOF, 2-DOA commercial anthropomor-
22 2.3. UNDERACTUATED ROBOTIC PROSTHETIC HANDS
phic prosthetic hand. It includes 2 actuators, one for closing all the fingers and another one for changing the angle of the thumb. A small motor changes the path that the thumb will take when the main motor actuates to close the hand either in a palmer or lateral grasp [45] [46].
Five Actuators iLIMB (Fig. 2.16c) is a 6-DOF, 5-DOA commercial prosthetic hand. It includes 1 actuator per each finger (total 5 actuators) which directly ac- tuates the respective metacarpophalangeal joint flexion. The thumb ab- duction/adduction movement is not motorized and is performed manually. The abduction/adduction movement is actually limited to two possible po- sitions at approximately 90o around an axis parallel to the wrist axis. At these positions a locking mechanism locks the thumb position. To alter- nate this position an external force is applied by the other hand, so that the thumb rotates around the mentioned axis until it locks in the second position [47], [48].
BeBionic (Fig. 2.16d) is a 6-DOF, 5-DOA commercial prosthetic hand. It includes 1 actuator per each finger (total 5 actuators) but in contrast to iLIMB hand the motors are placed in the mid-hand (metacarpus). The thumb abduction/adduction is manual. [47], [49].
Six Actuators Vincent hand (Fig. 2.16e) is a 6-DOF , 6-DOA commercial prosthetic hand. It has 1 actuator for each finger except from the thumb that is double actuated,o ne for the thumb abduction/adduction movement and another one for the thumb flexion (total 6 actuators) [50].The metacarpophalangeal joint flexion is moved directly by gears. The metacarpophalangeal joint of the thumb, for flexion and abduction/adduction, is moved using two separate actuators. The hand prosthesis has 10 movable joints, which can be actively moved in the direction of flexion and extension [47].
23 Chapter 2. Background
(b) Michelangelo (a) Sensorhand [44] hand [45]
(c) iLimb [48] (d) Bebionic [49] (e) Vincent hand [50]
Figure 2.16: Commercial Prosthetic hands
2.3.2 Research Prosthetic Hands
Here, the defined DOF of each hand are the one mentioned by the authors of the developed robotic hands. The number of DOF presented for these hands are related to the number of joints that belong to the hand structure, as defined in Section 2.2.1 for the TUAT hand.
One Actuator TUAT hand (Fig. 2.17a) is a 21-DOF, 1-DOA research prosthetic hand. The thumb’s rotation axis is placed at 6.5o from the wrist axis. The thumb only operates to fix the object position as a fulcrum [25]. Other details about the TUAT hand structure were already defined in Section 2.2.1.
Two Actuators KNU hand (Fig. 2.17b) is a research prosthetic hand with 16-DOF and
24 2.3. UNDERACTUATED ROBOTIC PROSTHETIC HANDS
2-DOA. It includes 2 actuators, one for the thumb flexion, another actuator for the other 4 fingers and one Geneva wheel. The approach used for the ab/ad of the thumb is the same as in the MANUS hand [7], but as the interphalangeal joint is coupled with the carpometacarpal joint a complex driven path is required to transmit the motor’s power. Thus to achieve this feature an external Geneva and crank-slider mechanism is used [51].
Three Actuators Kazuki Mitsui et al. (Fig. 2.17c) developed a 3-DOA underactuated anthropomorphic hand. It includes 3 actuators and one solenoid. One actuator for the thumb flexion, one for the index flexion and another one for the other three fingers. Yet through an innovative design a solenoid is embedded into the thumb axis, which enables the ab/ad of the thumb when necessary [52].
MANUS hand (Fig. 2.17d) is a 3-DOF, 3-DOA research anthropomor- phic prosthetic hand. It includes 3 actuators and one Geneva wheel. One actuator for the thumb, one for the other four fingers and one for the wrist. A different design purpose was tested using a Geneva-wheel based mecha- nism which enables the thumb to move into 2 planes with only one motor actuating it, the thumb has a coupled flexion and abduction/adduction [7].
Four Actuators Smarthand (Fig. 2.17e) is a 16-DOF, 4-DOA underactuated anthropo- morphic hand. It includes 4 actuators all located inside the palm structure. The first actuator drives the thumb flexion/extension, the second one drives the index flexion/extension, the third one actuates the middle, ring and little finger flexion/extension and the fourth one actuated the thumb ab- duction/adduction [53]. The flexion/extension metacarpophalangeal joint is directly connected onto an extension of the brushed DC motor shaft; A certain degree of non-back-drivability is achieved by means of a high re-
25 Chapter 2. Background
duction, this actually, allows slight adaptation of the thumb axis while it is closed against the other fingers in a precision grasp [54], [55].
Five Actuators Meka H2 (Fig. 2.17f) is a 12-DOF, 5-DOA compliant four finger hand (the little finger is eliminated). There is 1 actuator per each finger and another one for the thumb abduction/adduction movement (total 5 actuators) [56], [57].
(a) TUAT hand [25] (b) KNU hand [51] (c) Kazuki Mitsui et al. (2013) [52]
(d) MANUS hand [7] (e) Smarthand [53] (f) Meka H2 [56]
Figure 2.17: Research Prosthetic hands
2.3.3 Summary
In some designs, some innovative features allowed to use a single actuator for actuation of more than one axis, mostly by combining the thumb flexion and abduction, thus allowing for reduction of the total number of actuators. This
26 2.3. UNDERACTUATED ROBOTIC PROSTHETIC HANDS can be seen in the 3-DOF prosthetic hand presented in [7], [52], where a solenoid enables or disables the abduction/adduction movement of the hand, and thus one actuator with the help of a small solenoid operates both flexion and abduction of the thumb. In some cases the thumb flexion and ab/ad movements are coupled in a single movement [58], [59], [60].
27 Chapter 2. Background o 5 , Thumb’s axis of rotation at 6 Ball joints External Geneva wheel and crank-slider mechanism Solenoid Geneva wheel One actuator for the wrist MCP joint flexion connected onto an extensionMotors of allocated the in brushed the DC metacarpus motor shaft Manual ab/ad of the thumb Compliant four fingers hand with tactile sensors. † † † † * Underactuated Hands’ Details and Design Features. Table 2.1: The authors do not define how many DOF the hand have. The definition of DOF here is different from the one in Section 2.2.1. This happen frequently for research hands in which the number of DOF is considered Underactuated HandsSensorHand [44] Hand type #actuators #DOFTUAT Hand [25]KNU Commercial Hand [51]Michelangelo [45] 1 ResearchKazuki Mitsui et al. [52] 1MANUS 1 Hand Research [7] Commercial ResearchSmartHand Design [53] 21 Features 2 2 3Bebionic [47] Research 16 2 - iLimb [48] 3 ResearchMeka H2 [56]Vincent 4 Commercial Hand 3 [50] 5 16 Commercial Commercial Research 6 5 6 5 6 6 Manual 12 ab/ad of the MCP thumb joint moved by gears. * † to be equal the number of joints of a robotic hand.
28 Chapter 3
Actuation Strategies for Underactuated Hands
This chapter aims to analyze the number of actuators as well as the actuation strategy for an underactuated hand. 16 possible configurations in five categories of 1 to 5 actuators were defined. Criterias were defined in order to analyze which of the grasps are possible for each actuation policy.
Then, based on these actuation strategies, the configurations are evaluated in terms of grasp diversity and functionality. A performance metric was defined in the first analysis, based on all possible grasps by the human hand, whereas in the second one, only the top grasps with the highest usage frequencies were considered. According to this, results are obtained regarding the best actuation strategies for underactuated hands.
29 Chapter 3. Actuation Strategies for Underactuated Hands
3.1 Categorization of the Grasps
As mentioned previously in Section 2.2.10, several analyses have been per- formed in order to define the grasps used by human hand. From those, the one from Feix et al. [30] [40] has shown to be the most comprehensive study, contain- ing 33 different grasps.
First of all, for a detailed and a valid analysis, several criterias were defined. Based on these criterias the grasps will be categorized, which facilitates the anal- ysis for the “Grasp Diversity” in Section 3.4 and consequently for the “Grasp Functionality” in Section 3.5.
3.1.1 Grasps Details
From the list of 33 grasps [40], several characteristics were identified and listed, as shown in Table 3.1. These aspects were noted down for all grasps regarding the position and the role of each finger during the grasp.
The following five aspects for each grasp were defined:
1. The closing of the fingers: Do all fingers close for the grasp or not?
2. The thumb CMC joint position: Adduction (0o), Abduction (90o) or in an intermediate position (I).
3. Temporal delay between the closing of the fingers: Do all fingers close simultaneously or not?
4. The direction of the applied force by the thumb: To realize the grasp, Should the thumb apply a flexion force or also a side force is applied?
5. The need of having an abduction/adduction actuator for the index (2) and middle (3) fingers (A2,3). Note that this aspect is different from aspect 4
30 3.1. CATEGORIZATION OF THE GRASPS
Table 3.1: Detailed List of each Grasp, [X] means that the condition is checked.
Grasp Fingers closed Thumb at Closing Force applied A2,3 No. All Not all 90o I 0o delay flexion side 1 X X X 2 X X X X 3 X X X X 4 X X X X 5 X X X 6 X X X 7 X X X 8 X X X 9 X X X 10 X X X 11 X X X 12 X X X 13 X X X 14 X X X 15 X X X 16 X X X 17 X X X 18 X X X 19 X X X 20 X X X 21 X X X 22 X X X 23 X X X X 24 X X X 25 X X X X 26 X X X 27 X X X 28 X X X 29 X X X X 30 X X X 31 X X X 32 X X X 33 X X X 23 10 19 5 9 30 3 Total 5 1 33 33 33
as here the side force is applied by the index and middle fingers and not by the thumb.
3.1.2 Criteria Definition
For a simpler analysis and presentation of the results, three criterias based on the above 5 aspects were defined. Note that the criterias were applied after several attempts of categorization of the grasps. Some of the above aspects can be combined in order to form three more comprehensive criterias. For instance the closure of the fingers (aspect 1) and the temporal delay between their closure (aspect 2) are two unique aspects of each grasp. There are grasps (for instance, grasp no. 2) that check aspect 1, but cannot check aspect 2. For instance, in grasp no. 2, the thumb needs to be closed after other fingers. But, for a more clear presentation of the results, the main criterias were limited to three, and aspect 2 was not considered as a criteria, but it will be still considered during the analysis, as will be seen in the next section.
31 Chapter 3. Actuation Strategies for Underactuated Hands
Therefore the defined criterias are:
Fingers’ Closure
For a selected grasp which finger(s) close, and if all of them close simultane- ously. This is important to distinguish in order to know if the finger/set of fingers require an independent actuator or can be actuated along others.
CONSEQUENCE:
• A: If a finger is closed/flexed it means that it has to be actuated.
• NA: For a particular grasp, if a finger does not close/flex, or closes less than the other fingers, or close with a delay in respect to others, it means this finger has to be actuated independently.
Position of the Thumb
Here three subcategories are possible:
• 90o - Abduction: The thumb is perpendicular to the palm.
• Intermediate (I): The thumb is in an intermediate position (between 0o and 90o).
• 0o - Adduction: The thumb is parallel to the palm.
CONSEQUENCE:
• If the grasp belongs to the first category (90o) it means that the thumb does not need to be ab/ad actuated.
• If it belongs to the second category (I) it has to be ab/ad actuated
• If it belongs to the third (0o) it means that the ab/ad of the thumb should be actuated, but the manual thumb actuation is also a valid choice for the
32 3.1. CATEGORIZATION OF THE GRASPS
grasp.
It should be noted that in this case the thumb is considered to be at the first option (Thumb at 90o) as default. This will be later described more. But basically in order to minimize the number of actuators, the default position chosen is the one which contains a higher number of grasps in its category.
Direction of the Applied Force
In some grasps the force applied by the fingers is in the direction of the fingers’ flexion whereas in other grasps the force is applied by the side of the fingers.
CONSEQUENCE:
• f: If the force is applied by the flexion action it means that an actuation is needed for the finger’s flexion.
• s: If the force is applied by the side of the fingers it means that to per- form this grasp the actuation of the abduction/adduction of the finger(s) is needed.
3.1.3 Categorization of the Grasps according to the Se-
lected Criterias
Following the information provided in Section 3.1.2 it is possible to reschedule Table 3.1 with the defined criterias. The results are shown in Table 3.2. While based on the defined criterias, it was straight forward to categorize the grasps, in order to be sure about a valid categorization and the actuation forces, all of the 33 grasps were performed by a human hand, and also by the ISR-Softhand.
ISR-Softhand is a recent development of ISR investigation group [61], that takes advantage of elastic joints and is based on the 3.0M configuration (described
33 Chapter 3. Actuation Strategies for Underactuated Hands
Table 3.2: Grasp List based on the Criterias defined in Section 3.1.2.
Fingers Thumb Force Fingers Thumb Force No. Name Picture No. Name Picture closed at __º applied closed at __º applied
Large Power 1 A 90 f 11 Diameter Sphere A 90 f
Small Precision 2 A 90 f 12 Diameter Disk A 10-20 f Medium Precision 3 A 40-60 s 13 Wrap Sphere A 90 f
Adducted 4 A 0 f Thumb 14 Tripod A 90 f
Fixed 5 Light Tool A 0 f 15 Hook NA 0 f Prismatic 6 A 90 f 4 Finger 16 Lateral A 0 f
Prismatic Index 7 A 90 f 3 Finger 17 Finger NA 0 f Extension Prismatic Extension 8 A 90 f 18 A 40-60 s 2 Finger Type
Palmar Distal 9 NA 90 f 19 NA 90 f Pinch Type
Power Writing 10 A 90 f 20 A 40-60 f Disk Tripod
Fingers Thumb Force Fingers Thumb Force No. Name Picture No. Name Picture closed at __º applied closed at __º applied Tripod 21 Variation A 40-60 f 30 Palmar NA 0 f
Parallel 31 Ring 22 NA 90 f Extension A 90 f 32 Ventral NA 0 f Adduction 23 NA 90 s Grip Inferior 33 NA 90 f Pincer 24 Tip Pinch NA 90 f
A All fingers are closed. Lateral 25 Tripod A 90 f
Fingers Closure NA Not all the fingers are closed
Sphere 4 The thumb is perpendicular to the palm 26 90 Finger A 90 f at its rest position
I The thumb is in an intermediate position 27 Quadpod
A 90 f Position Thumb’s The thumb is parallel to the palm at its 0 rest position Sphere 3 28 The force is applied in the direction of Finger A 0 f f the fingers’ flexion
Force The force is applied by the side of the Applied s 29 Stick A 0 f Direction fingers
34 3.1. CATEGORIZATION OF THE GRASPS in 3.2.1). With these experiments, several details that were not visible from the grasp images were noticed, which helped to perform a precise analysis. As an example, in grasp no. 18. Only after experiments it was noticed that this grasp requires a side force from the thumb to be realized.
