Human-machine-centered design and actuation of lower limb prosthetic systems Vom Fachbereich Maschinenbau an der Technischen Universität Darmstadt zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Dissertation vorgelegt von Dipl.-Ing. Philipp Beckerle aus Wiesbaden Berichterstatter: Prof. Dr.-Ing. Stephan Rinderknecht Mitberichterstatter: Prof. Dr. rer. nat. Oskar von Stryk Tag der Einreichung: 06.05.2014 Tag der mündlichen Prüfung: 08.07.2014 Darmstadt 2014 D17 Abstract People with lower limb loss or congenital limb absence require a technical substi- tute that restores biomechanical function and body integrity. In the last decades, mechatronic prostheses emerged and especially actuated ones increased the biome- chanical functionality of their users. Yet, various open issues regarding the energy efficiency of powered systems and the impact of user-experience of the prosthesis on technical design remain. As tackeling the latter aspect urgently requires the con- sideration of user demands, this thesis proposes a novel human-machine-centered design (HMCD) approach for lower limb prosthetics. Further, it contributes to the design and control of elastic (prosthetic) actuation. The HMCD approach describes a framework that equally considers technical and human factors. Therefore, seven human factors influencing lower limb prosthetic design are determined, analyzed, and modeled using human survey data: Satis- faction, Feeling of Security, Body Schema Integration, Support, Socket, Mobility, and Outer Appearance. Based on the application of quality function deployment (QFD), those factors can be considered as a HMCD focus in systems engineering. As an exemplary application, a powered prosthetic knee concept is elaborated with the HMCD approach. The comparison of the HMCD focus with a purely technical one, which is determined with a control group, reveals distinct differences in the weighting of requirements. Hence, the proposed method should lead to different prosthetic designs that might improve the subjective user-experience. To support this by integrating users throughout the systems engineering process, two concepts for human-in-the-loop experiments are suggested. As an enabling technology of powered lower limb prostheses, variable (series) elastic actuation and especially such with variable torsion stiffness (VTS) is inves- tigated. Inverse dynamics simulations with synthetic and human trajectories as well as experiments show that the consideration of the actuator inertia is crucial: Only by including it in advanced models, the whole range of natural dynamics and antiresonance can be exploited to minimize power consumption. A corresponding control strategy adapts the actuator to achieve energy efficiency over a wide range of operational states using these models. The exemplary design of the powered prosthetic knee with respect to the HMCD prioritization of requirements confirms the fundamental suitability of VTS for in- tegration in prosthetic components. In this, considering actuator inertia enables the determination of an optimal stiffness for serial elastic actuation of the human knee during walking that is not found in previous studies. A first simulation con- sidering the changed dynamics of prosthetic gait indicates the potential to reveal lower design requirements. The designed knee concept combines promising biome- i chanical functionality and long operating time due to elastic actuation and energy recuperation. Beyond lower limb prosthetics, the proposed HMCD framework can be used in other applications with distinct human-machine interrelations by adjusting the human and technical factors. Likewise, the insights into variable elastic actuation design and control can be transferred to other systems demanding energy-efficient performance of cyclic tasks. ii Kurzfassung Menschen mit Beinamputation oder angeborener Beinverkürzung benötigen einen technischen Ersatz, der biomechanische Funktion und Körperintegrität wiederher- stellt. Mit der Entwicklung mechatronischer und speziell aktuierter Prothesen wurde die biomechanische Funktionalität der Nutzer in den letzten Jahrzehn- ten erweitert. Dennoch verbleiben offene Fragen bezüglich der Energieeffizienz von aktuierten Prothesen und zum Einfluss des Nutzererlebens von Prothesen auf deren technische Entwicklung. Da die Bearbeitung des zweiten Aspekts die Berück- sichtigung von Nutzeranforderungen dringend benötigt, schlägt diese Arbeit einen neuartigen Ansatz zur Mensch-Maschine-zentrierten Entwicklung (MMZE) in der Beinprothetik vor. Sie liefert zudem Beiträge zum Entwurf und der Regelung von elastischen (Prothesen-)antrieben. Der Ansatz zur MMZE stellt ein Rahmenwerk zur gleichwertigen Berücksichti- gung von Human Factors und technischen Aspekten dar. Dazu werden sieben Hu- man Factors mit erhobenen Daten bestimmt, analysiert und modelliert: Zufrieden- heit, Sicherheitsempfinden, Körperschemaintegration, Unterstützung, Schaft, Mo- bilität und Außenwirkung. Durch die Anwendung von Quality Function Deploy- ment (QFD) finden diese Faktoren im Systems Engineering als MMZE-Schwerpunkt Berücksichtigung. Als Anwendungsbeispiel dient hierbei die Konzeptionierung eines aktuierten Prothesenknies mit dem MMZE-Ansatz. Der Vergleich des MMZE- Schwerpunkts mit einem rein technischen, der mit einer Kontrollgruppe erar- beitet wurde, zeigt deutliche Unterschiede in der Priorisierung von Anforderungen. Demnach sollte die vorgeschlagene Methodik zu neuartigen technischen Lösungen führen, die das subjektive Erleben von Beinprothesennutzern verbessern könnten. Um dies durch die Einbeziehung der Nutzer im gesammten Systems Engineer- ing zu unterstützen, werden zwei Konzepte für Human-in-the-loop Experimente vorgeschlagen. Als Grundlagentechnologie für aktuierte Beinprothesen werden variable (seriell-) elastische Aktuatoren und besonders solche mir variabler Torsionssteifigkeit (VTS) untersucht. Rückwärtsdynamik-Simulationen mit synthetischen und am Men- schen gemessenen Trajektorien sowie Experimente zeigen, dass die Berücksich- tigung der Aktorträgheit hierbei von entscheidender Bedeutung ist: Nur durch ihre Einbeziehung in erweiterte Modelle können Eigendynamik und Antiresonanz zur Senkung des Leistungsverbrauches ausgenutzt werden. Eine entsprechende Regelungsstrategie passt auf Basis dieser Modelle den Aktuator für einen effizienten Betrieb über einen breiten Bereich an. Die beispielhafte Konzeptionierung der aktuierten Knieprothese anhand der MMZE-Priorisierung bestätigt die grundsätzliche Eignung von VTS zur Integra- iii tion in prothetischen Komponenten. Hierbei erlaubt die Berücksichtigung der Ak- tuatorträgheit im Gegensatz zu früheren Studien die Bestimmung einer optimalen Steifigkeit für die seriell-elastische Aktuierung des menschlichen Knies beim Gehen. Eine erste Gang-Simulation, die zudem die veränderte Dynamik mit der Prothese berücksichtigt, deutet auf das Potential hiermit niedrigere Anforderungen für den Entwurf zu ermitteln hin. Das konzeptionierte Prothesenknie kombiniert durch die elastischen Aktuierung und Energierückgewinnung vielversprechende biomechanis- che Funktionalitäten und eine lange Betriebszeit. Neben der Beinprothetik kann das vorgeschlagene MMZE-Rahmenwerk in an- deren Anwendungen mit starken Mensch-Maschine-Wechselwirkungen durch die Anpassung der Human Factors und der technischen Aspekte verwendet werden. Ebenso können die Erkenntnisse zum Entwurf und der Regelung von elastischer Aktuierung auf andere Systemen übertragen werden, die eine energieeffiziente Durchführung von zyklischen Aufgaben verlangen. iv Contents Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aim and structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Biomechanics and state-of-the-art 9 2.1 Biomechanics of human gait . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Variable stiffness actuation . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Actuator designs . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Motion control . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.3 Stiffness control . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Powered lower limb prosthetics . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Psychological evaluation . . . . . . . . . . . . . . . . . . . . 23 2.3.2 Design approaches . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Human-machine-centered design approach 27 3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 Technical factors . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.2 Human factors . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.3 Transfer methodology . . . . . . . . . . . . . . . . . . . . . . 36 3.1.4 Systems engineering . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.1 Technical factors . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.2 Human factors . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.3 Transfer methodology . . . . . . . . . . . . . . . . . . . . . . 54 3.2.4 Systems engineering . . . . . . . . . . . . . . . . . . . . . . . 57 3.2.5 Human-machine-centered design framework . . . . . . . . . . 62 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 v 4 Actuator design considering natural dynamics 67 4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1.1 Actuator configurations . . . . . . . . . . . . . . . . . . . . . 68 4.1.2 Advanced modeling . . . . . . . . . . . . . . . . . . . . . . . 69 4.1.3 Natural dynamics analysis . . . . . . . . . . . . . . . . . . . 72 4.1.4 Power consumption analysis . . . . . . . . . . . . . . . . . . 75 4.1.5 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 78 4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.1 Natural dynamics analysis . . . . . . . . . . . . . . . . . . . 85 4.2.2 Power consumption analysis . . . . . . . . . . . . . . . . . . 88 4.2.3 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 93 4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5 Variable stiffness control exploiting natural dynamics 105 5.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.1.1 Modeling of stiffness adjustment mechanism . . . . . . . . . . 106 5.1.2 Stiffness control strategy . . . . . . . . . . . . . . . . . . . . 108 5.1.3 Forward dynamics simulation . . . . . . . . . . . . . . . . . . 110 5.1.4 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 112 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2.1 Forward dynamics simulation . . . . . . . . . . . . . . . . . . 113 5.2.2 Experimental evaluation . . . . . . . . . . . . . . . . . . . . 119 5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6 Exemplary design of a powered prosthetic knee 127 6.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.1.1 Human-machine-centered requirement analysis . . . . . . . . 128 6.1.2 Concept of the actuation system . . . . . . . . . . . . . . . . 128 6.1.3 Optimization with respect to human data . . . . . . . . . . . 128 6.1.4 Actuation integration and implementation . . . . . . . . . . . 130 6.1.5 System integration issues . . . . . . . . . . . . . . . . . . . . 131 6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2.1 Human-machine-centered requirement analysis . . . . . . . . 134 6.2.2 Concept of the actuation system . . . . . . . . . . . . . . . . 136 6.2.3 Optimization with respect to human data . . . . . . . . . . . 138 6.2.4 Actuation integration and implementation . . . . . . . . . . . 144 6.2.5 System integration issues . . . . . . . . . . . . . . . . . . . . 148 6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 vi Contents 7 Overall discussion and conclusion 155 7.1 Overall discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.1.1 Human-machine-centered design . . . . . . . . . . . . . . . . 155 7.1.2 Variable stiffness actuation . . . . . . . . . . . . . . . . . . . 157 7.2 Overall conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 A Appendix 165 A.1 Human and technical factors . . . . . . . . . . . . . . . . . . . . . . 165 A.2 Model parameters of the proposed prosthetic concept . . . . . . . . 173 A.3 Component list of the variable torsion stiffness prototype . . . . . . 