For an easier preview of the results, some diagrams were made based on the defined criterias, as can be seen in Fig. 3.1 and 3.2.
As can be seen in Fig. 3.1, the grasps were first categorized based on the first criteria (Fingers’ Closure) that resulted in 23 “A” grasp Vs. 10 “NA” grasps. Then, based on the second criteria each category is divided according to the thumb position in: 90o (perpendicular), I (Intermediate) or 0o (parallel). Finally, the few grasps that require a side force were distinguished. Note that in each category of A/NA the grasps will be divided into three different subcategories which emphasizes even more their differences.
For the sequence A-T90-f the flexion of the active fingers that participate in grasping of the object is the main feature of the category. While in some grasps, all fingers participate, in others, only two fingers participate in the grasp. Yet, this grasp can be categorized in this group, only because both active fingers close simultaneously. On the other side, grasps which are categorized in the sequence NA-T90-f, are those who cannot close all fingers simultaneously for some reason. As can be seen in Fig. 3.1, many of the grasp in this sequence require the non active finger to stay open.
For a better understanding of the categorization here a comparison is made between two grasps and then it is explained how they are categorized. When comparing different ways of grasping a cylinder, the difference between the grasp no. 1 and grasp no. 31 can be seen. In grasp no. 1 (called large diameter), all fingers close in order to grasp the cylinder and thus this grasp is placed in the left sequence of Fig. 3.1(A-T90-f ). On the other side, what differentiates grasp no.
35 Chapter 3. Actuation Strategies for Underactuated Hands
Figure 3.1: Fluxogram for Grasp Categorization.
36 3.1. CATEGORIZATION OF THE GRASPS
Figure 3.2: Categorization Diagram of the Grasps.
31, from grasp no. 1, is that in grasp no. 31, which is called a ring grasp, this should be performed only by the thumb and the index finger, and the interference of the other 3 fingers with the object is not desired. Therefore, they cannot be simultaneously actuated along with others.
In this analysis, special care was taken into account in order to be very accurate in placing the grasps in different categories and analyze the position and the effect of each finger on the grasp. However, some of the grasp, such as grasp 31, are probably not among the highly used grasps and for this reason, two analysis are performed, one based on grasp diversity that includes all grasps, and a second analysis based on grasp functionality that contains the highly used grasps.
Table 3.3 and 3.4 summarize the results obtained from the categorization in Table 3.2.
Table 3.3: Quantitative Classification, Total Number of Achievable Grasps by the three defined Criterias.
f s f s f s A 13 0 3 2 5 0 NA 5 1 0 0 4 0 90o I 0o
37 Chapter 3. Actuation Strategies for Underactuated Hands
Table 3.4: Quanlitative Classification, Grasps Numbers of the Achievable Grasps by the three defined Criterias.
f s f s f s A 1 2 6 7 8 10 11 13 14 22 25 26 27 - 12 20 21 3 18 4 5 16 28 29 - NA 9 19 24 31 33 23 - - 15 17 30 32 - 90o I 0o
3.2 Configurations
As can be seen from Section 2.3, the underactuated hands developed up to now may include 1 to 6 actuators, with several different configurations. While in some hands, each finger is actuated separately, in others several fingers are connected to the same actuator. Even with the same number of actuators, the actuation strategy varies among the anthropomorphic hands developed so far.
In this regard, in this section the underactuated hands are divided into 5 groups based on their number of actuators, and within each group several config- urations which differ in their actuation strategy are proposed, i.e. which DOFs are actuated with a unique actuator.
3.2.1 Configurations Description
Sixteen configurations were created for this analysis. A number/symbol is assigned to each finger and movement of the hand, where numbers were given to all different fingers except for the thumb that is by the capital letter ‘T’. Index, middle, ring and little fingers are given by numbers 2, 3, 4 and 5 respectively (Fig. 3.3). Here, actuators are allocated to one finger or set of fingers or to abduction/adduction movement of the hand because the metacacarpal (MCP) joint allows two kinds of movement: flexion/extension and abduction/adduction as shown in Fig. 3.3.
38 3.2. CONFIGURATIONS
Figure 3.3: Number and Symbol Designations (Right Hand Palmar View); Range of Motion of the MCP Joint (A) Abduction/Adduction of the Thumb and (F) Flexion of the Fingers.
In all of the prosthetic hands described in Section 2.3, the thumb is actuated in flexion/extension and in some of them it is also actuated around the circumduc- tion axis. The circumduction rotation, which is also called abduction/adduction of the thumb is the movement required to alternate between a lateral grasp and a power or precision grasp. The circumduction axis is not always oriented parallel to the wrist rotation axis. In some designs this axis is placed at an angle from the wrist axis [62]. This is usually performed when the flexion and the ab/ad movement of the thumb are coupled. This can be beneficial to achieve desired hand openings and a better anthropomorphic motion while keeping the complex- ity low. The coupling can also help the timing of the grasp if all of the fingers are actuated simultaneously.
In the 16 configurations that were designed for this analysis the thumb is at one of the following status:
• Only the thumb flexion is actuated.
• The thumb flexion is actuated and its ab/ad movement is achieved manually. In this case the thumb can be at any of its extreme positions located 90o from each other around the circumduction axis, but intermediate positions are not possible.
39 Chapter 3. Actuation Strategies for Underactuated Hands
• The thumb flexion and ab/ad are coupled and is performed with a single actuator. In this case the thumb is usually at zero flexion at the adduc- tion position for lateral grasp. The thumb is at maximum flexion at the abduction position for power grasp and precision grasp.
• Both flexion and circumduction of the thumb are actuated independently.
The configuration name is given by two numbers: the first is related to the number of actuators and the second one is allocated in order to differentiate configurations with the same number of actuators. Configurations that appeared with the capital letter means:
• ‘M’ - The thumb is manually actuated.
• ‘C’ - The thumb’s flexion and ab/ad movement are coupled.
The actuation strategy for all configurations are defined in detail in Table 3.5.
Letters were used before the number/letter of the finger or set of actuated finger(s) in order to specify which movement is actuated:
• ‘A’ for abduction/adduction.
• ‘F’ for flexion/extension.
For example, ‘F2’ means flexion of the ring finger and ‘AT’ means abduc- tion/adduction of the thumb independently actuated. ‘F2,3,4,5’ means that the flexion of all fingers except the thumb is actuated by a single actuator. The same designations was used for the existing prosthetic hands (the ones defined in Section 2.3) in order to summarize their actuation strategies, as can be seen in Table 3.6.
As an example, as can be seen in Table 3.5, in configurations 3.1 one actuator is allocated for ab/ad of the thumb, a second actuator for the thumb flexion and a third actuator drives the flexion of the other four fingers.
40 3.2. CONFIGURATIONS
Table 3.5: Configurations and Actuated Parts. [+] means that a new actuator is added. [,] means that the actuation of the joints are coupled and is performed with a single actuator.
Configurations Actuated Parts 1.0 FT,2,3,4,5 2.0 FT + F2,3,4,5 2.0C AT,FT + F2,3,4,5 FT + F2,3,4,5 2.0M Manual AT 3.0 FT + F2 + F3,4,5 3.0C AT,FT + F2 + F3,4,5 FT + F2 + F3,4,5 3.0M Manual AT 3.1 AT + FT + F2,3,4,5 3.2 AT + FT,3,4,5 + F2 3.3 AT + FT,2 + F3,4,5 4.0 AT + FT + F2 + F3,4,5 FT + F2 + F3 + F4,5 4.0M Manual AT 4.1 AT + FT,2 + F3 + F4,5 4.2 FT + F2 + F3 + F4,5 4.3 FT + F2 + F3,4 + F5 5.0 AT + FT + F1 + F2 + F3,4,5
Table 3.6: Existing Underactuated Hands and Actuated Parts. [+] means that a new actuator is added. [,] means that the actuation of the joints are coupled and is performed with a single actuator.
Underactuated Hands #Actuators Actuated Parts
SensorHand [44] 1 FT,2,3
TUAT Hand [25] 1 FT,2,3,4,5
KNU Hand [51] 2 FT + F2,3,4,5
Michelangelo [45] [46] 2 AT + FT,2,3,4,5
Kazuki Mitsui et al. [52] 3 FT + F2 + F3,4,5
3 FT + F2,3,4,5 MANUS Hand [7] Wrist
SmartHand [53] 4 AT + FT + F2 + F3,4,5
5 FT+F2+F3+F4+F5 Bebionic [47] [49] Manual AT
5 FT+F2+F3+F4+F5 iLimb [47] [48] Manual AT
Meka H2 [47] [56] 5 AT+FT+F2+F3+F4
Vincent Hand [50] [47] 6 AT+FT+F2+F3+F4+F5
41 Chapter 3. Actuation Strategies for Underactuated Hands
In configuration 3.0M, one actuator is allocated for the thumb flexion, another for the index flexion and a third actuator for the flexion of the other 3 fingers. In this configuration, the thumb ab/ad movement is done manually and the thumb has two rest positions around the ab/ad axis.
3.2.2 Evolution of Configurations
First of all there is the need to analyze how many grasp are possible with a single actuator hand. Here, a configuration with a single actuator is defined as FT,2,3,4,5 where the flexion of the thumb (T), index (2), middle (3), ring(4) and little (5) happen at the same time and the thumb is at 90o (perpendicular to the palm). Following this hypothesis, the conditions for a grasp to be executable with only one actuator are:
1. All fingers should close simultaneously.
2. The thumb has to be perpendicular to the palm of the hand at its rest position.
3. The force applied to give the grasp stability to the grasp has the same direction as the fingers flexion.
According to the defined criterias in Section 3.1.2, thirteen grasps belong to the sequence A-T90-f, as can be seen in Fig. 3.1. Yet not in all of them, all fingers close simultaneously. Thus, from the thirteen grasps of the sequence A-T90-f, 4 are not possible to achieve with only one actuator since the fingers do not close simultaneously, or as the fingers do not close to the same extent. To perform these grasps an additional actuator is required.
As can be seen in Fig. 3.4, there are different options for where to add the second actuator.It was chosen to actuate independently the flexion of the thumb, which guarantees a bigger number of grasps compared the other two options.
42 3.2. CONFIGURATIONS
Now if a manual ab/ad is added to the thumb, some of the grasps of the sequence A-T0-f and the sequence NA-T0-f will be possible. From the total 9 grasps of both sequences, 6 are achievable with a 2.0M configuration. Three of them are not achievable by the chosen actuation strategy - which are grasps no. 17, 29 and 32. These grasps need an actuation strategy where the index is actuated independently from the other fingers.
Please note that, this is an example that shows how categorization of the grasps helps in achieving the analysis. This also helped to define possible configurations. However, in analyzing each configuration, each grasps will be categorized as pos- sible or not possible with the selected configuration.
A similar approach was used to analyze the evolution of configurations for hands with three actuators. These configurations are more complex than the ones mentioned before. In Fig. 3.5, 5 different actuation strategies and the achievable grasp of each of them are demonstrated.
Five different configurations with three actuators are presented with different features according to the thumb and index flexion where: 3.0 has the thumb and index actuated independently (two separate actuators: FT+F2), 3.0M is the same as 3.0 with a manual ab/ad actuator for the thumb, 3.1 has the thumb actuated independently (FT), 3.2 has the index actuated independently (F2) and 3.3 has the combination thumb+index flexion actuated together (FT,2). Note that 3.1, 3.2 and 3.3 have the ab/ad movement of the thumb actuated. It is also important to say that grasps no. 7, 8 and 23 are the only grasps that do not appear in Fig. 3.5 which is justified latter in Section 3.4 (Tables 3.9 and 3.10). Here, there are some grasps that are common to all configurations: the achievable grasps from a configuration with one actuator and six other grasps that are common to the configurations which dedicate an actuator to the abduction/adduction of the thumb.
43 Chapter 3. Actuation Strategies for Underactuated Hands
Figure 3.4: Fluxogram of the Evolution Idea from a 1 Actuator to a 2 Actuators Configuration.
44 3.2. CONFIGURATIONS Fluxogram of the Evolution Idea from a 1 Actuator to a 3 Actuators Configuration. Figure 3.5:
45 Chapter 3. Actuation Strategies for Underactuated Hands
3.3 Case Study: Validation of the Categoriza-
tion
Here, a case study is performed in order to compare the grasps that can be performed by an anthropomorphic hand with the grasps that can be performed based on this analysis. In this case ISR-Softhand 3.6 was used for the analysis. ISR-Softhand has the same actuation strategy as configuration 3.0M.
(a) Thumb Abducted (90o). (b) Thumb Adducted (0o).
Figure 3.6: ISR-Softhand.
ISR-SoftHand can perform 20 of the 33 grasps, with an exact or very similar imitation of the images shown in the grasp list, as can be seen in Table 3.7. These grasps are shown in Table 3.7 by sign ‘+’. 10 more grasps are achievable, in a different way than the original demonstration of the grasp list. That is, the ISR-Softhand can grasp the object, but cannot exactly imitate the grasp.
The 20 grasps are possible to imitate are also listed in the possible grasps of the configuration 3.0M in Table 3.8. Yet based on this analysis, the 3.0M configuration should be able to achieve 20 grasps.
There are four grasps (10, 17, 29, 32), that were marked achievable with a 3.0M configuration, however their exact imitation was not possible with the ISR-Softhand. Yet, the cause of this is not the actuation strategy of a 3.0M configuration in general. This constraint is caused because of some aspects of the
46 3.3. CASE STUDY: VALIDATION OF THE CATEGORIZATION
Table 3.7: Representation of 33 Grasps and imitation by the ISR-Softhand. 1st, 5th and 9th column: number of the grasp ( [40]); 2nd, 6th and 10th column: Scheme of the respective grasp ( [40]); 3rd, 7th and 11th column: Photograph of the prototype performing the grasp; 4th, 8th and 12th column: Level of equality between the scheme and photograph, rated from identical (+/-) to exactly equal (+).
No. Grasp ISR-Softhand Imitation No. Grasp ISR-Softhand Imitation No. Grasp ISR-Softhand Imitation
1 + 12 +/- 23 Impossible --
2 + 13 + 24 +
3 +/- 14 + 25 +
4 + 15 + 26 +
Not possible 5 with this first -- 16 + 27 + prototype
6 + 17 +/- 28 +
7 +/- 18 +/- 29 +/-
8 +/- 19 + 30 +
9 + 20 +/- 31 +
10 +/- 21 +/- 32 +/-
+ 11 + 22 33 +
47 Chapter 3. Actuation Strategies for Underactuated Hands
ISR-Softhand design and implementation, that can be improved.
1. Regarding the implementation, the four fingers cannot bend enough to grasp thin objects (which is the case for grasps no. 10, 29 and 32).
2. Regarding the design, the circumduction axis of the thumb is parallel to the wrist. While this is the case for many prosthetic hands, in some other hands and also in the human hand, the circumduction axis is placed at an angle from the wrist toward the little finger (e.g. from 10 to 45o - as in [12]). In this case, the exact imitation of the grasps 17, 29, and 32 will be possible, even if the thumb is in adduction (without effecting any other grasp).
Additionally, there are other 3 grasps that differs from configuration 3.0M and ISR-Softhand. The first graps is grasp no. 5. This grasp is achievable with a 3.0M actuation strategy, however for the same reason mentioned above: the four fingers can not bend enough to grasp thin objects, then the grasp is not possible with the ISR-softhand. Grasps no. 7 and 8, which are not possible with a 3.0M configuration, are achievable by the ISR-Softhand. The ISR-Softhand reproductibility for these two grasps is not perfect but still executable due to the fingers’ selfadaptability caused by the underactuated mechanism.
Then, the ISR-Softhand can perform 20 of the 33 grasps (plus ten more grasps that it can perform an approximate grasp, but cannot imitate the exact grasp) whereas the analysis shows it should be able to achieve 25 grasps. There are four grasps that the analysis says it can do, but the ISR-softhand can’t do (10, 17, 29, and 32). All these four grasps are not achievable, only because the fingers of ISR-Softhand can not bend enough.
48 3.4. GRASP DIVERSITY
Table 3.8: Comparison between the Results of Configuration 3.0M and ISR-Softhand. ‘’ means that the grasp is achievable by the configuration or by the ISR-softhand and ‘X’ means that the results between 3.0M and the ISR-Softhand are not the same.
ISR-Softhand Exact Similar Grasp 3.0M Same Results? Imitation Imitation 1 2 3 X 4 5 X 6 7 X 8 X 9 10 X 11 12 X 13 14 15 16 17 X 18 X 19 20 X 21 X 22 23 24 25 26 27 28 29 X 30 31 32 X 33 TOTAL 25 20 10 20
3.4 Grasp Diversity
The idea behind this part of the analysis is to find out the number of achievable grasps out of the 33 possible grasps for each configuration. The status of each finger and its relation to other fingers for each grasp are reviewed in order to find out if that grasp is achievable with the defined configurations. For instance considering the ‘Medium Wrap’ grasp (no. 3) (Table 3.9), in which the thumb requires to apply lateral force to the cylinder. Thus, a configuration which does not have the thumbs ab/ad actuated cannot achieve this grasp.
In Tables 3.9 and 3.10, there is a summary of the extensive analysis where the achievable grasps for each configuration are marked. Also in those tables, some notes and assumptions that were made during the analysis can be found. Based on this analysis the total number of grasps which is achievable by each configuration were calculated as demonstrated in Fig. 3.7. The results are discussed at the end
49 Chapter 3. Actuation Strategies for Underactuated Hands of this chapter.
3.5 Grasp Functionality
In the previous analysis special focus was given to grasp diversity without considering their usage frequency. Many of the 33 grasps introduced in [40] are not frequently used by humans. In order to analyze each configuration in terms of functionality an analysis based on the highly used grasps is necessary. To do so, the need to know what are the most used grasps by humans arises. Some analysis were made in order to find out the most used grasp grasps by humans [63], [41], [64]. However, a more recent study [65] showed to be more comprehensive.
In this analysis I. Bullock et al. (2013) performed an extensive analysis and presented the results from a study of prehensile human hand use during the daily work activities of four subjects: two housekeepers and two machinists. “Subjects wore a head-mounted camera that recorded their hand usage during their daily work activities in their typical place of work. For each subject, 7.45 hours of video was analyzed, recording the type of grasp being used and its duration” [65]. Then they extracted the overall grasp frequency, and duration distributions for each grasp. They showed that for 80% of the study duration the housekeepers used just five grasps and the machinists used ten. They averaged also the grasps used by all the four subjects and then created the top 10 grasps with their frequency of usage for all four subjects. Therefore, in this section, the evaluation of all configurations against the top 10 grasps is based on these four subjects. The result of the analysis will show how the number of actuators and the actuation strategy affects the percentage of the achievable top grasps. This can be a performance metric for usability and functionality of each hand.
The most used grasps were: medium grasp (3), lateral pinch (16), precision
50 3.5. GRASP FUNCTIONALITY disk (12), lateral tripod (25), tripod (14), power sphere (11), thumb-2 finger (8), light tool (5), thumb-3 finger (7) and index finger extension (17), presented in Tables 3.9 and 3.10.
The previous analysis provides the achievable grasps by each of the proposed configurations. Therefore, for each of the configurations the sum of the usage frequencies of achievable grasps from the TOP10 gives the functionality of the actuation strategy. Results presented in [65] only provides frequencies of the grasps that belongs to the top 10 grasps that sums up to 71% of the total usage frequency. Thus, a mapping of [0;71] to [0;100] was done for an easier comparison. The TOP10 grasps with their usage frequencies are shown in Table. 3.11.
Summing the frequencies of grasps for each configuration resulted in a com- parison graph that can be seen in Fig. 3.8. Using this graph one can compare the functionality index of each configuration.
51 Chapter 3. Actuation Strategies for Underactuated Hands f the o
flexion
. actuation strategy
n f the other fingers (F5
o
it’s achievable by all the it’s achievable by all the it’s achievable by all the it’s achievable by all the it’s achievable by all the it’s achievable by all the bigger bigger than the
flexion
4 & 5) are
(
s parallel to the palm, so it has to be actuated be ithasto palm,so the to parallel Notes or be actuated together. so the these fingers have to be actuated r. r. finger
) . First the thumb has to be flexed and then adducted
. ab/ad actuato ab/ad actuato
n n 4,5 > FT,2,3
the ring and little f f the little finger (5) is bigger than the so the little finger has to be actuated independently from the other o o
(FT < F2,3,4,5).
thumb applies side force This grasp is possible with a one actuator strategy so configurations. The thumb has to close after the other fingers are flexed so a where the thumb is independent from the other fingers is needed The in order to provide the side force needed. The thumb has to be actuated independently from the other fingers because it is less flexed The thumb has to be actuated independently from the other fingers because it is less flexed (FT < F2,3,4,5) This grasp is possible with a one actuator strategy so configurations. The flexion > FT,2,3,4) fingers. The flexion other fingers (F independently from the other fingers or actuated together. Grasps 9, 24, 31 and 33 are similar. The thumb independent from the other fingers and index fingers have to be This grasp is possible with a one actuator strategy so configurations. This grasp is possible with a one actuator strategy so configurations. The thumb needs to be actuated ab/ad. This grasp is possible with a one actuator strategy so configurations. This grasp is possible with a one actuator strategy so configurations. hastoposition,be rest at thumb,The manually or with a actuated be ithasto palm,so the to parallelhasto position,be rest at thumb,The manually or with a
X X X X X X X X X X X X X X X 5.0
X X X X X X X X X 4.3
X X X X X X X X X 4.2
X X X X X X X X X X X 4.1
X X X X X X X X X X X X X 4.0M
X X X X X X X X X X X X X X 4.0
X X X X X X X X X X 3.3
X X X X X X X X X 3.2
X X X X X X X X X X X X X 3.1
X X X X X X X X X X X X Configurations 3.0M
X X X X X X X X X X X 3.0C
X X X X X X X X 3.0
X X X X X X X X X X X 2.0M
X X X X X X X X X X 2.0C
X X X X X X X 2.0
X X X X X X 1.0
Picture
Grasp Disk Small Name Large finger Finger Finger Tripod Lateral Thumb Sphere Diameter Diameter Precision Precision Adducted Light Tool Prismatic 4 Prismatic 3 Prismatic 2 Power Disk Power Fixed Hook Palmar Palmar Pinch Medium Wrap Power Power Sphere
Grasps [40] and Configurations List - PART I - [X] means that the grasp is achievable with the configuration concerned.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 No. Table 3.9:
52 3.5. GRASP FUNCTIONALITY
it’s achievable by all the it’s achievable by all the it’s achievable by all the actuator is needed for the
n
Notes
r. independently. similar. The thumb and index fingers have to be The thumb applies side force. First the thumb has to be actuated independently.
ab/ad actuato
adducted in order to provide the side force needed. n F2,3,4,5). be actuated independently.
The flexion of the index finger is less than the flexion of the other fingers FT,3,4,5). The index(F2 has to < The thumb has to be actuated independently from the other fingers because it is less flexed (FT < F2,3,4,5). be flexed and then The flexion of the index finger is less than the flexion of the other fingers FT,3,4,5). The index(F2 has to be actuated independently. < The thumb needs to be actuated ab/ad. The thumb needs to be actuated ab/ad. This grasp is possible with a one actuator strategy so configurations. This grasp is impossible for every configuration as a (3) (2)fingers. and middle the índex ab/ad of Grasps 9, 24, 31 and 33 are independent from the other fingers or be actuated together. The thumb has to be actuated independently from the other fingers because it is less flexed (FT < This grasp is possible with a one actuator strategy so configurations. This grasp is possible with a one actuator strategy so configurations. actuated be ithasto palm,so the to parallelhasto position,be rest at thumb,The manually or with a The flexion of the index finger is less than the flexion of the other fingers FT,3,4,5). The index(F2 has to be actuated independently. < The thumb needs to be actuated Grasps 9, 24, 31 and 33 are similar. The thumb independent from the other fingers or be actuated together. and index fingers have to be The index has to Grasps 9, 24, 31 and 33 are similar. The thumb independent from the other fingers or be actuated together. and index fingers have to be
X X X X X X X X X X X X X X X X 5.0
X X X X X X X X 4.3
X X X X X X X X 4.2
X X X X X X X X X 4.1
X X X X X X X X X X X X X 4.0M
X X X X X X X X X X X X X X X X 4.0
X X X X X X X X X X 3.3
X X X X X X X X 3.2
X X X X X X X X X 3.1
X X X X X X X X X X X X X 3.0M
X X X X X X X X X X X 3.0C
X X X X X X X X 3.0
X X X X X X 2.0M
X X X X X X X 2.0C
X X X X 2.0
X X X 1.0
Picture
Grip Ring Type Stick Name Finger Finger Tripod Tripod Palmar Ventral Writing Parallel Parallel Sphere 4Sphere 3Sphere Variation Quadpod Tip Pinch Extension Extension Extension Adduction Distal Type Index Finger Lateral Tripod Inferior Pincer Grasps [40] and Configurations List - PART II - [X] means that the grasp is achievable with the configuration concerned.
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 No. Table 3.10:
53 Chapter 3. Actuation Strategies for Underactuated Hands
Table 3.11: TOP10 Grasps with Valid Configurations and Frequencies of Usage.
Grasp Valid Frequency Frequency Grasp Picture No. configurations [65] mapped in100%
Medium 3.1 3.2 3.3 3 14,0±0,5% 19,7±0,7% Wrap 4.0 4.1 5.0 2.0C 3.0C Precision 12 3.1 3.2 3.3 8,2±0,4% 11,5±0,6% Disk 4.0 4.1 5.0 2.0M 3.0C 3.0M 3.1 Lateral 16 3.2 3.3 9±2% 12,7±2.8% Pinch 4.0 4.0M 4.1 5.0 14 Tripod ALL 7,4±0,5% 10,4±0,7% 2.0 2.0C 2.0M Lateral 3.0 3.0C 3.0M 3.1 25 8±1% 11,3±1,4% Tripod 4.0 4.0M 4.2 4.3 5.0 Power 11 ALL 7,0±0,3% 9,9±0,4% Sphere
Thumb- 8 4.0M 4.1 4.2 5,5±0,4% 7,7±0,6% 2 finger
Index finger 3.0M 3.2 17 3,6±0,2% 5,1±0,3% extension 4.0 4.0M 5.0 2.0M 3.0M 3.1 5 Light tool 4,3±0,2% 6,1±0,3% 4.0 4.0M 5.0 Thumb-3 4.3 7 4,0±0,4% 5,6±0,6% finger 5.0
3.6 Human Gestures
Besides grasping or more skilfully, manipulating objects, sometimes the hands are used when people want to express themselves while speaking or acting. For example, waving to someone across the street, pointing or hand shaking.