173 Acknowledgements 175 Bibliography 177 Contents vii Symbols a(x) Part of the input transformation in feedback linearization bξ Numerator coefficient ξ of a transfer function cξ Denominator coefficient ξ of a transfer function C(q̇l, ql) Matrix of coriolis and centrifugal effects (general) d (Walking) distance Dp Matrix of parallel damping Ds Matrix of serial damping E Energy f Frequency f(x) Vector function of nonlinear state space representation F Force g Gravitational acceleration g(x) Vector function of nonlinear state space representation G(ql) Matrix of gravitational effects (general) iξ Gear ratio of transmission ξ) Iξ Inertia of segment(s) ξ It Torsional moment of inertia kξ Vector of state feedback control gains for coordinate ξ kξ,a Acceleration gain for coordinate ξ kξ,i Integral control gain for coordinate ξ kξ,j Jerk gain for coordinate ξ kξ,p Position gain / proportional control gain for coordinate ξ kξ,v Velocity gain / differential control gain for coordinate ξ Kp Matrix of parallel stiffness Ks Matrix of serial stiffness Ks,ξ (Serial) stiffness of component(s) ξ Ks,a (Serial) stiffness for adjustment to antiresonance Ks,n2 (Serial) stiffness for adjustment to the second natural mode K̄s,ec(qs) Analytical solution of torsional stiffness characteristics lξ Length of segment(s) ξ lstr Stride length m,mξ Mass (of segment / component ξ) M(ql) Matrix of inertial effects (general) Mp(ql) Matrix of inertial effects (DA/PEA) Nξ Number of participants of study ξ pξ Position of the center of gravity of segment ξ regarding its axis of rotation viii Contents P Power Pk Knee power Pm,ξ Mechanical power of actuator ξ P̄m,ξ Mechanical power of actuator ξ (calculated as in [98]) Pm,ξ,a Average mechanical power consumption of actuator ξ without energy recuperation Pm,ξ,r Average mechanical power consumption of actuator ξ with energy recuperation q Vector of joint variables / coordinates qξ Variable / coordinate of joint ξ s Laplace variable S(ql) Matrix of inertial couplings Sξξ(ω) Power spectral density of signal ξ r (Inner) radius R Outer radius t Time tm Duration of measurement/evaluation u Eigenvector U Unity matrix v Control input of feedback-linearized state space system va Angular velocity of a actuator-transmission unit (= q̇a) x State vector z Transformed state vector γ Linearized gravitational torque of a pendulum Γ Material-specific modulus of elasticity in shear ηa Efficiency of an actuator-transmission unit λ Ratio factor of inner radius and outer radius in a cylinder µ Friction coefficient π Ratio of a circle’s circumference to its diameter % Product-moment correlation coefficient (Pearson) τ Torque vector τξ Torque at degree of freedom ξ ωξ (Natural) angular frequency �d Desired value of a variable �eq A variable in equilibrium state ∆� Relative error d� dq Derivative of a variable with respect to the vector of joint variables Contents ix �̇, d� dt Derivative of a variable with respect to time �̈ Second derivative of a variable with respect to time... � Third derivative of a variable with respect to time �(n) nth derivative of a variable with respect to time �̂ Peak value of a variable / signal �̃ Control error of a variable (= �d −�) Abbreviations ABIS Amputee body image scale [28] ACT Actuation / drive train (technical factor) AC1 Agreement Coefficient 1 [85] AMASC Actuator with mechanically adjustable series compliance [105] ANELS Auator with non-linear elastic system [120] AMP-Foot 2.0 Ankle Mimicking Prosthetic Foot 2.0 [33] AMP Amputee mobility predictor [66] AwAS Actuator with adjustable stiffness [111, 110] BAVS Bidirectional antagonistic variable stiffness [65] BSI Body schema integration (human factor) cap. Capacity CCEA Continuous-state coupled elastic actuation [101] comp. Component CON Controls (technical factor) DA Direct actuation DC motor Direct current motor DLR Deutsches Zentrum für Luft- und Raumfahrt e. V. (German Aerospace Center) FOS Feeling of security (human factor) FSJ Floating spring joint [249] FUN Functionality (technical factor) GATECH-SEA Serial elastic actuator of Georgia Institute of Technology [150] GER Germany GPR Gait planning / state recognition (technical factor) HDAU Hybrid dual actuator unit [118, 203] HF Human factor HM Human-machine HMCD Human-machine-centered design x Contents MACCEPA Mechanically adjustable compliance and controllable equilibrium position actuator [229] MARIONET Moment arm adjustment for remote induction of net effective torque [214] MEC Mechanics / kinematics (technical factor) MESTRAN Mechanism for varying stiffness via changing transmission angle [173] MIA Mechanical impedance adjuster [153] MMZE Mensch-Maschine-zentrierte Entwicklung MOB Mobility (human factor) OPT Operating time (technical factor) OUT Outer appearance (human factor) PDAU Parallel dual actuation unit [203] PEA Parallel elastic actuation PEQ Prosthesis evaluation questionnaire [133, 132] P/I/D Proportional (P), integral (I) and derivative (D) feedback / control PPAM Pleated pneumatic artificial muscle [232] PWM Pulse width modulation QA-Joint Quasi-antagonistic joint [56] QFD Quality function deployment ran. Rank recup. Recuperation REJ Reject rel. Relative req. Required rHEA Rotational hydro-elastic actuator [212] SAT Satisfaction (human factor) SEA Series elastic actuation / actuator [172] SEMG Surface electromyography SEN Sensors (technical factor) SIZ Size / volume (technical factor) SOC Socket (human factor) SUP Support (human factor) sys. System TAPES Trinity amputation and prosthesis experience scales [67] TF Technical factor US(A) United States (of America) val. Value Contents xi VnSA Variable negative stiffness actuation [251] VSJ Variable stiffness joint [34] VS-Joint Variable stiffness joint [250] VSA Variable stiffness actuator [222, 187] vsaUT Variable stiffness actuator (of University of Twente) [175, 81] VSA-HD Variable stiffness actuator based on harmonic drives [31] (V)-SLIP Variable spring-loaded inverted pendulum [30] VSSEA Variable stiffness series elastic actuator [221] VTS Variable torsion stiffness [195] V2E2 Very versatile energy efficient (actuator) [213] w/ With WEI Weight (technical factor) w/o Without xii List of figures 1.1 Basic aims and approach. . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Thesis structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Human gait cycle and phases. . . . . . . . . . . . . . . . . . . . . . 9 2.2 Model and coordinate definitions from [137]. . . . . . . . . . . . . . 11 2.3 Averaged human gait data for walking and running. . . . . . . . . . 11 2.4 Principle of series elastic actuation. . . . . . . . . . . . . . . . . . . 12 2.5 Variable stiffness: Basic categories and examples. . . . . . . . . . . . 13 2.6 Examples of powered prostheses. . . . . . . . . . . . . . . . . . . . . 22 3.1 Fundamental concept of the human-machine-centered design frame- work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Human survey data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Pair-wise comparison of technical factors based on [63]. . . . . . . . 30 3.4 Human factor model according to [10, 246] inspired by [70]. . . . . . 32 3.5 Principle template of quality function deployment based on [109]. . . 37 3.6 V model as a macro cycle according to [231]. . . . . . . . . . . . . . 40 3.7 Structured list of technical solutions, criteria and further information. 42 3.8 Exemplary V model application. System: Powered prosthetic knee. Component example: Series elastic actuation. . . . . . . . . . . . . . 58 3.9 Functional concept and units of Prosthesis-User-in-the-Loop based on [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.10 Functional concept and interfaces of the Int2Bot based on [14]. . . . 61 3.11 Complete framework of the human-machine-centered design approach. 62 4.1 Mechanical models of the investigated mechanical actuator-elasticity configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2 Sketch of the investigated pendulum and actuator-elasticity config- urations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 Concept of variable torsion stiffness and elasticity implementation. . 78 4.4 Prototype of a variable torsion stiffness actuator with series elasticity and stiffness adjustment mechanism. . . . . . . . . . . . . . . . . . . 79 4.5 Schematic lateral section of the variable torsion stiffness prototype. . 80 4.6 Transfer functions from τa to ql of SEA and PEA. . . . . . . . . . . 85 4.7 Transfer functions in serial elastic actuation (τa to qa and qa to ql). . 87 xiii 4.8 Average power consumption Pm,a,a for sinusoidal trajectories with- out recuperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.9 Average power consumption Pm,a,r for sinusoidal trajectories with recuperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.10 Natural frequencies in comparison with power contour plots for si- nusoidal trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.11 Average power consumption Pm,a,r for dual-sine trajectories with recuperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.12 Natural frequencies in comparison with power contour plots for dual- sine trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.13 Maximum actuator torque τa of SEA (left) and PEA (right) for dual sine case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.14 Experimental evaluation of the elastic element. . . . . . . . . . . . . 94 4.15 Contour plots of elastic torque τe compared with natural frequencies. 95 4.16 Positions, torques and powers during chirp experiments at different stiffness values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.17 Positions, torques and powers during sinus experiments at lower stiff- ness values and different frequencies (1). . . . . . . . . . . . . . . . . 97 4.18 Positions, torques and powers during sinus experiments at lower stiff- ness values and different frequencies (2). . . . . . . . . . . . . . . . . 98 4.19 Positions, torques and powers during sinus experiments at higher stiffness values and different frequencies. . . . . . . . . . . . . . . . . 99 5.1 Mechanical model of the investigated pendulum incorporating rota- tional serial elastic actuation and stiffness adjustment. . . . . . . . . 106 5.2 Sections of the variable torsion stiffness prototype. . . . . . . . . . . 107 5.3 Block diagram of stiffness control strategy based on [13]. . . . . . . . 108 5.4 Sinusoidal trajectory matched with antiresonance or second natural frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.5 Chirp trajectory matched with antiresonance or second natural fre- quency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.6 Spectrograms and stiffness trajectories Ks for chirp trajectory. . . . 116 5.7 Dual-sine trajectory matched with antiresonance or second natural frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.8 Spectrograms and stiffness trajectories Ks for dual-sine trajectory. . 118 5.9 Dual-sine trajectory matching frequencies deviating from antireso- nance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.10 Positions, torques and powers during dual-sine experiments at lower stiffness values and different frequencies. . . . . . . . . . . . . . . . . 119 xiv List of figures 5.11 Positions, torques and powers during dual-sine experiments at higher stiffness values and different frequencies. . . . . . . . . . . . . . . . . 120 5.12 Variable stiffness control for sinusoidal and dual-sine trajectories. . . 121 5.13 Variable stiffness control for a chirp trajectory. . . . . . . . . . . . . 123 6.1 Peak powers related to subject weight versus stiffness and powers required during a gait cycle for peak power optimization. . . . . . . 139 6.2 Angular velocity va versus torque τa at the transmission output for peak power optimization. . . . . . . . . . . . . . . . . . . . . . . . . 140 6.3 Optimized energy consumptions related to subject weight and stride length versus stiffness and powers required during a gait cycle with- out recuperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.4 Angular velocity va versus torque τa at the transmission output for energy consumption optimization. . . . . . . . . . . . . . . . . . . . 