From the first analysis, the configurations and achievable grasps from Ta- bles 3.9 and 3.10 were taken and then related them to the following gestures which are describe in Table 3.12:
54 3.6. HUMAN GESTURES
• Hand shaking;
• Waving;
• Pointing/Clicking;
• Like (Thumb Up)/Dislike (Thumb Down);
• Tap/Hold/Slide/Flick on a smartphone/tablet;
• Pinch/Spread on a smartphone/tablet.
Table 3.12: Hand Gestures and Valid Configurations.
Gesture Picture Similar to grasp Configurations Comments
Hand For hand shaking the 2.0M 3.0M Shaking thumb ab/ad need to be - 3.1 3.2 3.3 actuated manually or 4.0 4.0M 4.1 5.0 Waving with an actuator.
Need the flexion of all 2.0C 2.0M the fingers except from Like/ 3.0C 3.0M 3.1 the thumb and a manual Dislike 4.0 4.0M or actuated ab/ad (15) 5.0 movement of the thumb. Pointing 3.0M 3.2 3.3 Index’s flexion should be Clicking 4.0 4.0M independent from the Tap/Hold/ (17) (32) 5.0 other finger’s flexion Slide/Flick
3.0 3.0C 3.0M 3.3 We only consider the Pinch/ 4.0 4.0M (9) (24) flexion of the thumb and Spread 4.1 4.2 4.3 the index. 5.0 (31) (33)
55 Chapter 3. Actuation Strategies for Underactuated Hands
3.7 Results
Figure 3.7: Results from the First Analysis: Grasp Diversity: Total Number of Achievable Grasps for each Configuration; * - configurations with ab/ad of the thumb.
Figure 3.8: Results from the Second Analysis; Grasp Functionality: Frequency of Usage from the TOP10 [65] of each Configuration; * - configurations with ab/ad of the thumb.
3.8 Discussion
Both analyses lead to some very interesting conclusions, that will be discussed here. It is clear that increasing the number of actuators improves the hand’s functionality in terms of number of achievable grasps. But based on the results of these analyses it is important to discuss how those actuators should be allocated
56 3.8. DISCUSSION to the hand’s degrees of freedom. For this reason, the comparision is mostly based on the comparision and discussion of the configurations with the same number of actuators, with a special focus on the hands with 3 actuators.
3.8.1 Grasp Diversity
Configurations 3.0 and 3.0M are similar in terms of actuation, except that 3.0M benefits from manual ab/ad locking and releasing mechanism. An improvement of about 27%(Fig. 3.7) is observed when the thumb is manually actuated (the thumb can assume 0 or 90º positions). Comparing 3.0 with 3.0C there is an improvement of 18%.
In the same group of 3 actuators configurations, when adding an independent actuator for the ab/ad, specifications of some of the independent flexion have to be done. 3.1, 3.2 and 3.3 are configurations with the actuated thumb ad/ad. In comparison with 3.0, in 3.1 there is the coupled flexion of the finger 2 with 3,4,5, in 3.2 there is the coupled flexion of the thumb with fingers 3,4,5, and in 3.3 there is the coupled flexion of the index and the thumb. All these 3 configurations achieve better results compared to 3.0.
The first conclusion is that, for a better grasp diversity it is feasible to sacrify one of the independent flexion and couple it with another flexion, in order to allocate an actuator for the ab/ad movement of the thumb because it allows the hand to perform a larger number of grasps. On the other hand, comparing the slight improvement of 3.3 compared to 3.2, it is clearly shown that it is more advantageous to have the index finger independent from the middle, ring and little finger than having it independent from the thumb. Also in 3.1, if the flexion of all 4 fingers is coupled and instead allocate 2 actuators for the thumb, more grasps can be achieved compared to 3.2 and 3.3.
According to the first analysis (Fig. 3.7) the best four configurations are 3.0M,
57 Chapter 3. Actuation Strategies for Underactuated Hands
4.0, 4.0M and 5.0, which allows the hand to do, respectively, about 76%, 91%, 79% and 94% of the grasps from the database [30]. Here, the 5.0 configuration shows an ideal situation of an underactuated hand as there are two actuators for the thumb (AT & FT) and the index and middle finger are actuated separately and independently from the ring and little finger. Regarding 4.0 and 4.0M once more it is observed that the actuated abduction/adduction of the thumb is really important due to the difference of 12% between the configurations. Note that 4.0M has the advantage of manual actuation of one DOF over 4.0, but yet it can achieve a smaller number of grasps compared to 4.0.
3.8.2 Grasp Functionality
The results of the second analysis are shown in Fig. 3.8. Since this result is based on the actual frequency of use in the grasps, several important conclusions can be derived from this analysis. As can be seen from the figure, the actuation policy is very important. In some cases a hand with more actuators presents a lower functionality compared to a hand with lower number of actuators (as seen for example 4.3).
A bad actuation policy (2.0, 3.0, 4.2 and 4.3) do reduces dramatically the hand’s functionality. The common feature of the configurations with a usage frequency lower than 50% -configurations mentioned previously- is that none of them have an actuated ab/ad thumb. A hand with 3 actuators (3.1, 3.2 and 3.3) expresses much higher usage frequency than 4.2 and 4.3 with one more actuators, since the former group dedicate an actuator for ab/ad movement.
Furthermore, a common practice in many commercial and under-research an- thropomorphic hands is to use an external intervention to move the thumb in two extreme poses for the ab/ad.
Considering the 3.0M configuration, the manual moving and locking of the
58 3.8. DISCUSSION thumb on its extreme positions increases the usage frequency by almost 3 times compare to the configuration 3.0 (55,5% for 3.0M vs. 21,7% for 3.0). However, 3.0M is still limited compared to other configurations with the same number of actuators 3.1, 3.2 and 3.3 with more than 50% of achievable frequency percentage. This again admits that driving the ab/ad movement is very important for grasps that are used everyday.
In the category of three actuators 3.1 is probably the best selection (best grasp functionality and second best grasp diversity). This configuration demands for 2 actuators for the thumb and a single actuator for the other 4 fingers. On the other side one can see that while 3.0C performs quite good in terms of diversity, its performance is poor in terms of grasp functionality. This can also be said about 3.0M which received the best score in terms of diversity in the hands with 3 actuators, but not a good score in terms of functionality.
Finally, comparing the results of 4.0 and 4.1 in the first and second analysis, for a better functionality (4.0) it is advantageous to couple the flexion of 3,4,5 and instead have independent flexion of the thumb, and independent flexion of the index finger.
3.8.3 Actuation Strategy for performing all 33 grasps
Here the actuation strategies are analyzed by which makes the hand able to perform all 33 grasps. Configuration 5.0 can perform 31 of 33 achieved grasps. From Table 3.6 and Tables 3.9 and 3.10 it can be seen that this configuration cannot perform the grasps no. 8 and 23.
• Grasp 8: This grasps is not achievable because of the actuation F4,5. There- fore, the independent actuation of the flexion of the ring and little fingers is necessary, and thus another actuator is needed.
• Grasp 23 - In order to perform this grasp, it is necessary to actuate the
59 Chapter 3. Actuation Strategies for Underactuated Hands
abduction/adduction movement of the fingers. Possible actuations are to actuate the ab/ad of the set of fingers index, middle, ring and little fingers (A2,3,4,5), or only the index and middle fingers (A2,3).
For grasp no. 23, the only imagined applications are smoking or handling a syringe. Excluding this grasp a configuration with six actuators, where flexion of all five fingers and ab/ad of the thumb are actuated is a complete hand that can perform all grasps. Including grasp 23, another actuator should be added that can actuate ab/ad of the index and middle finger or alternatively actuate ab/ad of fingers 2,3,4,5 with a single actuator.
60 Chapter 4
Evaluation of Anthropomorphic Performances
This chapter aims to analyze different actuations strategies for underactuated robotic hands in order to compare their level of anthropomorphism. 11 possible configurations, from 3 to 5 actuators, are tested against different synergies. The action manifold of the hand, in other words, the achieved postures according to the defined synergies, were projected onto a 2D space with the aim of estimate the level of anthropomorphism. The degree of overlap between the human and artificial hands’ dynamics and functionality define their anthropomorphic mo- tion capability. Then, the similarity between the human hand and the actuation strategies capabilities provided a way of measuring the level of anthropomor- phism.
61 Chapter 4. Evaluation of Anthropomorphic Performances
4.1 Anthropomorphism
The development of complex robotic hands lies nowadays on the capability to mimic human hand anthropomorphism and dexterity [6].
Generally speaking, the term anthropomorphism denotes the capability of a robotic hand to mimic the human hand in external perceivable properties (size, shape, color and so on). Meanwhile, dexterity is related to the actual functionality of the hand, i. e., a measure of what the hand can do [6]. Thus, there is the need to define a way where an artificial robotic hand mimics the human hand in its dynamics and functionality which is defined as anthropomorphic motion capability.
4.2 Methodology
The basic concept of this analysis is to sample all possible fingertip configura- tions (positions and orientations of the five fingers) of several proposed actuation strategies for a hand model defined. That dataset is then compared against hu- man dataset by the projection to a low dimensional space where the comparisons can be visualized and measured. This method turns possible to calculate an Anthropomorphism Index (AI) for the selected configurations, resulting then a percentage value that indicates to what extend the defined configurations are similar to the human hand.
Therefore, this analysis is divided in five steps:
1. 11 configurations with different actuation strategies, that will be explained in Section 4.3.
2. Three of five defined synergies were chosen in order to test the actuation strategies defined in the previous step.
62 4.2. METHODOLOGY
3. Extraction of all fingers trajectories to perform the executable synergies by each configuration.
4. Each executable synergy is represented in the latent space and then su- perposed all possible synergies of one configuration in order to compute a global Anthropomorphic Index (AI) for each configuration.
5. The Anthropomorphic Indices are compared for all configurations, resulting then some conclusions.
4.2.1 System Overview
The idea is to compare the action manifolds between the human hand and prosthetic/robotic hands, where the term action manifold is defined as all the postures that a hand can achieve. Depending on the kinematics of the hand, the action manifold may be different possibly due to hands having many independent actuators. This leads to a higher number of available hand configurations [39].
While comparing the different action manifolds between the human hand and the artificial hands there will be an overlap between the two manifolds. Thus, the aim is to estimate the degree of overlap between human and artificial (pros- thetic/robot) action manifolds.
An easier visualization of the system is shown in Fig. 4.1 [39]. “Robot 1”, “Robot 2” and “Human” are the action manifolds spanned by three different hands. As the kinematics of the hand are different, the action manifold may be different: for instance, the action manifold of “Robot1” is bigger than the other two. It is observed that there is some overlap between the manifolds which is closely related to the degree of similarity between the hands’ capabilities.
Then, the goal is to determine the level of anthropomorphism of a hand from the manifold in the fingertip space. According to the manifold in the finger-
63 Chapter 4. Evaluation of Anthropomorphic Performances
Figure 4.1: Hypothetical Visualization of the High Dimensional Fingertip Space - xi, xj show two axes of a dimensional fingertip pose space [39]. tip space, the level of anthropomorphism of a hand can be determined where a large overlap between the robot and human manifolds indicates a high level of anthropomorphism.
The data from the different hands are difficult to compare directly. The mani- folds can have complex shapes, requiring then special metrics to be defined for the stimation of overlap. To do so, a toolbox called “Grade your hand” was created in MATLAB®.
4.2.2 ‘Grade your hand’ Toolbox Description
The toolbox represented in [66] compares the action manifolds between the human hand and prosthetic/robotic hands.
Once the data from different hands is available, a direct comparison in the fingertip space is difficult. Apart from the need to generate a high number of example points through sampling, the manifolds, as said before, can have very complex shapes, requiring special metrics to be defined for the estimation of overlap. To make the comparison and visualization feasible, the manifold spanned by the human hand motion is projected onto a lower dimensional space using a dimensionality reduction algorithm: Gaussian Process Latent Variable Models (GP-LVM).
64 4.2. METHODOLOGY
All possible fingertip configurations of an artificial hand are then projected onto this low-dimensional space. Once projected in the latent space, the overlap between the human and robotic hand manifolds are measured, creating a new measure: Anthropomorphic Index (AI).
To sum up, the system consists of 5 steps, as shown in Fig. 4.2. The white background represents all human hand movements projected to two dimensions and the colored trajectories are the projected movements of a prosthetic hand.
Figure 4.2: System Overview: The human hand movements (1) are projected onto a 2D space (2). The movements of the artificial hand (3) is then projected to that space (4), and the overlap is for comparision (5) [67].
In the toolbox the workflow is the following:
1. Creation of a hand model.
2. Calculation of the fingertip poses via forward kinematics.
65 Chapter 4. Evaluation of Anthropomorphic Performances
3. Scaling of the fingertip data.
4. Projection of the data to 2D.
5. Calculation of the coverage.
6. Visualization of the results in the 2D space.
4.2.3 Latent Space
The visualization of high dimensional data can be achieved through the pro- jection of a data-set onto a lower dimensional manifold. For this purpose, the Gaussian Process Latent Variable Model (GP-LVM) was used. The GP-LVM have been used in some research works for modelling human motion [68] [69].
The need of using a low dimensional (latent) space is justified by its suitability for the visualization and comparision of the data-set. The GP-LVM method con- sists in the mapping from a high dimensional to a latent space using a Gaussian Process. This mapping is defined by its mean (prediction of the high dimensional location of the point) and its variance [68]. The inverse of the variance, or con- fidence, is related to how certain the model is when reconstructing that point. The confidence is scaled into the interval [0, 1], where the white area in the latent space plots corresponds to maximal confidence.
GP-LVM Theory
GP-LVM is a probabilistic generative method. Let D denote the dimension of the data space and q the dimension of the latent space. Given N observations, the matrix containing the data points is denoted Y ∈ RN×D and the matrix of the corresponding points in the latent space is X ∈ RN×q. The marginal likelihood P of the datapoints, given the latent positions and the hyper parameters θ, is a
66 4.2. METHODOLOGY product of D independent Gaussian processes [70]:
D Y 1 1 j −1 − 2 yT K yj P (Y |X, θ) = 1 e (4.1) N 2 j=1 (2π) 2 |K|
N×1 N×N where yj ∈ R is the j th column of the data matrix and K ∈ R is the covariance matrix. The matrix defines the notion between the points in the latent space and is dependent on the hyper parameters; thus K = K(X, θ).
In order to obtain the latent representation of Y equation 4.1 has to be max- imized with respect to X and θ.
4.2.4 Tested Hands
The creators of the ‘Grade your hand’ toolbox [66] have already tested some commercial hands (Sensorhand, Michelangelo and FRH-4 hand) and rated them with their toolbox. The first two hand were already described in Section 2.3.
The FRH-4 hand has eight independent fluidic actuators, it has a much more complex actuation system than the two prosthetic hands previously mentioned. One major design difference is in the palm setup, the FRH-4 hand has one DOF in the metacarpus, which allows the palm to flex in the middle. The index and the middle finger both have 2 actuators, one for the MCP joint of the human, and the other one is in between the proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints. The ring and little fingers have one actuator, that is, a common flexion in the MCP joint. The thumb has two actuators, which actuate the CMC joint and the joint between the MCP and IP (interphalangeal) joint of the thumb [71].
67 Chapter 4. Evaluation of Anthropomorphic Performances
(a) Sensorhand [44], (b) Michelangelo [45], (c) FRH-4 Hand [71], AI=0.25% [67]. AI=2.8% [67]. AI=5.2% [67].
Figure 4.3: Tested Hands and Respective Projection and Anthropomorphism Index (AI) of the Fingertip Movements to the Latent Space.
Fig. 4.3 shows the tested hands with their respective projection and Anthropo- morphism Index (AI) of the fingertip movements to the latent space. In Fig. 4.3b the following postures were attributed and then done in the sequences shown in the right top corner of the figure: 1) hand open for tripod pinch (OT); 2) hand open for lateral pinch (OL); 3) neutral position (NP); 4) tripod pinch (TP); 5) lateral pinch (LP) [67].
4.3 Specifications
The first application of the introduced overlap measure is to determine the score of several configurations presented in the following section. Therefore, 11 actuation strategies, from 3 to 5 actuators, are tested against three synergies. In order to test the configurations a hand model need to be created. The hand model used here is created using a robotic MATLAB®toolbox [72], in which the kinematic structure is defined via DH parameters.
4.3.1 Hand Model
The Hand model chosen for this study consists of a 14 joints hand: where each finger has 3 joints except for the thumb that only has 2 joints. The fingers with 3
68 4.3. SPECIFICATIONS joints include MCP, PIP and PIP joints while the thumb has only the MCP and IP joints. The kinematics parameters of the hand used in this study is based on ISR-Softhand [61]. These parameters are shown in Tables 4.1 and 4.2. The values presented in the Tables mentioned before - handlength, fingers’ segment length and the joints’ orientation and positions - were taken from the ISR-Softhand.The fingers’ segment length, orientation and position on the palm are then used as parameters of the Denavit-Hartenberg formalism in the MATLAB®toolbox [66].
Table 4.1: Hand Model Specifications.
#DOF Hand Length (cm) Opening Angle (o) 14 20.10 ± 0.01 58.99 ± 0.01
Table 4.2: Hand Model Details: Segments’ Length, Joints’ Position Coordinates and Orientation.
MCP Joint Position Coordinates* Orientation Fingers Segment Length (cm)* x y z θ (o) 1 5.35 3.59 3.59 2.96 - Index 2 2.93 - - - - 3 2.79 - - - - 1 4.26 3.59 3.59 8.23 - Thumb 2 2.44 - - - - 1 5.73 1.29 3.59 2.96 - Middle 2 3.32 - - - - 3 2.66 - - - - 1 5.05 -1.26 3.59 2.32 5 Ring 2 2.73 - - - - 3 2.42 - - - - 1 4.79 -3.11 3.59 3.96 5 Little 2 2.79 - - - - 3 2.32 - - - - *There is an error of ±0.01 associated to the variables ’Length’ and ’Position Coordinates’ as they were measured directly from the ISR-Softhand prototype.
4.3.2 Configurations
Eleven configurations were used in order to perform this analysis. Eleven actuation strategies were taken from Section 3.2.1, Table 3.5, which are shown in Table 4.3.
69 Chapter 4. Evaluation of Anthropomorphic Performances
Table 4.3: Configurations and Actuated Parts. [+] means that a new actuator is added. [,] means that the actuation of the joints are coupled and is performed with a single actuator.
Configurations Actuated Parts 3.0 FT + F2 + F3,4,5 FT + F2 + F3,4,5 3.0M Manual AT 3.1 AT + FT + F2,3,4,5 3.2 AT + F2 + FT,3,4,5 3.3 AT + FT,2 + F3,4,5 4.0 AT + FT + F2 + F3,4,5 FT + F2 + F3 + F4,5 4.0M Manual AT 4.1 AT + FT,2 + F3 + F4,5 4.2 FT + F2 + F3 + F4,5 4.3 FT + F2 + F3,4 + F5 5.0 AT + FT + F2 + F3 + F4,5
4.3.3 Synergies
In order to calculate the AI for each configuration, first the possible grasping patterns for each configuration should be analyzed. The global AI for each con- figuration is then calculated by superposing the areas occupied by all grasping patterns in the latent space.
Here, the grasping patterns define groups of grasps that can be performed by a single synergy. The term synergy was already defined in Section 2.2.11 but generally speaking, for an anthropomorphism hand, synergies should be similar to those of humans. Yet, due to limitations of the robotic hands in terms of independent actuation of each joint, and control complexity, one tries to form the minimum number of synergies
Now, regarding the anthropomorphic hands, top synergies are similar for many robotic hands and the human hand. Several tests were performed with the ISR- Softhand against an extensive grasp list [40]. Within these tests the maximum number of grasps was tested within the minimum number of synergies.
70 4.3. SPECIFICATIONS
Table 4.4 shows the result of the tests done with the ISR-Softhand against the 33 grasp list. As a result of this study the top 5 synergies that could perform 31 grasps were defined as:
• Synergy I.A & I.B - All the fingers close. In order to cover the whole range of grasps, 4 intermediate points were defined between fully open and fully closed hand. In I.A the thumb is abducted, i. e., at 90o perpendicular do the palm of the hand (at its rest position), and in I.B the thumb is adducted, i. e., at 0o parallel to the palm of the hand (at its rest position).
• Synergy II - Only the thumb and the index close.
• Synergy III - The thumb is static. The index and the other three fingers close together in a way which is possible to grasp different objects with different sizes.
• Synergy IV - All fingers are fully closed except for the index that is flexed in a small amount.
• Synergy V - Here the same as in I.A happen, although the fingers do not flex as much as in I.A. this synergy is used to grasp objects with a parallelepiped form.
From these 5, the following 3 synergies - I, II and IV - could perform 26 grasps out of 31 achievable grasps of the list, making a total of 84%. Results seems to be fitting very well with a previous research done by Santello et al. [41] where 90% of the hand movements of five tested subjects can be reproduced by three defined synergies.
Therefore, the three synergies defined for the present study are:
• Synergy I (combined synergies I.A & I.B from Table 4.4) - All the fingers close (Fig. 4.4a).
• Synergy II (same as synergy II from Table 4.4) - Only the thumb and index
71 Chapter 4. Evaluation of Anthropomorphic Performances
Table 4.4: Representation of 33 Grasps and Imitation by the ISR-Softhand with the Five tested Synergies. Level of Equality between the scheme and photograph, rated from identical (+ / -) to exactly equal (+). The red circumference represents the chosen configuration, when there is two possible ways to do the grasp.
No. Grasp ISR softhand Synergy Imitation No. Grasp ISR softhand Synergy Imitation No. Grasp ISR softhand Synergy Imitation
1 I.A + 12 I.A +/- 23 Impossible -- --
I.A +
2 I.A + 13 I.A + 24
II +
3 I.A +/- 14 I.A + 25 I.A +
4 III + 15 III + 26 I.A +
Not possible with 5 -- -- 16 I.B + 27 I.A + this first prototype
6 I.A + 17 IV +/- 28 I.B +
I.A +\-
7 I.A +/- 18 29 IV +/-
V +/-
I.A +/-
8 I.A +/- 19 30 III +
IV +
I.A +
9 20 I.A. +/- 31 II +
II +
10 I.A +/- 21 I.A +/- 32 IV +/-
I.A +/- I.A +
11 I.A + 22 33
V + II +
72 4.4. ANALYSIS: CONFIGURATIONS VS. SYNERGIES
finger close (Fig. 4.4b).
• Synergy III (similar to synergy IV from Table 4.4) - All the fingers close except from the index (Fig. 4.4c). Here the small flexion amount of the index finger is not take into account, the index does not close at any time.
(a) Synergy I (b) Sinergy II (c) Synergy III
Figure 4.4: Representation of the three different synergies when the hand is closed. The demonstrated synergies are related to the moment when the configurations have the thumb abducted (oriented at the considered rest position 90o).
Then, the trajectories which are executable by the AI calculation have to be defined. That is, one synergy might require to be divided to several trajectories to be executable. The possible synergies and number of the derivative trajectories for each configuration is shown in Section 4.4 in Table 4.5.
Note that the number of synergies and trajectories do not reveal anything about the AI of the configuration, and this will be revealed only after estimation of the global AI of each configuration.
4.4 Analysis: Configurations vs. Synergies
According to the configurations and synergies mentioned before the possible synergies were selected for each configuration, and then associated to the trajec- tories.
Trajectories are defined for being executable with the AI calculation. If the thumb MCP joint is fixed at a single point, each synergy is associated only with a single trajectory. This is for instance the case for configuration 3.0, 4.2 and
73 Chapter 4. Evaluation of Anthropomorphic Performances
4.3 (Table 4.3). But if the thumb is manually actuated (0o or 90o), the possible trajectories are 6 (3 closing synergy at two thumb positions) which is the case for 3.0M and 4.0M.
The results are shown in Table 4.5, where ‘X’ means that the synergy is doable by the respective configuration, ‘M*’ means that the thumb ab/ad movement is manually actuated (0o or 90o) and ‘A**’ means that the thumb ab/ad is actuated. In order to simplify the projection of the fingertip movements it was assumed that the possible values for the thumb ab/ad position are 0o (adduction),10o, 20o, 30o, ..., 70o, 80o and 90o (abduction) so there are 10 different positions for each executable synergy.
Table 4.5: Configurations and Executable Synergies; [X] means that the synergy is doable by the respective configuration, [M*] means that the thumb ab/ad movement is manually actuated (0o or 90o) and [A**] means that the thumb ab/ad is actuated.
Synergies Thumb’s #Sets of Configurations #Projections I II III ab/ad Trajectories 3.0 X X X - 1 3 3.0M X X X M* 2 6 3.1 X A** 10 10 3.2 X X A** 10 20 3.3 X X A** 10 20 4.0 X X X A** 10 30 4.0M X X X M* 3 6 4.1 X X A** 10 20 4.2 X X X - 1 3 4.3 X X X - 1 3 5.0 X X X A** 10 30
4.5 Results
Looking at Table 4.5 it is predictable that the mapping of the trajectories in the latent space for some actuation strategies will be the same. Thus, to simplify the analysis six different groups were created.
Please note that each synergy is represented by a different color so it easier
74 4.5. RESULTS to distinguish them while their fingertip movements are represented in the latent space. So, the color red is for synergy I, green is for synergy II and blue is for synergy III.
It is also important to state that here, although the hands have more than 1- DOF, they are modeled as a 1-DOF hand. This means that all of the base joints (MCP) move together as one. Here, the focus is given on how do an actuation strategy can achieve or execute the synergies and how this affects the AI.
4.5.1 Group I
To this group belongs configurations 3.0, 4.2 and 4.3. This group represents all configurations that do not have the thumb ab/ad movement (neither manual nor actuated), therefore the thumb for these configurations is placed at 90o, i. e., the position in which the thumb opposes the finger .
As can be seen in Table 4.5, these configurations can perform all the three proposed synergies, resulting then in one set of trajectories with three projections. The global AI is of 0.41% as shown in Fig. 4.5a.
4.5.2 Group II
Configurations 3.0M and 4.0M compose this group. The actuation strategies that belong to this group have the thumb ab/ad actuated manually (Manual AT). Here the thumb can be at positions 0o or 90o. The first position allows the thumb to be parallel to the palm at its rest position and then, when closing, close perpendicularly to the others fingers’ flexion.
Here, the three presented synergies are executable. In addition to the previous group, 2 sets of trajectories are projected, resulting then in 6 different projections.
These actuation strategies show a big improvement comparing to the ones of
75 Chapter 4. Evaluation of Anthropomorphic Performances
(a) Group I: 3.0, 4.2 & 4.3 (b) Group II: 3.0M & 4.0M
(c) Group III: 3.1 (d) Group IV: 3.2
(e) Group V: 3.3 & 4.1 (f) Group VI: 4.0 & 5.0
Figure 4.5: Projection of the Fingertip Movements onto the Latent Space for the Possible Synergies (Synergies: I-red, II-green, III-blue).
76 4.5. RESULTS the previous group as the AI is four times larger, reaching 1.67% (Fig. 4.5b). The idea of moving the thumb abduction/adduction manually (0o or 90o) seems to be a good idea when the option of using an extra actuator (motor) to move the thumb ab/ad is not considered. The projection of the actuation strategies where the thumb is at 90o are represented on the left side of the figure (latent space) whereas the ones at 0o are on the right side.