142 6.5 Optimized energy consumptions related to subject weight and stride length versus stiffness and powers required during a gait cycle with recuperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.6 CAD models of the proposed prosthetic knee in combination with an active foot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.7 Spectrograms of shank motion trajectories and comparison of natural limb dynamics with power consumption contour. . . . . . . . . . . . 149 6.8 Inverse dynamics simulation of human gait with and without pros- thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 A.1 Complete list of technical solutions, criteria and further information. 172 List of Tables 2.1 Categorized overview on actuation concepts with variable elasticity based on [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1 Items of the English questionnaire investigated in [38]. . . . . . . . . 34 3.2 Additional items regarding body schema integration. . . . . . . . . . 35 3.3 Description of technical factors. . . . . . . . . . . . . . . . . . . . . 43 3.4 Data from pair-wise comparison by NP = 6 experts: Individual sums of higher importance rating of specific factors. . . . . . . . . . 44 3.5 Correlation matrix of the items from [38]. . . . . . . . . . . . . . . . 46 3.6 Satisfaction correlations of data from [36]. . . . . . . . . . . . . . . . 48 3.7 Human factor set and factor descriptions. . . . . . . . . . . . . . . . 50 xv 3.8 Frequency distribution for category assignments from [191]. . . . . . 52 3.9 Results of quality function deployment with 0/1/3/9 rating scale. . . 54 3.10 Results of quality function deployment with 0/1/2/3 rating scale. . . 55 3.11 Comparison of technical factor rankings obtained with the purely technical and the human-machine-centered approach based on QFD with 0/1/3/9 scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.1 Inertial and gravitational parameters of the pendulum based on the VTS test rig [17, 59]. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Numerator coefficients of transfer functions. . . . . . . . . . . . . . . 73 4.3 Denominator coefficients of transfer functions. . . . . . . . . . . . . 73 5.1 Inertial and friction parameters (param.) of the stiffness adjustment mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.1 Dynamics properties of the right leg in the human model from [248]. 132 6.2 First version of the (human-machine-centered) list of requirements considering actuation of a powered prosthetic knee. . . . . . . . . . . 135 6.3 Stiffness, peak power and related energy consumption values for op- timization of peak power and energy consumption. . . . . . . . . . . 142 6.4 Updated (human-machine-centered) list of requirements considering actuation of a powered prosthetic knee. . . . . . . . . . . . . . . . . 145 6.5 Characteristic frequencies of natural dynamics in the prosthetic system.149 A.1 German items of the custom-built questionnaire. . . . . . . . . . . . 165 A.2 English items of the custom-built questionnaire. . . . . . . . . . . . 168 A.3 German items on body schema integration. . . . . . . . . . . . . . . 170 A.4 English items on body schema integration. . . . . . . . . . . . . . . 171 A.5 Dynamics properties of the proposed prosthetic concept. . . . . . . . 173 A.6 Component list of variable torsion stiffness prototype. . . . . . . . . 174 xvi List of Tables 1 Introduction People with lower limb loss or congenital limb absence have the need for a techni- cal substitute of the missing part of their body. Freely translating the definition from [121], prostheses can be described as “artificial substitutes for parts of the human body made from non-body material“. Specifically, the recreation of biome- chanical function as well as appearance of the lost limb by prosthetic components reflect basic design requirements: In case of the lower limb, this comprises the replacement of the (partially) missing leg and the function of the musculoskeletal system in combination with the recovery of an intact appearance. Thus, from a mechatronic perspective, prostheses should replace leg mechanics, actuation, sensing, and control in postural and movement tasks. Among those tasks, the realization of stance and swing phase of different types of gaits is a crucial one, as it has a direct impact on mobility and security of users [19]. Beyond this, various non-technical challenges occur, as prosthetic devices are also required to create an intact outer appearance of their users and give them the feeling of body integrity [243]. In the last three decades, mechatronic approaches led to a significant progress in lower limb prosthetic technology especially regarding biomechanical function and comfort regain. As shown in [19, 252], development started from micro-processor controlled knees adjusting the dynamic characteristics of the system in swing phase and evolved those to vary dynamic parameters in stance phase and provide addi- tional functionalities, e. g., different types of gait or specific modes for activities like cycling. Recently, first commercial knee and ankle devices integrate active compo- nents like electrical motors to further provide power to the human-machine system comprising user and prosthesis during locomotion [19, 233], while academic research starts focusing on multi-joint prosthetic systems often aiming at optimizing power consumption as in [71]. 1.1 Motivation A motivation of this work and prosthetic research in general is the high and increas- ing number of people with amputation shown in various studies: In [92], 55,000 lower limb amputations are counted in Germany in 2003. Another German study estimates 40,000 to 50,000 amputations per year [77]. Major reasons of amputa- tions are diabetes mellitus and arterial diseases [92, 171] or country-specific causes like veterans suffering from limb loss in the United States of America (US) [171]. 1 The development of the number of people with amputation in the US is estimated in [253]. According to this study, 1.6 million persons with lower limb amputations were living there in 2005 and an increase to 3.6 millions is projected for 2050. As loosing a limb has an enormous psychological impact [157], people with lower limb amputation are confronted with several challenges in multiple domains in- cluding physical as well as psychological factors: As stated in [183], their disability is not only a result of the obvious physical impairment but also caused by social and personal issues. The study further reports a relation of those psychological variables to prosthetic use and thus recommends to consider them in prescription. In [8], it is pronounced from a medical and orthopedic point of view that the pa- tient should always be the focus of treatment as well as rehabilitation and not the medical intervention method or prosthetic technology. The positive impact of modern approaches, such as micro-processor controlled or even powered lower limb prosthetic devices, on the biomechanical disability has been shown for knee [19] and ankle parts [233]. However, various open questions result in psychological issues concerning the users as well as technical potentials compared to the versatile and efficient biological counterpart. Technical potentials concern functional aspects like gait flexibility or energy con- sumption of user or prosthesis: Although current prostheses allow for selecting walking speed in a specific range, only few like those in [95, 18] enable the user to run for instance. Regarding energy consumption, powered prostheses are able to improve walking economy of the user [6], while actuation concepts incorporating elasticity can additionally reduce power required from the prosthesis [98]. There- fore, stiffness has to be designed “to work at resonance in rhythmic tasks like walking“ [62], which can be adapted to “different activities or walking speeds and for rejecting unexpected disturbances“ [242]. Yet, the usage of such elastic actu- ation at varying gait velocities demands additional power to adjust the variable elastic actuator [229, 13] that might (but not necessarily will) affect the benefit of the concept. Potentials regarding human factors are indicated by ingruent ques- tionnaire feedback in [38], where users reported satisfaction with their prosthesis although regularly experiencing pain, for instance. In contrast to the advice from [8], prosthetics research is scientifically not only motivated by user demands, but also by the multi-disciplinary challenge connecting a variety of aspects like: • Mechatronic design, actuation, and integration. • Robot kinematics, dynamics, and control. • Biomechanical understanding, simulation, and inspiration. 2 1 Introduction • Psychological background, impact, and intervention. • Medical care, treatment, and assistance. Anyhow, the translation of findings in these fields into practical benefits for the users of prostheses should finally be possible and thus be in compliance with the requirements of [8] again. Yet, a completely human-centered design might overvalue human factors [94] and thus affect the technical solution in a way that the final result is not optimal for the user. Hence, a human-machine-centered approach in analogy to the general idea from [94] is expected to be more appropriate to cover the (partially implicit) user demands in prosthetics. Beyond this, insights from investigations of the fields mentioned above might be useful in other applications concerning human-mechatronic systems with distinct human-machine interaction. 1.2 Aim and structure The fundamental approach of this thesis is based on the assumption that prosthetic technology can be improved in a novel human-machine-centered way by equally con- sidering human and technical factors. This finally aims at the design of prostheses that integrate with the human as a synergetic human-mechatronic system. To satisfy the multi-disciplinary nature of this task, psychological issues have to be considered as well as biomechanical requirements and technical possibilities. In consequence, issues from different disciplines have to be solved. Regarding human factors in lower limb prosthetics, crucial open questions are: • Which human factors are relevant and what is their impact on design? • How can human factors be considered in technical design to meet user re- quirements? • What goals can only be achieved by considering human factors in technical design? As powered lower limb prostheses show the capability of decreasing energy re- quired from the user and elastic actuation can increase energy efficiency, those technical approaches are expedient to overcome biomechanical deficits accompany- ing limb loss or congenital limb absence. Thus, engineering issues include mecha- tronic hardware and control software design resulting in the following fundamental questions: • How can variable elastic actuation support system energy efficiency and the user? 1.2 Aim and structure 3 • What technical requirements emerge when considering human factors in de- sign? • Can the interactions of human user and technical system be considered in design? Figure 1.1 presents the basic aims and approach of this thesis. With the initial situation of limb loss or absence shown in the middle, the subject suffers from biome- chanical deficits and experiences a psychological impact. Contemporary technical solutions focusing on technical and biomechanical requirements in design lead to an artificial replacement of the lost limb (left in Figure 1.1). Such replacements are assumed to deliver a functional regain without completely restoring biomechanical capabilities and to leave open relevant psychological issues. It is further hypothe- sized that the final goal of a fully integrated replacement can only be achieved by human-machine-centered design and considering the changed dynamics of the pros- thesis instead of those of the biological leg (right in Figure 1.1). The consideration of human factors and changed dynamics is assumed to enable the design of pros- theses that lead to completely restored biomechanical functionality and the feeling of body integrity. Therefore, a set of human factors is determined, assessed and modeled based on survey data from users and experts to enrich common product design schemes regarding user issues and requirements leading to a human-machine- centered design approach. To foster this, human-in-the-loop experiments allowing for the integration of users during all phases of technical design or the investigation of specific human factors are proposed. As variable stiffness actuation is a promis- Artificial replacement  Functional regain  Psychological issues Limb loss  Biomechanical deficits  Psychological impact Integrated replacement  Restored mechanics  Body integrity Technical focus, biomechanics HMCD-focus, new dynamics Figure 1.1: Basic aims and approach. 4 1 Introduction ing enabling technology for powered prostheses, such designs and their control are examined in detail. To illustrate the approach, methods, and results of this thesis, the development of a powered prosthetic knee joint is selected as an application example. The structure of this thesis is based on this concept and shown in Figure 1.2. A comprehensive and research-oriented state-of-the-art of variable stiffness actuation and powered lower limb prostheses is given in Chapter 2 along with biomechanical fundamentals of human gait. In this, variable stiffness actuation designs as well as corresponding stiffness and motion control algorithms are reviewed. The pros- thetic part covers technical solutions, psychological issues, and design approaches regarding (powered) lower limb prosthetics. Subsequently, Chapter 3 presents the novel human-machine-centered design ap- proach. After a description of the determination, assessment, and modeling of the technical and human factors, a transfer methodology is utilized to bridge the gap between the user and engineering domain. Applying it, a design focus considering human and technical factors equally is determined and compared to a purely techni- cal approach. In systems engineering, the design methodology considers this focus by a prioritization of technical design aspects. Further, it aims at geometric and functional system integration and involving users throughout the whole design pro- cess utilizing survey data and human-in-the-loop experiments. For that purpose, the Prosthesis-User-in-the-Loop simulator concept [12], which is meant to allow for 3 Human-machine-centered design approach  Technical and human factors  Transfer and design methods  Human-in-the-loop experiments 4 Actuator design considering natural dynamics  Configuration and modeling  Dynamics and power analysis 1 Introduction  Motivation and approach  Aim, structure, contributions 2 Biomechanics and state-of-the-art  Human gait and amputation  Variable stiffness actuation  Powered lower limb prostheses 5 Stiffness control exploiting natural dynamics  Spectral trajectory analysis  (Anti)resonance adaptation 7 Overall discussion and conclusion  Global discussion of results 6 Exemplary prosthetic application  Application to powered knee device  Stiffness optimization (new dynamics) Figure 1.2: Thesis structure. 1.2 Aim and structure 5 simulating mechanical interactions between user and prosthesis in a virtual envi- ronment for pre-prototype testing, is suggested. Additionally, the Int 2Bot [11] is presented as a specific human-in-the-loop approach regarding the feeling of body integrity with the prosthesis. As an aspect of enabling technologies, Chapter 4 deals with the consideration of natural dynamics in the technical actuator design process. Using advanced mod- els, possible actuator-elasticity configurations are analyzed regarding their natural dynamics and mechanical power requirements to clarify impacts of natural behav- ior on energy efficiency. The findings are validated with the prototypical test rig of Variable Torsion Stiffness (VTS) [195, 17]. To exploit the optimized dynamics of the mechatronic actuation system with respect to energy efficiency, Chapter 5 deals with a control strategy for adjusting stiffness in variable stiffness actuation. It utilizes spectral analysis of the desired trajectory and adapts stiffness based on the advanced models. Those investigations are performed by simulative analyses and experiments with the prototype. In Chapter 6, an exemplary prosthetic device to substitute the biological knee joint is designed with focus on actuation based on measured human data from [137]. By considering the determined human-machine-centered design focus, the potential of the design framework is evaluated. Further, the example is used to examine possibility to integrate variable torsion stiffness in a prosthesis. Therefore, the elastic drive train is optimized by design simulations and the potential of considering the changed dynamics of the human-mechatronic system is discussed based on first simulations using the model from [248]. To provide a clear separation, Chapters 3 – 6 are each subdivided into sections describing the utilized methods, presenting the results, and concluding those. Based on these chapter-specific conclusions, Chapter 7 gives a global discussion of the overall results of this thesis, along with concluding remarks and an outlook to future works. 1.3 Contributions In prosthetic design, this thesis contributes a novel human-machine-centered ap- proach and proposes a corresponding set of human factors. This set is modeled based on statistical evaluations of user and expert studies with a custom-built questionnaire (see A.1) that is specifically designed for this purpose. Yet, it is not statistically validated to this point and thus remains subject to future research. Anyhow, the new insights on human factors enable to determine insights on user requirements. The application of a transfer methodology reveals the impact of the modeled human factors on lower limb prosthetic design for the example of a powered 6 1 Introduction knee device. Further, a common method from systems engineering is extended to suit user requirements based on the results from the transfer step and integrating human-in-the-loop experiments. With Prosthesis-User-in-the-Loop and Int2Bot, experimental setups for involving users in the design process and investigating the experience of body integrity are presented. Indications regarding the influence of human and technical factors in prosthetic systems engineering are given along with an outlook suggesting a user-stereotype-specific adaptation. Regarding variable stiffness actuation, possible actuator-elasticity configurations are assessed considering their natural dynamics and the interrelation of those to en- ergy efficiency. In contrast to other studies, the impact of drive inertia is considered by advanced modeling and discussed intensively with respect to power consump- tion. Comparing natural dynamics with stiffness values yielding minimum power consumption, the interrelations of those are clarified and can be considered in de- sign and control. As an experimental example, the very first implementation of variable torsion stiffness is presented and experimental results on its mechanical power requirements are shown. This thesis further contributes to the field of variable stiffness control. Based on the advanced models and spectral trajectory analysis, stiffness is adapted to match the natural dynamics of the system to the trajectory frequency. By this, energy efficiency and functional versatility of the actuation system can be improved. As the adjustment of stiffness itself requires additional energy, modeling is extended to cover and analyze this aspect. Aiming at prosthetic application, such investigations could be used to assess which frequency of adjustment is beneficial: Varying stiffness during the gait cycle, once every cycle or once during several cycles. A concept for the implementation of variable torsion stiffness in a powered knee prosthesis is proposed using design simulations with human data. By this, the po- tential of energy recuperation in mechatronic prosthetic knees is examined. The application of advanced modeling in optimization simulations shows essential as- pects of natural dynamics to be considered in design. In the simulations, a step towards considering the change of dynamics through the prosthesis is done by introducing the inertial parameters of the prosthetic leg for a first approximation. 1.3 Contributions 7 2 Biomechanics and state-of-the-art Based on biomechanical fundamentals, this chapter reviews state-of-the-art pow- ered prosthetics and variable stiffness actuation as a key technology for such sys- tems. Regarding human biomechanics, a brief introduction to human gait is given based on [244] and gait data from [137]. Further, different types of amputation are explained. As many prosthetic concepts from research rely on actuation with (variable) elasticity, this basic technology from robotics is described by a compre- hensive review of actuator designs and corresponding approaches to motion and stiffness control are explained. Subsequently, technical solutions of powered lower limb prostheses are presented and analyzed regarding their hardware and software components based on the systematic review from [247]. A focus is set on powered knee devices, as such a system is used as an application example in the remainder of this thesis. Beyond this, tools for evaluating psychological issues in general pros- thetics and approaches to technical design are briefly described. A review and an analysis of the human factors themselves is presented as a main aspect of Chapter 3. 2.1 Biomechanics of human gait Human gait and its cyclic nature can be described by a sequence of events and phases that are depicted in Figure 2.1. In [244], one gait cycle is defined as the Heel strike Opposite toe o� Feet adjacent Heel rise Opposite heel strike Toe o� Feet adjacent Tibia vertical Heel strike swing phasestance phase 100%0% ~60% Loading response Mid-stance Terminal stance Pre-swing Initial-swing Mid-swing Terminal swing Figure 2.1: Human gait cycle and phases (Copyright: Jochen Schuy and Sabine Backhaus, In- stitute for Mechatronic Systems in Mechanical Engineering, Technische Universität Darmstadt, modified with permission and based on [244]). 9 duration between two successive occurrences of the repetitive events of the gait cycle. A common way to interpret the gait cycle is starting with heel strike of the leg in consideration (black in Figure 2.1). The observed sequence of events and phases is divided into a stance and a swing phase depending on the ground contact of the considered foot [244]: Starting with heel strike, the stance phase comprises loading response, opposite toe off, mid-stance, heel rise, terminal stance, opposite heel strike and pre-swing. The transfer from stance to swing takes place with toe off of the considered leg. Swing phase is described by initial swing, feet adjacent, mid-swing, tibia vertical, terminal swing and ends with heel strike of the considered foot marking the beginning of the next cycle. Stance phase lasts about 60%, while swing phase is about 40% of the gait cycle [244]. Between heel strike of one leg and toe off of the other, a phase of double support, where both feet are on the ground, is observed in walking [244]. With increasing gait speed, the duration of swing phase increases and double support duration decreases until it finally disappears and a flight phase occurs marking the transition from walking to running [244]. The spatial distance covered by two heel strikes represents the stride length [244]. Gait speed is often reflected as a distance per time in m s−1 or as a cadence in steps min−1 according to [244]. An important aspect of gait for users of lower limb prostheses is their energetic effort. It is often assessed via the metabolic cost, which can be determined by measuring the oxygen consumption of the human [239]. In [239], which is fre- quently cited, the effects of different levels of amputation on the efforts of users, their walking speeds and stride lengths are compared to those of unharmed hu- mans: Considering the results obtained for subjects with amputation above knee level (transfemoral) and below knee level (transtibial) shows that reduced cadence and stride length is observed in both. Additionally, metabolic efforts are found to increase by 42% and 63% for subjects with transtibial and transfemoral amputa- tion, respectively. Anyhow, subjects experienced lower energetic cost when using a prosthesis instead of crutches. Since the study presented in [239] was performed in 1976, it can be assumed that mechanical prostheses without any actuation have been considered, as those did not emerge even in academic research before the 1980s [252]. Later works report that subjects using any kind of mechatronic pros- theses show decreased metabolic efforts (e. g., [19, 6]), although the situation of an unharmed human is so far not restored. For prosthetic design, analyzing the requirements during gait from human data is crucial. Therefore, gait analysis as performed in [137] can provide insights in desired joint motion ranges and velocities as well as in torque and power requirements. The corresponding model of the lower limbs is reduced to sagittal plane, which divides the body into left and right portions [244]. It is given in Figure 2.2 in 10 2 Biomechanics and state-of-the-art 𝑞𝑘 𝑞𝑓 Hip Thigh Knee Shank Ankle Foot 𝑞ℎ Figure 2.2: Model and coordinate definitions from [137]. 