4.5.3 Group III
There is only one actuation strategy in this group - 3.1 - due to the flexion of the set of fingers 2,3,4,5 (F2,3,4,5) that are actuated together and an actuator is dedicated to the ab/ad thumb movement (AT). Then, the thumb can achieve 10 different positions, from 0,10,20,30... till 90o.
Therefore, the configuration 3.1 can only achieve one of the three defined syn- ergies (synergy I), as demonstrated in Fig. 4.5c. As only one of the synergies is achievable and there is an actuator that actuates the thumb ab/ad allowing 10 different positions , there are 10 sets of trajectories, resulting then into 10 pro- jections. Although there is only one synergy possible, due to the ab/ad actuator for the thumb movement, it is possible to reach an AI of 2.29%.
Here, it can be seen that the less is the angle between the palm and the thumb, the wider is the spread of the fingertip projections and consequently bigger is the global AI. As for group II from left to right the angle of rotation of the thumb goes from 90º to 0º.
4.5.4 Group IV
Again, as in the previous group, there is only one actuation strategy that belongs to this group: 3.2. This configuration has the index finger flexion (F2)
77 Chapter 4. Evaluation of Anthropomorphic Performances actuated independently from the other fingers and has an ab/ad actuator for the thumb (AT).
As a result of the actuation of the thumb ab/ad movement and, as shown in Table 4.5, two synergies are achievable - synergies I and III - there are here 10 sets of trajectories with two possible synergies for each set which means that there are 20 projections. Fig. 4.5d shows the related projections and the consequent anthropomorphic index which is of 2.45%.
4.5.5 Group V
This group consists of two actuation strategies: 3.3 and 4.1. These two config- urations have an actuator dedicated to the ab/ad movement of the thumb (AT) and have the thumb and index finger flexion actuated together (FT,2).
Two of the proposed synergies are executable, and as the thumb is actuated, 10 different positions are reachable. Then, resulting in 10 different trajectory sets with 20 projections.
There is a little decrease in the anthropomorphic index comparing to the previ- ous situation (Group IV). Here an AI of 2.37% is reached. The difference between these two results 4.5d and 4.5e is due to the bigger expansion of synergy III as compared with synergy II, as its spread in the latent space is wider (probably due to the projection of synergy III at 0º).
4.5.6 Group VI
Finally, this last group is formed by configurations 4.0 and 5.0. To this group belongs the actuation strategies that have the thumb and index actuated inde- pendently (two separated actuators: FT + F2) and do have an actuator dedicated to the ab/ad movement of the thumb (AT).
78 4.6. DISCUSSION
According to Table 4.5, all the three synergies are possible and as the thumb ab/ad is actuated, 10 sets of trajectories are achievable, forming a possibility of 30 projections.
The expectation for this group of two configurations (4.0 and 5.0) is that the global AI, that is equals to 2.45% (Fig. 4.5f), should be bigger than the rest of the groups because it is the only group that can execute all of the three synergies with 10 different thumb’s ab/ad positions. However, this do not happen as the spread of the fingertip movements in the latent space are still the same as the ones in group III or IV. As the spread of the second synergy (green) is not as wide as the spread of third synergy (blue), one can assume that the second synergy in this projection will not influence the AI because it is overlapping the space covered by the red and blue trajectories.
A detailed summary is presented in Table 4.6 where the groups, configurations and achievable synergies are included. Also in this table, details about the thumb ab/ad actuation can be found - M* for manually actuated and A** if there is an actuator for the ab/ad movement -, thumb flexion, wherever it is coupled (C) or independent (i) and the respective details about the coupled flexion of the thumb with other fingers. In the last column the global AI of each group/configuration can be find.
4.6 Discussion
It is quite obvious that generally increasing the number of actuators, increases the Anthropomorphic Index (AI). But the main question is with the same number of actuators: What are the best configuration in terms of the Global AI? It can be seen from some of the results above that a configuration with 3 actuators performs better than a configuration with 4 actuators. Here, the results presented above
79 Chapter 4. Evaluation of Anthropomorphic Performances
Table 4.6: Detailed Summary of the Groups presented in Section 4.5; [M*] thumb manually actuated, [A**] means there is an ab/ad actuator, [C] Coupled flexion, [i] independent flexion.
Thumb Main Characteristics Executable ab/ad Coupled Global Groups Configurations Flexion Synergies Actuation Detail AI (%) 3.0 I I 4.2 II - i - 0.41 4.3 III I 3.0M II II M* i - 1.67 4.0M III III 3.1 I A** i - 2.29 I IV 3.2 A** C FT,3,4,5 2.45 III 3.3 I V A** C FT,2 2.37 4.1 II I 4.0 VI II A** i - 2.45 5.0 III are discussed in order to compare the actuation strategies.
4.6.1 3-Actuators Configurations Comparision
There are 5 configurations with 3 actuators, and not any two of them are in the same group, meaning that groups 1 to 5 have one configuration with 3 actuators. Comparing the results of these five groups, it is predictable that the bigger the number of actuators the bigger is the overlap between the fingertip movements of the robotic and the human hand. Then, the following conclusion are drawn:
1. It is more beneficial to dedicate one actuator for the ab/ad of the thumb than having all three actuators for independent flexion of the fingers. This is easily visible by looking at the very poor performance of Group I. In Group II, where the ab/ad movement of the hand is done manually a big improvement of the AI is observed, to 4 times bigger than the AI of the first group. It might be discussed that the second group has a manual ab/ad of the thumb, which means that it is somehow actuated.
80 4.6. DISCUSSION
However, the results of the following groups III, IV, and V are confirming the importance of actuation of the ab/ad movement. For configurations with 3 actuators in these groups, the thumb’s ab/ad is actuated by sacrifying independent actuation of one of the fingers’ flexion, which should be coupled by flexion of another finger. But it can be seen that all these three groups outperform group I and even group II with the helping factor of manual movement of the thumb.
2. Now, the question is: Which of the independent flexions should be sacrified in favor of actuation of the ab/ad of the thumb? To answer this question the results of group III, IV and V have to be compared. As can be seen the results for all groups are very close to each other, but group IV (configu- ration 3.2) slightly outperforms other configurations. In this configuration, the flexion of the index finger is actuated independently, while the flexion of the thumb and the other 3 fingers are coupled. Nevertheless, due to the insignificant difference between the 3 groups, one may decide between any of the three groups based on other characteristics.
4.6.2 4-Actuators Configurations Comparision
There are 5 configurations with 4 actuators, which are located in group I (4.2 and 4.3), II (4.0M), V (4.1) and VI (4.0). From the results of the four actuation policies, it is shown that even though 4.2 and 4.3 can achieve all three synergies, they have a low AI. Once more this shows that the thumb abduction/adduction movement needs to be actuated for a better anthropomorphism index.
Configuration 4.0(Fig 4.5f) benefits from the best AI between all others our performing slightly better configuration 4.1 (Fig. 4.5e) (+0.08% in the AI). The reason for this is that in 4.1, the flexion of the thumb and the index finger is coupled (FT,2) which makes it impossible to perform the third synergy. This
81 Chapter 4. Evaluation of Anthropomorphic Performances shows that if enough actuators are available, it is better to actuate independently the flexion of the thumb and the index finger and couple the flexion of the other 3 fingers.
82 Chapter 5
Conclusion
Despite many research works in the area of categorization of the grasps, and also after development of several types of prosthetic hand, there are no exist- ing studies that compares the functionality of the hands based on their actuation strategy. This study was performed in order to find out the best actuation strate- gies for the prosthetic hands with 1 to 5 actuators. 3 metrics were defined: grasp diversity, grasp functionality and the hand antropomorphism in term of function- ality.
While the exact decision on selection of the actuation strategy depends on many factors (cost, weight, control complexity, etc.), this study provides a good guideline for investigators in order to find out the best actuation strategy for a prosthetic hand, based on the objective of the project.
Table 5.1 summarizes the results of this study for all three metrics.
The actuation strategy of robotic hands plays an important role in its per- formance. While it is clear that usually more actuators leads to a better per- formance, it was not clear how to allocate these actuators to the hands DOF. Two analysis were done following this purpose. The categorization of the grasps done in the beginning of the chapter have shown to be a great point for making
83 Chapter 5. Conclusion
Table 5.1: Summary of the Results for the 3 Metrics
Grasp Diversity Grasp Functionality AI Configuration (out of 33) (%) (%) 1.0 9 20,3 - 2.0 11 31,6 - 2.0C 17 43,1 - 2.0M 17 40,5 - 3.0 16 21,7 0,41 3.0C 22 43,1 - 3.0M 25 55,5 1,67 3.1 22 81,6 2,29 3.2 17 69,3 2,45 3.3 20 64,2 2,37 4.0 30 86,7 2,45 4.0M 26 63,2 1,67 4.1 20 71,9 2,37 4.2 17 50,8 0,41 4.3 17 37,2 0,41 5.0 31 92,3 2,45 these analysis as strict as possible. First, the number of achieved grasps for each actuation strategy was analyzed, and afterwards as not all of the grasps are used with the same frequency in routine tasks, each configuration was analyzed based the TOP10 most used grasps. The allocation of the actuators for fingers/set of fingers was demonstrated as being an important factor that should be taken into account while designing a robotic hand. Also the abduction/adduction of the thumb (manual or actuated) helps to increase the hand’s performance. The cou- pled flexion of other fingers have shown to be useful while making actuator free in order to be used for the thumb ab/ad.
The results from the comparison of configurations 3.0M and the ISR-Softhand showed that the design of the robotic hand should be changed in order to be more performant. The alignment between the thumb and the index fingers’ flex- ion showed that sometimes, even if the grasp is possible, the stability of the executed grasp is compromised by the position of this fingers’ base joints. A solution for this problem would be to set the thumb circumduction axis, the axis
84 that allows the thumb to realize the ab/ad movement, to a different position: for example, setting the circumduction axis of the thumb to 30o with the wrist axis. The circumduction axis of existing robotic hands is not always oriented parallel with the wrist axis. By angling this axis towards or away from the little finger, thumb flexion and circumduction rotation can be jointly approximated in a single DOF. This can be beneficial to achieve desired hand openings and a more anthropomorphic motion while keeping complexity low.
A different way for testing the proposed configurations is defined in the second part of this thesis, in which several synergies were tested against the configura- tions and they projected onto a 2D space using a MATLAB®toolbox based on the fingertips movement of a hand. The comparison between the human data acquired by the authors of the toolbox was then compared to the projections of each possible synergies in the latent space and with the superposition of these two data-set a measure of the anthropomorphism level was obtained. Again, the option of using an actuator for the ab/ad movement of the thumb showed to be favorable for the actuation strategies as well as the coupling flexion of the fingers.
Gathering the two different approaches, for a configuration with 3-actuators the configuration 3.3 has shown the best results with 20 out of 33 grasps, 64,2% of functionality and an AI equals to 2.37%. The coupled flexion of the thumb and index allows the hand to have an actuator dedicated to the ab/ad of the thumb. This results in a higher number of achievable grasps and anthropomorphism level. For a 4-actuators configuration, 4.0 revealed to be the best actuation against the other four configurations with the same number of actuators. 4.0 resulted in 30 out of 33 grasps, 71.9% of functionality and an AI of 2.45%. In addition, this configuration is capable of executing all the three synergies “designed” for the evaluation of the anthropomorphism.
Overall, it was shown that an increase in the level of actuation increase the de- gree of diversity, functionality and anthropomorphism of a robotic hand. The un-
85 Chapter 5. Conclusion deractuated system used is also of great importance as less Degrees-of-Actuation have to be taken into account resulting in a simpler control of the hand.
5.1 Future Work
While this study focused on the actuation strategies for a better performance, one can continue this work for optimizing the geometry of the hand for a better functionality. That is to answer the question of where and at which angle one should place the joints of the finger, what should be the length of phalanges, and how much each of the joints should be able to move. It should be noted that this study cannot be generalized, and depends on the actuation strategy and other design and implementation limitations, this study should be made for a specific design. This can be done by optimization of the Antropomorphism Index (AI) for that specific design.
The result of this study will be also used in development of the next versions of the ISR-Softhand. A 3 actuator version that will be with the 3.3 configuration, and a simpler 2 actuator version that will be with the 2.0M configuration.
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94 Appendices
95
Publications
Accepted
“Actuation Strategy for Underactuated Anthropomorphic Hands” accepted for publication in the Proceedings of the 2014 IEEE/RSJ International Con- ference on Intelligent Robots and Systems (IROS 2014).