0 0.2 0.4 0.6 0.8 100 150 200 Walking q k in ° 0 0.2 0.4 0.6 0.8 0 1 2 τ k in N m k g− 1 0 0.2 0.4 0.6 0.8 −10 −5 0 5 P k in W k g− 1 t in s 0 0.2 0.4 0.6 100 150 200 Running 0 0.2 0.4 0.6 0 1 2 0 0.2 0.4 0.6 −10 −5 0 5 t in s Figure 2.3: Averaged human gait data for walking at 1.6 m s−1 (left column) and running at 2.6 m s−1 (right column) from [137]: Knee angle qk, knee torque τk and knee power Pk related to body weight. compliance with the one used for gait analysis in [137]. In this, the joints and segments of both human legs are depicted as circles and lines, respectively. Further, coordinates describing hip qh, knee qk, and foot motion qf of the considered leg are defined. Based on these coordinates, Figure 2.3 gives knee joint motions qk, torques τk and power Pk of one gait cycle with respect to time t. Those are averaged from measurements with 21 subjects without amputation (average height 1.73 m, average weight 70.9 kg). In the left column plots of Figure 2.3, results for walking at 1.6 m s−1 are shown, while such for running at 2.6 m s−1 are given on the right. It becomes clear that a wider range of joint motion is covered during running and higher joint velocities occur due to this. Further, the knee torque τk increases by about a factor of 2 regarding its peak value. It is depicted related to body weight for comparability between subjects. Hence, required joint power of the knee Pk is distinctly increased in running, as it depends on motion and torque. Anyhow, from an engineering point of view, the alternating nature of power in both gait types appears promising with respect to reusing energy due to the repetition of the gait cycle. According to [244] positive powers have to be generated by the muscles, while negative powers have to be absorbed by those in humans. 2.2 Variable stiffness actuation 11 2.2 Variable stiffness actuation Generally, robot mechanisms are built as serial, parallel or hybrid structures of links that are connected by joints and driven by actuators [134]. Conventional approaches require precise, fast, repetitive positioning and thus benefit from high mechanical stiffness in motion control with strategies as given in [116, 201]. Hence, conventional robots are designed based on rigid links and joints using actuators with high output power. Therefore, such robots usually work in restricted areas avoiding interaction with humans and preventing those from being harmed. In the last two decades, design and control paradigms changed in the field of robotics due to an increasing demand for closer human-robot interaction [86, 166, 135]. Resulting from this, series elastic joint actuation concepts coupling actuator and joint by an elastic element are increasingly applied, and various concepts to vary its stiffness depending on the actual operating conditions were introduced [227, 135]. The principle of series elastic actuation (SEA) is shown in Figure 2.4, where the link (dotted) is moved around a rotational joint by a motor M1 via a linear elasticity. As the introduced elastic elements are passive mechanical structures, this kind of actuation is commonly referred to as passive compliant or elastic actuation (e. g., [227]). Based on the SEA approach, variable stiffness (series elastic) actuation concepts provide high stiffness to enable enhanced precision, repeatability, and speed, while they can change to low stiffness, if safety is required in human-robot interaction. Further, such actuators allow for increasing energy efficiency in performing cyclic motions by matching the natural behavior of the system to the frequency of the desired trajectory [172, 229]. Beyond this, elastic joints and actuators can protect the mechanical part of the robot by decreasing loads from impacts like ground contact and allow for better force control [172]. In powered lower limb prosthetics, series elastic actuation is often implemented for energetic reasons [6, 62] and the variation of stiffness is utilized to optimize efficiency depending on body mass [96] or gait velocity [80, 79]. Further, it can be used to adapt to different activities and to reject unexpected disturbances [242]. M1 Figure 2.4: Principle of series elastic actuation. 12 2 Biomechanics and state-of-the-art 2.2.1 Actuator designs Passive elastic actuation in robotics emerged in the middle of the 1990s with the presentation of the series elastic actuator [172] and the mechanical impedance adjuster (MIA) [153], which are both capable to change joint stiffness. The se- ries elastic actuator uses a fixed-stiffness spring in series with a stiff actuator and force-controlled stiffness variation [172], while the mechanical impedance adjuster is based on a leaf spring and stiffness can be varied by changing the active length of this spring [153]. After the introduction of those actuators, a variety of variable elas- tic actuators with different principles of stiffness adjustment has been presented. Those can be categorized into four groups considering their fundamental princi- ples [227]: Equilibrium-controlled, structure-controlled, mechanically controlled, and antagonistic-controlled stiffness. In a more recent review [228], the latter three are categorized as actuators with adaptable compliance properties in contrast to such with fixed compliance like the equilibrium-controlled ones. Those latter ones change the equilibrium position of a fixed-stiffness spring to generate a desired force or stiffness by means of control [96]. An overview of the three classes that are part of both categorizations (but not completely coherent) is given in Figure 2.5. In this, categories according to [227] are given in bold face, the depicted example is explained in brackets and the cor- responding category from [228] is printed bold and italic. All examples show a link element (dotted) that is attached to a rotational joint, while two motors M1 and M2 are used to move it and/or adjust joint stiffness. The antagonistic-controlled Antagonistic-controlled (antagon. nonlinear springs) Spring preload Antagonistic-controlled (antagon. nonlinear springs) Spring preload Structure-controlled (active elastic length) Physical properties Structure-controlled (active elastic length) Physical properties Mechanically controlled (lever length) Changing transmission Mechanically controlled (lever length) Changing transmission M 1 M 2 M 1 M 2 M 1 M 2 Figure 2.5: Variable stiffness: Basic categories and examples. 2.2 Variable stiffness actuation 13 principle depicted on the left is using two or more actuators, coupled antagonis- tically via fixed stiffness elastic elements and working against each other similar to human muscles [227]. Joint stiffness becomes variable, if nonlinear springs are chosen [227]. In structure-controlled elastic actuators, as shown in the middle of Figure 2.5, the variation of stiffness is achieved by modifying the physical structure of the elastic element, e. g. changing its moment of inertia or the effective elas- tic length [227]. In contrast to this, the characteristics of the elastic elements in mechanically controlled elastic actuators are constant and stiffness is adjusted by modifying the attachment of the elasticity to the structure, which corresponds to a change of pretension or preload [227], as presented on the right of Figure 2.5. Most actuator concepts can be sorted into the four categories of [227]: Beyond the original series elastic actuator [172], the SEA from the iCub robot [223] and the CompAct [124] belong to the group of equilibrium-controlled stiffness. Among structure-controlled approaches, JackSpring [96], VSJ [34], and VTS [195] are found besides the mechanical impedance adjuster [153]. The class of mechanically con- trolled concepts comprises MARIONET [214], Tunable Spring [225], V2E2 [213], rHEA [212], VS-Joint [250], MACCEPA [229], HDAU [118, 203], vsaUT [175, 81], AwAS [111, 110], MESTRAN [173], FSJ [249], and VNSA [251]. Concepts based on pneumatic muscles like PPAM are usually implemented in antagonistic se- tups [232] and are thus interpreted to belong to the antagonistic-controlled group. Other antagonistic-controlled stiffness concepts are AMASC [105], ANELS [120], GATECH-SEA [150], VSA [222, 187], VSSEA [221], PDAU [203], Edinburgh- SEA [152], CCEA [101], VSA-HD [31], and BAVS [65]. A related concept is found in the quasi-antagonistic approach QA-Joint [56] that combines a main, serial elastic actuator with stiffness variation through an additional antagonistic actuator. An overview over the mentioned variable elastic actuator examples sorted by category is given in Table 2.1. In addition to the type of stiffness variation, the configuration of elastic elements has a significant influence on the dynamic and energetic properties of an elastic actu- ator concept. Most contemporary concepts with variable stiffness utilize an elastic element in series with the actuator, as this allows increasing energy efficiency and safety in human-robot interaction. Yet, parallel elastic elements or combinations of serial and parallel elastic elements can also be used to reduce energy and peak power requirements as proposed in [149, 78]. Investigations using an underactuated planar two-link pendulum showed that the total energy consumption can signifi- cantly be reduced by applying a tuned parallel spring mechanism to the actuated joint [149]. In [78], peak power and total energy requirements of serial elastic, par- allel elastic, and combined serial and parallel elastic actuators are compared using simulations of a powered ankle-foot prosthesis. With appropriate parameters, all 14 2 Biomechanics and state-of-the-art configurations are able to decrease peak power and energy in comparison to direct actuation of the joint (without incorporating elasticity). It is shown that serial elastic configuration reduces total energy consumption best, while a pretensioned parallel elastic configuration is superior in decreasing peak power requirements and combinations resulted in a trade-off of these results. In [61] and [60], these inves- tigations are extended regarding unidirectional springs and damping showing that unidirectional parallel elasticity can further decrease energy requirements, while damping can be beneficial in descending stairs. Anyhow, safe human-robot inter- action benefits distinctly from a series elasticity due to resolving the rigid coupling of actuator and link. In the design of elastic actuators with variable stiffness, dynamic system proper- ties like inertial or gravitational effects have a high significance due to their distinct influence on the natural dynamics [15, 16]. Yet, design is mostly focused on drive properties in early publications like [172], although models for simulation include the properties of actuator and link as in [154]. Up to now, the dynamic interaction between actuator and link is not sufficiently considered for dimensioning in many cases, as current research focuses on energy efficiency by storing energy [227] and thereby often neglects the smaller inertia of the actuators through interpreting them Equilibrium- controlled Structure-controlled Mechanically controlled Antagonistic- controlled SEA [172] MIA [153] MARIONET [214] PPAM [232] iCub SEA [223] JackSpring [96] MACCEPA [229] AMASC [105] CompAct [124] VSJ [34] Tunable spring [225] ANELS [120] VTS [195] V2E2 [213] GATECH- SEA [150] rHEA [212] VSA [222, 187] HDAU [118, 203] VSSEA [221] VS-Joint [250] PDAU [203] AwAS [111, 110] QA-Joint [56] MESTRAN [173] Edinburgh- SEA [152] FSJ [249] CCEA [101] vsaUT [175, 81] VSA-HD [31] VnSA [251] BAVS [65] Table 2.1: Categorized overview on actuation concepts with variable elasticity based on [16]. Abbreviations explained in list of abbreviations of this thesis. 2.2 Variable stiffness actuation 15 as ideal torque or position generators. Thus, only link dynamics are considered and the impact of actuator properties is hence not investigated, e. g., in [110, 214, 250]. Such assumptions are also used in [229, 195] for the analysis of power consump- tion in various variable stiffness actuation concepts, which hence does not show the complete characteristics of those systems. This is also the case in several pub- lications aiming at prosthetic design like [98, 96, 97, 80, 79, 78, 195, 61, 60] due to the calculation of power for stiffness optimization or power analysis, which is explained in detail in Sections 4.1.4 and 4.2.2. So far, the properties of both com- ponents are especially considered in complex antagonistic-controlled concepts like AMASC [105] and VSA [222]. In AMASC, the influence of the interaction between the inertias does not show significant impact [105], while it is not examined in the case of VSA [222]. Among structure-controlled solutions, inertial properties of ac- tuator and link are considered in the complex VLJ [34], but comparably low as in AMASC. Based on linearized models of a prototypic implementation of the VTS concept from [195], the impact of inertial parameters and gravitation on the natural dy- namics of the elastic actuation system are investigated by the author of this thesis in [15, 17, 16]. Due to the relatively high value of actuator inertia, its impact on the natural frequencies is rather distinct and can be investigated well. Based on insights from these works, more versatile possibilities in selecting stiffness by exploiting natural frequencies and an antiresonance mode of the system are de- rived [17]. Hence, a wider range of operation can be covered. The effect of various actuator-elasticity configurations on these possibilities is examined in [16] and in Chapter 4. 2.2.2 Motion control A main challenge in motion control of variable stiffness actuated systems is nonlin- earity, as many of those have robotic structure with segmented link chains under the influence of gravity [3]. Thus, motion control techniques developed to cope with unintended elasticities in robotic joints since the 1980s can be applied as well as such designed for variable stiffness actuation. Beyond common criteria to assess control quality like stability and accuracy, control systems for (variable) elastic joint robots are often required to work without additional sensors compared to rigid systems [3, 162] and to be robust against unknown changing loads as it is also demanded in rigid ones [210, 211]. To reach these various goals, model-based strategies incorporating system knowledge are often used. Considering the review in [162], non-model-based methods like proportional (P), integral (I), and derivative 16 2 Biomechanics and state-of-the-art (D) feedback are mostly used in combination with model-based approaches rather than on their own. Important contributions on the model-based control of robots with flexible joints were made in the second half of the 1980s: In [205], a widely adopted model for robots with elastic joints and motion control based on feedback linearization is proposed. When model and real system match perfectly, the input and state trans- formations of feedback linearization lead to a globally decoupled linear system that can be controlled by linear techniques [50, 208]. Yet, feedback linearization tech- niques are stated to generally require accurate nonlinear modeling and to be com- putationally expensive [143]. Tracking performance improves with increasing joint stiffness according to [200]. To ensure the robustness of such controllers against model deviations, they can be extended by sliding mode control [205, 200]. A different class of strategies is based on singular perturbation theory that can be combined with integral manifolds [209, 208]. Those strategies are separated in a fast inner and a slower outer control loop. The inner control loop is used to dampen joint oscillations and enable the application of rigid robot control laws for the outer motion control loop in case of high joint stiffness [208]. Utilized methods from rigid robotics are computed torque control or adaptive algorithms [208, 206]. A com- prehensive review on major developments based on these initial works considering adaptive algorithms, robust stability and implementation issues is given in [162] for instance. Indications regarding the choice of an appropriate control algorithm are given in [208]: Feedback linearization is stated to yield good results in low stiffness scenarios as the modeled elasticity is integrated into control design, although ac- curacy increases with stiffness as found in [200]. In case of higher joint stiffness, good performance in combination with simple implementation can be reached using singular perturbation approaches. Both, feedback linearization as well as singular perturbation based approaches can further be used as a basis for force or impedance control instead of motion control, as shown in [207]. An extended version of the elastic joint robot model from [205] considering inertial coupling between subsequent joints is used in [51, 47]. Based on this, general feedback linearization [51] as well as feed-forward and PD-type feedback control are investigated [47, 3]. Further, extensions for the control of robots with visco-elastic joints by feedback linearization approaches are given in [48]. Pas- sivity based controllers represent a third common class of model-based nonlinear controllers and a promising approach to combine good tracking performance and robustness [29, 3, 161]. According to [161], where passivity based impedance con- trol is described, this approach virtually decreases the apparent motor inertia and thus improves the dynamic behavior of the controlled robot. 2.2 Variable stiffness actuation 17 In contrast to the observations from early flexible joint control reviewed pre- viously, non-model-based PD- and PID-based approaches are applied in variable stiffness actuator control. In [222], a PD-controller is used for control of the VSA. The HDAU [118] and the HSVA [119] are both controlled by PID-controllers, while in the DLR hand-arm system PD-control is applied in combination with a model- based compensation of gravity and coriolis effects [125]. Despite the nonlinear dynamics, linear state feedback controllers are proposed to control variable stiff- ness actuators in several publications: Gain-scheduled state feedback for active vibration damping in the VS-Joint and QA-Joint of a variable compliance arm [4], gain-scheduled state feedback for the linearized DLR hand-arm system that is de- coupled by eigenmode analysis after torque feedback aiming at robustness and damping [169], general linear quadratic regulation in MACCEPA and the Edin- burgh SEA [100] or gain-scheduled linear quadratic regulation with feed-forward components in AwAS [181, 182]. Among those, the ones based on gain-scheduling use the variation of feedback gains to cope with nonlinearities. Those effects are directly considered by the application of feedback linearization techniques like the combined approach to control motion and stiffness in VSA- II [49] or the control of VTS [17]. Further, a similar technique extended by a smooth sliding mode to improve robustness is shown in [164], while a combination of a sliding mode with gain adaptation by a neural network is used in VSA [104, 103]. Singular perturbation based approaches are proposed for application with VSJ [34] as well as in [165]. Beyond feedback techniques, feed-forward methods are applied in several vari- able stiffness actuators. In vsaUT-II, limit cycles are used to create motions [30]. Further approaches use optimal control methods to maximize link velocity in SEA and VSA [69] or the DLR hand-arm system [87]. In [88] optimal control is sug- gested to maximize potential energy in elastic joints. A method to optimize torque and stiffness control for throwing tasks with the DLR hand-arm system are given in [26, 27]. As an alternative to motion control, impedance and force control, which can be based on feedback linearization and singular perturbation techniques [207], can be applied especially to ensure safety in human-robot interaction. Since active impedance and force control are closely correlated with the stiffness control in variable stiffness mechanisms, such solutions are reviewed in the following. 2.2.3 Stiffness control For the variable stiffness actuation concepts described previously, various methods for controlling stiffness adjustment have been proposed. Common criteria that are 18 2 Biomechanics and state-of-the-art considered in stiffness control design are the reduction of power consumption [230, 17], the adjustment of global stiffness in workspace coordinates [165], keeping injury measures below certain constraints for user-safety [222] as well as stability [104, 103], damping and robustness [4, 169]. Simple stiffness controllers are using PD- or PID-type feedback. Considering VS- and QA-Joint, PD-controllers are used [4]. In [181, 182], stiffness of AwAS is derived analytically and adjusted by a PID-controller regarding the perceived stiffness on the link side. PID-controllers are also used in HSVA [119] and for damping control in CompAct [122, 123]. Further, a PD-approach is proposed to vary stiffness of VTS in a way to exploit natural frequencies and an antiresonance mode of the system aiming at reduced power consumption by the author of this thesis [17]. Another class of approaches to stiffness control relies on nonlinear feedback methods like sliding mode control and feedback linearization. The control of the VSA combines sliding mode control with a neural network for adaptation aiming at increased robustness [104, 103]. Feedback linearization is used for decoupled stiffness and motion control in the VSA-II [49] and combined with a smoothed sliding mode for robustness in the control design presented in [164]. Beyond feedback approaches, there are feed-forward stiffness control techniques and methods for stiffness distribution regarding the kinematics of the system. The aim of [230] is the reduction of energy consumption by adapting stiffness to the tra- jectory and exploiting natural dynamics of a PPAM driven bipedal robot. There- fore, stiffness is chosen as the analytical derivative of required torque with respect to the desired trajectory. A feed-forward method based on the specific charac- teristics of HDAU is proposed in [118]. In [100], required stiffness is calculated derivating the required joint torque with respect to the position in MACCEPA and the Edinburgh-SEA. For the distribution of joint stiffness to match desired values in workspace coordinates, inverse kinematics are considered in [165]. In [30], an ap- proach to generate stiffness commands from limit cycles is presented for vsaUT-II. Further, the calculation of stiffness from a V-SLIP model that models gait as a vari- able spring loaded inverted pendulum is set by a P-controller for the knee torque in [117] considering a bipedal robot actuated by vsaUT-II. In the DLR hand-arm system, quasi static variation of stiffness is assumed using motion trajectories gen- erated from limit cycles [125]. A subgroup of feed-forward techniques applied in stiffness control are such using optimal design. Investigating SEA and VSA, an optimal control scheme to maximize link velocity is suggested in [69]. In addition to maximizing link velocity [87], the potential energy in the DLR hand-arm system is maximized using methods of optimal control in [88]. The group of impedance and force control based methods can substitute motion control methods. Anyhow, it is directly connected to stiffness control, as effective 2.2 Variable stiffness actuation 19 joint stiffness can be influenced passively by a variable stiffness mechanism or ac- tively by means of impedance and force control. Considering pneumatic actuation, sliding mode control and linear optimization are used with additional PD-type loops for independent stiffness and force control in [199]. In [245], the effective stiffness of a cable/tendon mechanism of a finger in the DLR hand-arm system is controlled by combining inverse calculations of required tendon positions with impedance and force control. Further, the combination of passive joint stiffness and active impedance control is used to adjust Cartesian stiffness of the DLR hand-arm system in [168]. Considering a bipedal walking robot based on vsaUT-II, a con- troller switching between stiffness control in stance and motion control in swing phase is proposed in [117]. 