Submitted
“Adaptive Synergies of the ISR-Softhand” submitted to International Jour- nal of Robotics Research
“Underactuated Anthropomorphic Hands: Actuation Strategies for a Better Functionality ” submitted to Robotics and Autonomous Systems
Prepared
“Optimal Actuation Strategies for Underactuated Anthropomorphic Hands”
97 Appendix . Publications
98 MATLAB®Codes
All the MATLAB®codes presented below are based on the tooblox created by Feix et al. in [66]. Synergies:
Synergy I
% File name: sinergia_UM.m % Description: Definiton of SynergyI- All fingers close % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = sinergia_UM(alpha) handlength = 20.1;
%index: sl11 = 4.95+0.4; sl12 = 2.43+0.5; sl13 = 2.29+0.5; x1 = 3.59; y1 = 3.59; z1 = 2.96;
%thumb: sl21 = 4.26; sl22 = 2.44;
99 Appendix . MATLAB®Codes
x2 = 3.59; y2 = 3.59; z2 = 2.96+5.27;
%middle: sl31 = 5.73; sl32 = 3.32; sl33 = 2.66;
% Middle Finger (0,0,0) x3 = 1.29; %0 y3 = 3.59; %0 z3 = 2.96; %0
%ring: sl41 = 5.05; sl42 = 2.73; sl43 = 2.42; x4 = -1.26; y4 = 3.59; z4 = 2.96;
%little: sl51 = 4.79; sl52 = 2.79; sl53 = 2.32; x5 = -3.61+.5; y5 = 3.59; z5 = 3.96;
∆ = - [x3 y3 z3]; %to make sure MCP of middle is at [00 0]
100 %disp('######################## Creating Hand ... #####################');
%dof index thumb middle ring little dofs= [3 2 3 3 3];
%new order: thetaDA alpha DH = [0 0 sl11 0 0 deg2rad(24); ... %index 0 0 sl12 0 0 deg2rad(37.4); ... 0 0 sl13 0 0 deg2rad(33.1); ... 0 0 sl21 0 0 -deg2rad(31.01); ... %thumb 0 0 sl22 0 0 deg2rad(28.9); ... 0 0 sl31 0 0 deg2rad(24); ... %middle 0 0 sl32 0 0 deg2rad(37.4); ... 0 0 sl33 0 0 deg2rad(33.1); ... 0 0 sl41 0 0 deg2rad(20); ... %ring 0 0 sl42 0 0 deg2rad(35); ... 0 0 sl43 0 0 deg2rad(30); ... 0 0 sl51 0 0 deg2rad(20); ... %little 0 0 sl52 0 0 deg2rad(35); ... 0 0 sl53 0 0 deg2rad(30)];
%Base definition matrix %transX, transY, transZ, rotX, rotY, rotz base = [x1 y1 z1 pi/2 0 pi/2; ... x2 y2 z2 alpha 0 pi/2; ... x3 y3 z3 pi/2 0 pi/2; ... x4 y4 z4 pi/2+pi/36 0 pi/2; ... x5 y5 z5 pi/2+pi/36 0 pi/2];
%This loop creates the individual Fingers. the parameters are ... from the
101 Appendix . MATLAB®Codes
%matrix above. num_fing = 1; inc = 1; names = {'Index''Thumb''Middle''Ring''Little'}; for i = 1:size(DH,1) links(inc) = Link(DH(i,:)); if (inc == dofs(num_fing)) %disp(['Creating Finger:' num2str(num_fing)' DoF:' ... num2str(dofs(num_fing))]); temp = SerialLink(links(1:inc));
mat = transl(base(num_fing,1:3))*trotz(base(num_fing,6))*... troty(base(num_fing,5))*trotx(base(num_fing,4));
temp.base = transl(∆)*mat; temp.tool = trotz(-pi/2)*troty(-pi/2); temp.name = names{num_fing}; finger{num_fing} = temp; num_fing = num_fing +1; inc = 0; clear links; end
inc = inc + 1; end
data.finger = finger; data.dof = dofs; %data.pose= pose;
%disp('Creating Joint Values') openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; n = length(vals); offset = linspace(0,deg2rad(openingangle/10),n)';
102 values = [vals zeros(n,2) vals zeros(n,1) vals zeros(n,2) vals ... zeros(n,2) vals zeros(n,2)];
%LABELS lbls = ones(n,1); %Normal end
Synergy II
% File name: sinergia_TRES.m % Description: Definiton of SynergyII- Only the thumb and the ... index close % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = sinergia_TRES(alpha) handlength = 20.1;
%index: sl11 = 4.95+0.4; sl12 = 2.43+0.5; sl13 = 2.29+0.5; x1 = 3.59; y1 = 3.59; z1 = 2.96;
%thumb: sl21 = 4.26; sl22 = 2.44; x2 = 3.59; y2 = 3.59;
103 Appendix . MATLAB®Codes z2 = 2.96+5.27;
%middle: sl31 = 5.73; sl32 = 3.32; sl33 = 2.66;
% Middle Finger (0,0,0) x3 = 1.29; %0 y3 = 3.59; %0 z3 = 2.96; %0
%ring: sl41 = 5.05; sl42 = 2.73; sl43 = 2.42; x4 = -1.26; y4 = 3.59; z4 = 2.96;
%little: sl51 = 4.79; sl52 = 2.79; sl53 = 2.32; x5 = -3.61+.5; y5 = 3.59; z5 = 3.96;
∆ = - [x3 y3 z3]; %to make sure MCP of middle is at [00 0]
%disp('######################## Creating Hand ... #####################');
104 %dof index thumb middle ring little dofs= [3 2 3 3 3];
%new order: thetaDA alpha DH = [0 0 sl11 0 0 deg2rad(24); ... %index 0 0 sl12 0 0 deg2rad(37.4); ... 0 0 sl13 0 0 deg2rad(33.1); ... 0 0 sl21 0 0 -deg2rad(31.01); ... %thumb 0 0 sl22 0 0 deg2rad(28.9); ... 0 0 sl31 0 0 deg2rad(24); ... %middle 0 0 sl32 0 0 deg2rad(37.4); ... 0 0 sl33 0 0 deg2rad(33.1); ... 0 0 sl41 0 0 deg2rad(20); ... %ring 0 0 sl42 0 0 deg2rad(35); ... 0 0 sl43 0 0 deg2rad(30); ... 0 0 sl51 0 0 deg2rad(20); ... %little 0 0 sl52 0 0 deg2rad(35); ... 0 0 sl53 0 0 deg2rad(30)];
%Base definition matrix %transX, transY, transZ, rotX, rotY, rotz base = [x1 y1 z1 pi/2 0 pi/2; ... x2 y2 z2 alpha 0 pi/2; ... x3 y3 z3 pi/2 0 pi/2; ... x4 y4 z4 pi/2+pi/36 0 pi/2; ... x5 y5 z5 pi/2+pi/36 0 pi/2];
%This loop creates the individual Fingers. the parameters are ... from the %matrix above. num_fing = 1; inc = 1; names = {'Index''Thumb''Middle''Ring''Little'};
105 Appendix . MATLAB®Codes
for i = 1:size(DH,1) links(inc) = Link(DH(i,:)); if (inc == dofs(num_fing)) %disp(['Creating Finger:' num2str(num_fing)' DoF:' ... num2str(dofs(num_fing))]); temp = SerialLink(links(1:inc));
mat = transl(base(num_fing,1:3))*trotz(base(num_fing,6))*... troty(base(num_fing,5))*trotx(base(num_fing,4));
temp.base = transl(∆)*mat; temp.tool = trotz(-pi/2)*troty(-pi/2); temp.name = names{num_fing}; finger{num_fing} = temp; num_fing = num_fing +1; inc = 0; clear links; end
inc = inc + 1; end
data.finger = finger; data.dof = dofs; %data.pose= pose;
%disp('Creating Joint Values') openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; %sensorhand -40...0 n = length(vals); offset = linspace(0,deg2rad(openingangle/10),n)';
106 % ver offset values = [vals zeros(n,2) vals zeros(n,1) vals zeros(n,2) vals ... zeros(n,2) vals zeros(n,2)];
values(:,6)=vals(1).*ones(n,1); values(:,9)=vals(1).*ones(n,1); values(:,12)=vals(1).*ones(n,1);
%LABELS lbls = ones(n,1); %Normal end
Synergy III
% File name: sinergia_CINCO.m % Description: Definiton of Synergy III- All the fingers close ... except from the index % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = sinergia_CINCO(alpha) handlength = 20.1;
%index: sl11 = 4.95+0.4; sl12 = 2.43+0.5; sl13 = 2.29+0.5; x1 = 3.59; y1 = 3.59; z1 = 2.96;
%thumb: sl21 = 4.26;
107 Appendix . MATLAB®Codes sl22 = 2.44; x2 = 3.59; y2 = 3.59; z2 = 2.96+5.27;
%middle: sl31 = 5.73; sl32 = 3.32; sl33 = 2.66;
% Middle Finger (0,0,0) x3 = 1.29; %0 y3 = 3.59; %0 z3 = 2.96; %0
%ring: sl41 = 5.05; sl42 = 2.73; sl43 = 2.42; x4 = -1.26; y4 = 3.59; z4 = 2.96;
%little: sl51 = 4.79; sl52 = 2.79; sl53 = 2.32; x5 = -3.61+.5; y5 = 3.59; z5 = 3.96;
108 ∆ = - [x3 y3 z3]; %to make sure MCP of middle is at [00 0]
%disp('######################## Creating Hand ... #####################');
%dof index thumb middle ring little dofs= [3 2 3 3 3];
%new order: thetaDA alpha DH = [0 0 sl11 0 0 deg2rad(24); ... %index 0 0 sl12 0 0 deg2rad(37.4); ... 0 0 sl13 0 0 deg2rad(33.1); ... 0 0 sl21 0 0 -deg2rad(31.01); ... %thumb 0 0 sl22 0 0 deg2rad(28.9); ... 0 0 sl31 0 0 deg2rad(24); ... %middle 0 0 sl32 0 0 deg2rad(37.4); ... 0 0 sl33 0 0 deg2rad(33.1); ... 0 0 sl41 0 0 deg2rad(20); ... %ring 0 0 sl42 0 0 deg2rad(35); ... 0 0 sl43 0 0 deg2rad(30); ... 0 0 sl51 0 0 deg2rad(20); ... %little 0 0 sl52 0 0 deg2rad(35); ... 0 0 sl53 0 0 deg2rad(30)];
%Base definition matrix %transX, transY, transZ, rotX, rotY, rotz base = [x1 y1 z1 pi/2 0 pi/2; ... x2 y2 z2 alpha 0 pi/2; ... x3 y3 z3 pi/2 0 pi/2; ... x4 y4 z4 pi/2+pi/36 0 pi/2; ... x5 y5 z5 pi/2+pi/36 0 pi/2];
109 Appendix . MATLAB®Codes
%This loop creates the individual Fingers. the parameters are ... from the %matrix above. num_fing = 1; inc = 1; names = {'Index''Thumb''Middle''Ring''Little'}; for i = 1:size(DH,1) links(inc) = Link(DH(i,:)); if (inc == dofs(num_fing)) %disp(['Creating Finger:' num2str(num_fing)' DoF:' ... num2str(dofs(num_fing))]); temp = SerialLink(links(1:inc));
mat = transl(base(num_fing,1:3))*trotz(base(num_fing,6))*... troty(base(num_fing,5))*trotx(base(num_fing,4));
temp.base = transl(∆)*mat; temp.tool = trotz(-pi/2)*troty(-pi/2); temp.name = names{num_fing}; finger{num_fing} = temp; num_fing = num_fing +1; inc = 0; clear links; end
inc = inc + 1; end
data.finger = finger; data.dof = dofs; %data.pose= pose;
%disp('Creating Joint Values') openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; %sensorhand -40...0 n = length(vals);
110 offset = linspace(0,deg2rad(openingangle/10),n)';
% ver offset values = [vals zeros(n,2) vals zeros(n,1) vals zeros(n,2) vals ... zeros(n,2) vals zeros(n,2)];
values(:,1)=vals(1).*ones(n,1);
%LABELS lbls=ones(n,1); end
Trajectories:
Trajectories Definition for Group I and II
% File name: trajecto_alpha_1.m % Description: Definiton of the combined trajectories of ... synergiesI,II and III. % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = trajecto_alpha_1(alpha)
[data values lbls handlength] = sinergia_UM(alpha); values1=values;
[data values lbls handlength] = sinergia_TRES(alpha); values3=values;
[data values lbls handlength] = sinergia_CINCO(alpha); values5=values;
111 Appendix . MATLAB®Codes
values=[values1; values3; values5]; openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; n = length(vals);
%All trajectories A=[1 0 0]; lbls1 = repmat(A,n,1);
B=[0 1 0]; lbls3 = repmat(B,n,1);
C=[0 0 1]; lbls5 = repmat(C,n,1); lbls= [lbls1; lbls3; lbls5]; end
Trajectories Definition for Group III
% File name: trajecto_group_sinergiaUM.m % Description: Definiton of the trajectory of synergyI % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = ... trajecto_group_sinergiaUM(alpha) [data values lbls handlength] = sinergia_UM(alpha); values1=values; values=[values1]; openingangle = 90-31.01;
112 vals = deg2rad(-openingangle:0.1:0)'; n = length(vals);
% All trajectories A=[1 0 0]; lbls1 = repmat(A,n,1); lbls= [lbls1]; end
Trajectories Definition for Group IV
% File name: trajecto_group_3.m % Description: Definiton of the combined trajectories of ... synergiesI and III. % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = trajecto_group_3(alpha)
[data values lbls handlength] = sinergia_UM(alpha); values1=values;
[data values lbls handlength] = sinergia_CINCO(alpha); values5=values; values=[values1; values5]; openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; n = length(vals);
%All trajectories A=[1 0 0]; lbls1 = repmat(A,n,1);
113 Appendix . MATLAB®Codes
B=[0 0 1]; lbls3 = repmat(B,n,1); lbls= [lbls1; lbls3];
end
Trajectories Definition for Group V
% File name: trajecto_group_4.m % Description: Definiton of the combined trajectories of ... synergiesI andII. % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = trajecto_group_4(alpha)
[data values lbls handlength] = sinergia_UM(alpha); values1=values;
[data values lbls handlength] = sinergia_TRES(alpha); values3=values; values=[values1; values3]; openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; n = length(vals);
% All trajectories A=[1 0]; lbls1 = repmat(A,n,1);
114 B=[0 1]; lbls3 = repmat(B,n,1); lbls= [lbls1; lbls3]; end
Trajectories Definition for Group VI
% File name: trajecto_group_5.m % Description: Definiton of the combined trajectories of ... synergiesI,II and III. % input: alpha- rotation axis direction of the MCP joint of the ... thumb function [data values lbls handlength] = trajecto_group_5(alpha)
[data values lbls handlength] = sinergia_UM(alpha); values1=values;
[data values lbls handlength] = sinergia_TRES(alpha); values3=values;
[data values lbls handlength] = sinergia_CINCO(alpha); values5=values; values=[values1; values3; values5]; openingangle = 90-31.01; vals = deg2rad(-openingangle:0.1:0)'; %sensorhand -40...0 n = length(vals);
% All trajectories A=[1 0 0];
115 Appendix . MATLAB®Codes lbls1 = repmat(A,n,1);
B=[0 1 0]; lbls3 = repmat(B,n,1);
C=[0 0 1]; lbls5 = repmat(C,n,1); lbls= [lbls1; lbls3; lbls5]; end
Groups:
Group I
% File name: TRES_trajecto.m % Description: Definition of GroupI- configurations 3.0, 4.2 ... and 4.3 % SynergiesI,II and III. % This script grades the given hand model for groupI. clc, clear all
%loada hand model alpha=-pi/2; % Thumb MCP joint rotation [robot values lbls handlength] = trajecto_alpha_1(alpha);
%calculate the forward kinematics datamat = robotfkine(robot,values);
%scale the positions %if you did create the fingertip points externally you have to ... continue at
116 %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); load('model.mat') %load the data of the gplvm model.