2.3 Powered lower limb prosthetics Historically, lower limb prostheses developed from completely passive mechanisms to micro-processor controlled knees. The first realizations of the latter class were able to adjust the dynamic characteristics of the artificial limb in swing. Such concepts that provide this adaptation during swing and stance phase have been investigated in academic research since the middle of the 1980s before commercial products were introduced in the early 1990s [252]. Contemporary, manifold aca- demic research on powered lower limb prosthetics is performed (e.g., in [6, 71]) and first products like the PowerKnee from Össur, Reykjavík, Iceland or the BiOM An- kleSystem from Personal Bionics, Bedford, MA, USA are commercialized. Although the benefits of such mechatronic prostheses regarding biomechanical function have been shown for knee [19] and ankle parts [233], the versatility and efficiency of the biological counterpart is not yet met: As mentioned above, open issues con- cern walking economy of the users [6], power required from the prosthesis [98] and enabling activities like running, which is only possible with few systems [95, 18, 102]. Regarding their kinematic setup, the majority of knee devices reviewed in [247] combine a rotational single-axis joint or a multi-bar linkage with an electromechanic actuator via a ball-screw or belt transmission [114, 22, 64, 224, 99, 170]. Further, the knee part of the integrated powered ankle-knee prosthesis from [217, 218, 128] is implemented using a ball-screw and a slider-crank mechanism, while a combination of a four-bar linkage with a linear actuator is found in [72, 73]. Contrary designs are found in the agonist-antagonist knee from [146, 145, 144] that uses two series elastic actuators attached to the same joint and working against each other as well as the antagonistic setup with pneumatic actuation proposed in [240]. Two novel concepts aim at increased energy efficiency: In the first, a clutch added in parallel with the motor of a serial elastic actuator allows to disengage the motor 20 2 Biomechanics and state-of-the-art and make the system completely passive in certain situations [179]. In the second, a passive knee is coupled with an active ankle to exchange energy and thus decrease ankle requirements [71]. This is possible due to the dissipative nature of the knee during level walking described in [145]. Yet, this kinematic approach might not be beneficial in other gaits, as power has to be provided in the knee in stair climbing or running for example [176, 79]. Most actuators applied in powered knee prosthetic are electromechanic ones like brushed direct current (DC) motors [64, 22, 204, 146, 145, 217, 144, 224, 128, 99], brushless DC motors [218, 170] or linear stepper motors [72, 73]. Pneumatic actuation by means of double-acting cylinders [215, 216] or artificial muscles [240] as well as hydraulic actuation [52] both appear in significantly fewer concepts. While those concepts actuated by fluids use inherent elastic characteristics [215, 216, 240], others incorporate such to store and release energy during gait as the antagonistic setup from [146, 145, 144] or the clutched series elastic actuator in [179]. Yet, elasticity is used often in the ankle but not in the knee of systems like in [217, 218, 128]. Another solution uses a complex elastic mechanism in the knee but only actuates the ankle [71]. For power supply, all autonomous systems rely on (Lithium Polymer) batteries as energy source [146, 144, 218, 72, 128, 73, 99], while other prototypes use external power supplies [215, 64, 216, 217, 52]. Nearly all concepts comprise some kind of joint motion sensor like encoders or potentiometers, as such are often used for state recognition and control pur- poses [114, 215, 64, 216, 217, 22, 146, 145, 144, 218, 224, 240]. In some systems, mechanical loads of joints or actuators [64, 224, 99] are acquired, while the systems from [216, 217, 218] use an additional load cell under the socket to assess loads at the interface to the user. Two very common types of sensing are the acquisition of limb motions by accelerometers or inertial sensors [215, 204, 22, 146, 145, 218, 130, 128] and assessing ground contact using force resistors, Hall effect sensors or pneumatic bladders [64, 217, 146, 145, 144, 240, 99]. Based on such information, state recog- nition and controller selection are performed as in [218]. Another aspect of state recognition is the detection of user intentions. For this purpose, the sockets of two systems are equipped with surface electromyographic (SEMG) sensors that measure muscle activity to estimate human intent [204, 99]. In [99], this is applied to realize volitional control by the user, while it is used to extend Echo Control approaches in [204]. Echo control generates motions based on measuring motion of the intact leg and imitating it shifted by a half gait cycle on the prosthesis [22, 204] and is thus limited to walking even numbers of steps and to people with unilat- eral amputation. The extension with SEMG sensing in [204] solves the first of those issues. However, the most prevalent methods to recognize the state of 2.3 Powered lower limb prosthetics 21 the prosthesis, user intention and environmental conditions use finite-state ma- chines, which are also interpreted as high-level controllers, as they adapt the system to certain states by switching lower-level motion or force/torque con- trollers [114, 64, 215, 146, 216, 217, 218, 144, 130, 240, 128]. Techniques of artificial intelligence like adaptive fuzzy algorithms [22] or recurrent neural networks [52] as well as motion generation by bio-inspired central pattern generators that represent nonlinear oscillators [73] are only used in individual solutions. To finally perform motion tasks, feedback control approaches regarding posi- tion [22], actuator currents [52] or force [99] are applied. Yet, one of the most important types of such lower-level controllers is impedance control, which is used to adjust the mechanical characteristics of the limb, while providing power to it at the same time [64, 215, 216, 217, 218, 128]. Through the specific implementations, torques are generated according to those of a passive spring and damper system instead of controlling positions. With such algorithms, the prosthesis shows more predictable behavior and thus allows for better interaction with the user [216]. A comparable approach is used in [240], where a robust sliding-mode torque control is commanded by an impedance-based torque generator. Two other techniques aim at optimizing energy efficiency: In [146, 145, 144], a quasi-passive equilibrium point control is regulating the engagement of the springs in the antagonistic setup and thus the transformation of potential into kinetic energy, while the approach from [224] switches between a mode that imposes joint power and another that dissipates it by using the motor as a generator. Powered ankle Powered ankle Powered knee Powered knee Powered two-joint system Powered two-joint system Figure 2.6: Examples of powered prostheses (all with permission): AMP-Foot 2.0 (left, [33]), knee powered by pneumatic artificial muscles (middle, [240]) and powered two-joint system (right, [129]). 22 2 Biomechanics and state-of-the-art Considering these aspects regarding ankle, knee and two-joint lower limb prosthetic systems (refer to Figure 2.6 for examples), comparable components and specific characteristics are found: Many ankle prostheses like the ones from [95, 18, 6, 33] use series elastic actuation with electromechanic motors to cope with the high power requirements at the joint. In contrast to the ankle, cer- tain knees do not use series elastic actuation [217, 218, 224] or no actuation at all [71], since power can even be regenerated during level walking as shown in [224]. Yet, the activities of daily life comprise other types of gait [252] with higher power requirements and less potential of regeneration [176]. Prosthetic systems combining powered ankle and knee joints are not available as commercial products and are rather rare in research: A pneumatically actuated approach shown in [215, 216], one system with hydraulic actuation [52], an electromechanically actuated one including elasticity in the ankle drive train [217, 218], a second generation of the former one utilized and described in [102, 127, 129] and the cyberlegs-α prototype combining a passive knee and an ankle with series elastic actuation to exchange energy [71]. An approach similar to the cyberlegs-α prototype is successfully applied for the design of the completely passive WalkMECH prosthesis that transfers knee power to the ankle, which is not actuated [226]. In addition to avoiding conversion losses, such mechanical transfers allow for reducing required actuator power in contrast to electrical regeneration and transfer of energy between joints, as the mechanical re- quirements at the specific joint are reduced. Anyhow, purely mechanical solutions are not adaptable to different gait types or velocities. 2.3.1 Psychological evaluation As motivated in Chapter 1, amputation has a dramatic psychological impact on the life of the concerned persons. Currently, there are two major tools assessing psycho- logical issues in lower limb prosthetics: The Prosthesis Evaluation Questionnaire (PEQ) [133, 132] and the Trinity Amputation and Prosthesis Experience Scales (TAPES) [67]. In the PEQ, prosthetic function, mobility and psychosocial aspects are evaluated by different scales [133, 132]. The functional ones concern usefulness, residual limb health, appearance and sounds, while mobility is treated individually and differentiated in ambulation and transfers. The psychosocial scales are per- ceived responses, frustration and social burden. Further, the issue of well-being is treated as a scale itself. The subscales of the three sections of TAPES are deter- mined and validated by a factor analysis in [67]. Like the PEQ, TAPES contains psychosocial subscales that are general adjustment, social adjustment and adjust- ment to limitation. Functional restriction, social restriction and athletic activity restriction are clustered as subscales of activity restriction in contrast to the func- 2.3 Powered lower limb prosthetics 23 tional scales of PEQ. Further, TAPES comprises functional satisfaction, aesthetic satisfaction and weight satisfaction as satisfaction subscales. Beyond these general tools, questionnaires or measures for specific psycholog- ical issues exist. The Amputee Body Image Scale (ABIS) examines correlations between the body image of people with amputation and their self-esteem, anxiety and depression [28]. In [147], tools not specifically designed for people with ampu- tation are used to investigate their body awareness and schema. The body schema is an important aspect and describes the representation of the characteristics of the own body in a subconscious, neurophysiological and multisensory way [147, 68]. Research described in [186, 184] aims at exploring the values and preferences of prosthetic users towards their devices and their perception of alternative pros- thetic options. Based on combined user and practitioner knowledge, a list of the essential elements for prosthetic prescription to improve outcomes is developed to finally improve fitting rates and user satisfaction. A subsequent Delphi study [185] concludes that psychosocial factors related to service provision and prosthetic use are not widely recognized or incorporated into clinical practice and demands the creation of standardized measures incorporating psychosocial factors for optimal prosthetic prescription. In [70], the factors influencing prosthetic design are cat- egorized as enabling, predisposing and reinforcing factors. As only enabling ones can be influenced by technical development, the author of this thesis proposed to investigate the impact of human factors, the connections between enabling and predisposing factors and to use the obtained insight to consider such factors in technical design [9, 10]. According to this approach, several studies aiming at mod- eling human factors with focus on their integration to prosthetic design have been performed [57, 91, 36, 38, 246, 191, 192]. The survey data and results of those stud- ies represent the human data basis of this thesis and are used to tackle the impact of human factors and their impact on the design in Chapter 3 and Chapter 6. 2.3.2 Design approaches Analyzing the design and criteria of the powered prosthetic knee concepts de- scribed above, gives an overview over the main issues considered and the result- ing approaches. In most designs, important criteria are joint or actuator veloci- ties [114, 22, 216, 146, 170, 71, 179] and joint or actuator forces / torques [114, 215, 216, 217, 218, 146, 144, 72, 224, 240, 99, 170, 71, 179]. Further, common aims are to decrease power required from the actuator [216, 217, 218, 146, 99, 71, 179] and reducing the energetic effort [216, 146, 224, 179, 71] to find a technical solu- tion coping with the demanding biomechanical requirements. Considering those, mimicking stiffness [64, 146, 216, 217, 71] and damping [64] characteristics as well 24 2 Biomechanics and state-of-the-art as the kinematic functionality [146, 216, 217, 144, 218, 240, 99, 71] of the bio- logical limb are design objectives. The consideration of size or weight of the prosthetic component [146, 144, 240] is often connected with compliance to the anthropometric dimensions by adaptation to the size range of the user popula- tion [215, 216, 217, 218, 224, 240, 99] and sufficient structural strength to sustain the required range of user weights [215, 216, 217, 218, 240]. Although requirements like suiting anthropometric dimensions concern the user, they are rather technology-oriented than human- or human-machine-centered just like the resulting design processes. Furthermore, questionnaires like the PEQ are mainly used to evaluate existing designs as in [90, 115] but do not specifically aim at integrating human factors during design or at identifying related technological potentials. Other psychological evaluations presented in Section 2.3.1, focus more on the assessment of the psychological state of the person than on technical po- tentials. First steps towards considering psychological aspects in a human-centered way during technical design are described in [9, 10] by the author of this thesis and are treated in Chapter 3. In [94], the term human-machine-centered is used regarding ergonomic issues of machines in general. Although this concept has similar overall objectives as the approach proposed in this thesis, it rather considers aspects of classical ergonomics (e. g., [54]) than such distinct human-machine interrelations and interaction as those that occur in prosthetics. Due to these differences, the term human factor comprises more than the user-friendly design of the system or environment in this case and is subject to psychology as can be seen from [133, 132, 67]. Beyond the lack of considering human factors in prosthetic design, biomechan- ical requirements are usually determined based on gait analysis and simulation of unharmed subjects like in [98, 96, 97, 5, 234, 95, 80, 79, 78, 61, 60] and thus do not consider the changed dynamics of the prosthetic system. Those changes mostly find first consideration in experiments with prototypes as in [6, 218, 144] and can hence not influence design earlier than at prototype level. Specific simulation models enabling to consider the properties of the prosthesis during its design are avail- able [1, 248]. Further, such allowing for the simulation of pathological gait [53] or the investigation of muscle-reflex control for application in prosthetics [74] exist. Yet, they seem not to be used as tools for prosthetic design up to now. 2.3 Powered lower limb prosthetics 25 3 Human-machine-centered design approach According to [63], it is important for the success of products that those meet cus- tomer requirements, which results in an increasing consideration of such require- ments during the engineering design processes. This is a complex task in general, as only parts of the demands are expressed explicitly by the customer, while the other ones are implicit requirements that can negatively affect product acceptance if they are not covered [63]. In prosthetic design, the patient should always be the focus of treatment and rehabilitation as described above [8]. Anyhow, psycholog- ical factors in general and psychosocial ones in particular recently seem not to be incorporated into clinical practice, while standardized measures for that purpose are missing according to [185]. The human-machine-centered design approach presented in the following specifi- cally aims at coping with that and considers the open questions stated in Chapter 1. This comprises the investigation of which human factors are relevant and what is their impact on technical design. Beyond this, it is unclear how human factors can be considered in technical design and what can be reached by this. As a possible solution, a design framework aiming at a balanced consideration of human and technical factors is proposed. This strives for the long-term objective of designing prostheses that integrate with their users as synergetic human-mechatronic sys- tems. The approach is specifically applied to lower limb prosthetics here, but can be used to design other human-mechatronic systems with distinct body-proximity and human-machine interrelations as well. Therefore, technical and human factors can be adapted, since the framework relies on general approaches from product development. In the deduction of the framework, human factors and their impacts are emphasized, since the user perspective is less investigated and technical aspects are discussed extensively in the literature (compare review in Chapter 2). 3.1 Methods This section describes the methods used in the elaboration of the human-machine- centered design framework. Those comprise literature analysis, user and expert studies to assess user issues as well as product development and systems engineering techniques. The fundamental concept of the proposed human-machine-centered design framework is presented in Figure 3.1. The steps left open in this envelope are 27 Technical factors Technical factors Human factors Human factors Transfer Survey data Literature, questionnaires and interviews Systems engineering Systems engineering Biomech. data Human gait measurements Mechatronic assistance system Figure 3.1: Fundamental concept of the human-machine-centered design framework. elaborated and completed in the following. In contrast to the methodology de- scribed in [10, 246], this concept is intended to integrate technical and human factors within a human-machine-centered design approach leading to a closed de- velopment process instead of extending technical design regarding human factors. Therefore, two parallel analysis tracks for the consideration of technical and human factors are fed with different types of user data. While biomechanical data for tech- nical requirement analysis is acquired by human gait and motion measurements, survey data is obtained from literature as well as questionnaires and interviews with users and experts for human factor examination. In a transfer step, a methodology from product development is utilized to bring the results from the two parallel paths to a joint domain and make them usable for technical design. Therefore, a design focus that gives a human-machine-centered prioritization of design requirements is elaborated. This design focus is used in a systems engineering step for the final development of the mechatronic assistance system. While all methods regarding human factors are applied to (powered) lower limb prostheses in general, technical factors, transfer methodology and systems engineer- ing steps are performed for the application example of a powered prosthetic knee with focus on its actuation. Yet, the approach could be applied to other prosthetic or orthotic systems as well as wearable robotics in general. In this thesis, biomechanical data from gait analyses reported in [137] is utilized. Literature from the systematic review in [247] is analyzed to extract the main tech- nical factors and assess their impact based on contemporary powered prosthetic research. To cope with user requirements, a set of relevant human factors is pro- posed based on literature and questionnaire data as well as examined in an expert study. With the statistical analysis of the latter study from [191, 192], human fac- tor set is analyzed, first indications regarding the impact of the factors are given 28 3 Human-machine-centered design approach Expert data User data Pair-wise comparison NP = 6 Technical factor ranking, tech. development focus QFD discussion NQ = 5 Relations of human/tech. factors, HM-centered focus Questionnaire evaluation N1 = 29 Human factor modeling, technical potential Questionnaire evaluation N2a = 29, N2b = 21 Human factor modeling and correlations, tech. potential Interview study N3 = 11 Body integrity, proprioception Expert study NE = 22 Questionnaire optimization, human factor validation Figure 3.2: Human survey data utilized for: Ranking of technical factors, human factor iden- tification, assessment and modeling as well as determining the human-machine- centered design focus. and relations between them are described. To consider human and technical factors in design, the quality function deployment (QFD) method to be conducted with an expert team is proposed and performed. Inspired by [109, 246, 63], interrelations between technical and human factors are assessed to determine a human-machine- centered focus for technical development and component-specific consideration of user requirements. For mechatronic systems engineering, V model development methodology as given in [231] is presented as a common example. Beyond taking into account the development focus determined by QFD in the V model, indications for mapping human factors impact to it are given and the influences of technical factors are discussed. For better understanding, Figure 3.2 gives an overview on user and expert data acquired for the deduction of this approach. It presents the different studies and the corresponding numbers of participants (N). The objec- tives of the particular studies are printed italic. User data from the custom-built questionnaire given in Appendix A.1 and interviews as well as expert data are used in human factors investigation. Additional expert data is used for pair-wise com- parison of technical factors as well as an expert discussion within the QFD-method used in the transfer step. 3.1.1 Technical factors During early development of a technical product, the definition of a list of re- quirements that can be obtained from persons, products or documents is a crucial step [63]. The requirements on this list include interests of the customer and are thus not purely technical. To separate technical and human factors for an individ-