%Project the high dimensional data to2D with the use of the Back %Constraints of the GPLVM Model. latent = data2latent(model,datamatScaled);
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
RelativeArea = area/areaTot*100; disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)]) plotProjection
Group II
% File name: Group_DOIS.m % Description: Definition of GroupII- configurations 3.0M and ... 4.0M % SynergiesI,II and III % This script grades the given hand model for groupII. clc, clear all
117 Appendix . MATLAB®Codes
%loada hand model alpha=-pi/2; [robot values lbls handlength] = trajecto_alpha_1(alpha); alpha=0; [robot2 values2 lbls2 handlength2] = trajecto_alpha_1(alpha);
%calculate the forward kinematics datamat = robotfkine(robot,values); datamat2 = robotfkine(robot2,values2);
%scale the positions %if you did create the fingertip points externally you have to ... continue at %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); datamatScaled2 = scaleData(datamat2, handlength); load('model.mat') %load the data of the gplvm model.
%Project the high dimensional data to2D with the use of the Back %Constraints of the GPLVM Model. latent = data2latent(model,datamatScaled); latent2 = data2latent(model,datamatScaled2); latent= [latent; latent2]; lbls=[lbls;lbls2];
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
118 RelativeArea = area/areaTot*100; disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)]) plotProjection
Group III
% File name: Group_III.m % Description: Definition of Group III- configurations 3.1 % SynergiesI % This script grades the given hand model for group III. clc, clear all
%loada hand model alpha=-deg2rad(90); [robot values lbls1 handlength] = trajecto_group_sinergiaUM(alpha... ); alpha=-deg2rad(80); [robot2 values2 lbls2 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(70); [robot3 values3 lbls3 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(60);
119 Appendix . MATLAB®Codes
[robot4 values4 lbls4 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(50); [robot5 values5 lbls5 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(40); [robot6 values6 lbls6 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(30); [robot7 values7 lbls7 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(20); [robot8 values8 lbls8 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(10); [robot9 values9 lbls9 handlength] = trajecto_group_sinergiaUM(... alpha); alpha=-deg2rad(0); [robot10 values10 lbls10 handlength] = trajecto_group_sinergiaUM(... alpha);
%calculate the forward kinematics datamat = robotfkine(robot,values); datamat2 = robotfkine(robot2,values2); datamat3 = robotfkine(robot3,values3); datamat4 = robotfkine(robot4,values4); datamat5 = robotfkine(robot5,values5); datamat6 = robotfkine(robot6,values6);
120 datamat7 = robotfkine(robot7,values7); datamat8 = robotfkine(robot8,values8); datamat9 = robotfkine(robot9,values9); datamat10 = robotfkine(robot10,values10);
%scale the positions %if you did create the fingertip points externally you have to ... continue at %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); datamatScaled2 = scaleData(datamat2, handlength); datamatScaled3 = scaleData(datamat3, handlength); datamatScaled4 = scaleData(datamat4, handlength); datamatScaled5 = scaleData(datamat5, handlength); datamatScaled6 = scaleData(datamat6, handlength); datamatScaled7 = scaleData(datamat7, handlength); datamatScaled8 = scaleData(datamat8, handlength); datamatScaled9 = scaleData(datamat9, handlength); datamatScaled10 = scaleData(datamat10, handlength);
load('model.mat') %load the data of the gplvm model.
%Project the high dimensional data to2D with the use of the ... Back %Constraints of the GPLVM Model
latent= data2latent(model,datamatScaled); latent2= data2latent(model,datamatScaled2); latent3= data2latent(model,datamatScaled3); latent4= data2latent(model,datamatScaled4); latent5= data2latent(model,datamatScaled5); latent6= data2latent(model,datamatScaled6); latent7= data2latent(model,datamatScaled7);
121 Appendix . MATLAB®Codes
latent8= data2latent(model,datamatScaled8); latent9= data2latent(model,datamatScaled9); latent10= data2latent(model,datamatScaled10);
latent=[latent;latent2;latent3;latent4;latent5;latent6;... latent7;latent8;latent9;latent10]; lbls=[lbls1;lbls2;lbls3;lbls4;lbls5;lbls6;lbls7;lbls8;lbls9;... lbls10] latent; lbls;
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
RelativeArea = area/areaTot*100; disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)]) plotProjection
Group IV
% File name: Group_TRES.m % Description: Definition of GroupIV- configuration 3.2 % Projection of SynergiesI and III % This script grades the given hand model for groupI.
122 clc, clear all
%loada hand model alpha=-deg2rad(90); [robot values lbls1 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(80); [robot2 values2 lbls2 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(70); [robot3 values3 lbls3 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(60); [robot4 values4 lbls4 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(50); [robot5 values5 lbls5 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(40); [robot6 values6 lbls6 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(30); [robot7 values7 lbls7 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(20); [robot8 values8 lbls8 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(10); [robot9 values9 lbls9 handlength] = trajecto_group_3(alpha); alpha=-deg2rad(0); [robot10 values10 lbls10 handlength] = trajecto_group_3(alpha);
%calculate the forward kinematics
123 Appendix . MATLAB®Codes datamat = robotfkine(robot,values); datamat2 = robotfkine(robot2,values2); datamat3 = robotfkine(robot3,values3); datamat4 = robotfkine(robot4,values4); datamat5 = robotfkine(robot5,values5); datamat6 = robotfkine(robot6,values6); datamat7 = robotfkine(robot7,values7); datamat8 = robotfkine(robot8,values8); datamat9 = robotfkine(robot9,values9); datamat10 = robotfkine(robot10,values10);
%scale the positions %if you did create the fingertip points externally you have to ... continue at %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); datamatScaled2 = scaleData(datamat2, handlength); datamatScaled3 = scaleData(datamat3, handlength); datamatScaled4 = scaleData(datamat4, handlength); datamatScaled5 = scaleData(datamat5, handlength); datamatScaled6 = scaleData(datamat6, handlength); datamatScaled7 = scaleData(datamat7, handlength); datamatScaled8 = scaleData(datamat8, handlength); datamatScaled9 = scaleData(datamat9, handlength); datamatScaled10 = scaleData(datamat10, handlength); load('model.mat') %load the data of the gplvm model.
%Project the high dimensional data to2D with the use of the Back %Constraints of the GPLVM Model. latent= data2latent(model,datamatScaled); latent2= data2latent(model,datamatScaled2);
124 latent3= data2latent(model,datamatScaled3); latent4= data2latent(model,datamatScaled4); latent5= data2latent(model,datamatScaled5); latent6= data2latent(model,datamatScaled6); latent7= data2latent(model,datamatScaled7); latent8= data2latent(model,datamatScaled8); latent9= data2latent(model,datamatScaled9); latent10= data2latent(model,datamatScaled10); latent=[latent;latent2;latent3;latent4;latent5;latent6;latent7;... latent8;latent9;latent10]; lbls=[lbls1;lbls2;lbls3;lbls4;lbls5;lbls6;lbls7;lbls8;lbls9;... lbls10] latent; lbls;
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
RelativeArea = area/areaTot*100; disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)]) plotProjection
Group V
125 Appendix . MATLAB®Codes
% File name: Group_QUATRO.m % Description: Definition of GroupV- configurations 3.3 and 4.1 % SynergiesI andII % This script grades the given hand model for groupV. clc, clear all
%loada hand model alpha=-deg2rad(90); [robot values lbls1 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(80); [robot2 values2 lbls2 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(70); [robot3 values3 lbls3 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(60); [robot4 values4 lbls4 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(50); [robot5 values5 lbls5 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(40); [robot6 values6 lbls6 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(30); [robot7 values7 lbls7 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(20); [robot8 values8 lbls8 handlength] = trajecto_group_4(alpha); alpha=-deg2rad(10); [robot9 values9 lbls9 handlength] = trajecto_group_4(alpha);
126 alpha=-deg2rad(0); [robot10 values10 lbls10 handlength] = trajecto_group_4(alpha);
%calculate the forward kinematics datamat = robotfkine(robot,values); datamat2 = robotfkine(robot2,values2); datamat3 = robotfkine(robot3,values3); datamat4 = robotfkine(robot4,values4); datamat5 = robotfkine(robot5,values5); datamat6 = robotfkine(robot6,values6); datamat7 = robotfkine(robot7,values7); datamat8 = robotfkine(robot8,values8); datamat9 = robotfkine(robot9,values9); datamat10 = robotfkine(robot10,values10);
%scale the positions %if you did create the fingertip points externally you have to ... continue at %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); datamatScaled2 = scaleData(datamat2, handlength); datamatScaled3 = scaleData(datamat3, handlength); datamatScaled4 = scaleData(datamat4, handlength); datamatScaled5 = scaleData(datamat5, handlength); datamatScaled6 = scaleData(datamat6, handlength); datamatScaled7 = scaleData(datamat7, handlength); datamatScaled8 = scaleData(datamat8, handlength); datamatScaled9 = scaleData(datamat9, handlength); datamatScaled10 = scaleData(datamat10, handlength); load('model.mat') %load the data of the gplvm model.
127 Appendix . MATLAB®Codes
%Project the high dimensional data to2D with the use of the Back %Constraints of the GPLVM Model. latent= data2latent(model,datamatScaled); latent2= data2latent(model,datamatScaled2); latent3= data2latent(model,datamatScaled3); latent4= data2latent(model,datamatScaled4); latent5= data2latent(model,datamatScaled5); latent6= data2latent(model,datamatScaled6); latent7= data2latent(model,datamatScaled7); latent8= data2latent(model,datamatScaled8); latent9= data2latent(model,datamatScaled9); latent10= data2latent(model,datamatScaled10); latent=[latent;latent2;latent3;latent4;latent5;latent6;latent7;... latent8;latent9;latent10]; lbls=[lbls1;lbls2;lbls3;lbls4;lbls5;lbls6;lbls7;lbls8;lbls9;... lbls10] latent; lbls;
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
RelativeArea = area/areaTot*100; disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)])
128 plotProjection
Group VI
% File name: Group_CINCO.m % Description: Definition of GroupVI- configurations 4.0 and ... 5.0 % SynergiesI,II and III % This script grades the given hand model for groupVI. clc, clear all
%loada hand model alpha=-deg2rad(90); [robot values lbls1 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(80); [robot2 values2 lbls2 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(70); [robot3 values3 lbls3 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(60); [robot4 values4 lbls4 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(50); [robot5 values5 lbls5 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(40); [robot6 values6 lbls6 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(30); [robot7 values7 lbls7 handlength] = trajecto_group_5(alpha);
129 Appendix . MATLAB®Codes
alpha=-deg2rad(20); [robot8 values8 lbls8 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(10); [robot9 values9 lbls9 handlength] = trajecto_group_5(alpha); alpha=-deg2rad(0); [robot10 values10 lbls10 handlength] = trajecto_group_5(alpha);
%calculate the forward kinematics datamat = robotfkine(robot,values); datamat2 = robotfkine(robot2,values2); datamat3 = robotfkine(robot3,values3); datamat4 = robotfkine(robot4,values4); datamat5 = robotfkine(robot5,values5); datamat6 = robotfkine(robot6,values6); datamat7 = robotfkine(robot7,values7); datamat8 = robotfkine(robot8,values8); datamat9 = robotfkine(robot9,values9); datamat10 = robotfkine(robot10,values10);
%scale the positions %if you did create the fingertip points externally you have to ... continue at %this point and supply the function with the datamat and ... handlength values. datamatScaled = scaleData(datamat, handlength); datamatScaled2 = scaleData(datamat2, handlength); datamatScaled3 = scaleData(datamat3, handlength); datamatScaled4 = scaleData(datamat4, handlength); datamatScaled5 = scaleData(datamat5, handlength); datamatScaled6 = scaleData(datamat6, handlength); datamatScaled7 = scaleData(datamat7, handlength);
130 datamatScaled8 = scaleData(datamat8, handlength); datamatScaled9 = scaleData(datamat9, handlength); datamatScaled10 = scaleData(datamat10, handlength); load('model.mat') %load the data of the gplvm model.
%Project the high dimensional data to2D with the use of the Back %Constraints of the GPLVM Model. latent= data2latent(model,datamatScaled); latent2= data2latent(model,datamatScaled2); latent3= data2latent(model,datamatScaled3); latent4= data2latent(model,datamatScaled4); latent5= data2latent(model,datamatScaled5); latent6= data2latent(model,datamatScaled6); latent7= data2latent(model,datamatScaled7); latent8= data2latent(model,datamatScaled8); latent9= data2latent(model,datamatScaled9); latent10= data2latent(model,datamatScaled10); latent=[latent;latent2;latent3;latent4;latent5;latent6;latent7;... latent8;latent9;latent10]; lbls=[lbls1;lbls2;lbls3;lbls4;lbls5;lbls6;lbls7;lbls8;lbls9;... lbls10]; latent; lbls;
%Given the latent locations and the values for the discretized ... latent space %this function calulates the coverages. [areaTot area boxInds] = handMetricBox(latent,model);
RelativeArea = area/areaTot*100;
131 Appendix . MATLAB®Codes
disp('Results:') disp(['Total Volume occupied by this latent space:' num2str(... areaTot)]) disp(['Volume covered by this hand:' num2str(area)]); disp(['Relative Coverage [%]:' num2str(RelativeArea)]) plotProjection
132