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The Robotic Gait Simulator: A Dynamic Cadaveric Foot and Ankle Model for Biomechanics Research Patrick M. Aubin Department of Biomechanics,Vilnius Gediminas.

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Presentation on theme: "The Robotic Gait Simulator: A Dynamic Cadaveric Foot and Ankle Model for Biomechanics Research Patrick M. Aubin Department of Biomechanics,Vilnius Gediminas."— Presentation transcript:

1 The Robotic Gait Simulator: A Dynamic Cadaveric Foot and Ankle Model for Biomechanics Research Patrick M. Aubin Department of Biomechanics,Vilnius Gediminas Technical University, Vilnius Lithuania Department of Electrical Engineering, University of Washington, Seattle, WA RR&D Center of Excellence, Department of Veterans Affairs, Seattle, WA

2 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin2/86

3 Patrick Aubin3/78 Motivation Cadaveric models Introduction Olson SL, 2003, Muscular imbalances resulting in a clawed hallux. RGS Rembrandt, 1632 The Anatomy Lesson of Dr. Nicolaes Tulp Fidelity Utility R. Bahr, 1998, Ligament force and joint motion in the intact ankle: a cadaveric study.

4 Patrick Aubin4/78 State of the Art Challenges for gait simulators control the vertical GRF scaled body weight tibia degrees of freedom speed Introduction Cleveland Clinic Medical School at Hannover, Germany U. of Salford and Iowa State U.

5 Patrick Aubin5/78 General Problem Statement Develop an RGS in vitro tibia kinematics, tendon forces, and ground reaction force (GRF) Use the RGS to evaluate novel biomedical devices (e.g. prosthetic feet) model normal and pathological gait evaluate surgical treatment strategies determine optimal surgical objectives elucidate disease etiology determine biological function Introduction

6 The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin6/86

7 Patrick Aubin7/78 Methods RGS in vivo gait trial R2000RGS GRF tendon actuation muscle model tendon force plantar pressure cadaveric foot model GRF foot & tibia kinematics EMG, PCSA from literature living subject kinematics

8 Patrick Aubin8/78 R2000 parallel robot Force plate (C) Cadaveric foot (D) Tibia mounting frame (F) Steel frame (A) Tendon actuation (G) 9 brushless DC motors Series load cells 3D motion tracking camera system (H) Methods RGS

9 Patrick Aubin9/78 The R DOF 25 microns repeatability 120°/s yaw Methods © Mikrolar Inc. video

10 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin10/86

11 Patrick Aubin11/78 Iterative Learning Control Iteration domain vertical GRF control Simulation analyze vertical GRF adjust motion repeat Methods R2000 tendon actuators prosthetic foot plantar surface tendons GRF target kinematics ground motion target GRF target tibia kinematics iterative learning controller

12 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin12/86 ASB, Blacksburg, VA, 2006 NWBS, Seattle, WA, 2006

13 Patrick Aubin13/78 Prosthetic Gait Simulation Kinematics recorded from transtibial amputee Methods video

14 Patrick Aubin14/78 Simulation results (1.5s) ILC: 6 iterations to vGRF tracking 4.1% BW RMS error: simulated vs. in situ Results Prosthetic Gait Simulation P.M. Aubin, et al., IEEE Transactions on Biomedical Engineering, vol. 55, Mar. 2008

15 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin15/86

16 Patrick Aubin16/78 Manual vGRF Control Motivated to study the foot and ankle Improvements for cadaveric simulation Tendon force actuation Tibia mounting frame Liquid nitrogen freeze clamps Collaboration with Lyle Jackson UW medical student research training program Motivation

17 Patrick Aubin17/78 Tendon Force Actuation Nine motors + load cells + freeze clamp Force feedback PID control Matlab Simulink model Methods A/D tendon force torque command target force G c (z) + - ZOH1 current saturationPID drive actuator tendon system D/A load cell 1 G(s)

18 Patrick Aubin18/78 Manual vGRF Control Manual control block diagram Methods R2000 tendon actuators target tendon force cadaveric foot plantar surface tendons GRF target kinematics ground motion tendon force target GRF target tibia kinematics manual control

19 Patrick Aubin19/78 Manual vGRF Control Control heuristics 0-40% of stance phase vGRF achieved by translating the mobile platform 50-90% of stance phase vGRF achieved by adjusting the Achilles tendon force Methods

20 Patrick Aubin20/78 Manual vGRF Control In vitro vertical GRF matched in vivo data Results

21 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin21/86 ICRB, Banff, Canada, NACOB, Ann Arbor, MI, WSMRF, Carmel, CA, 2008.

22 Patrick Aubin22/78 Flatfoot Simulation Motivation flatfoot incidence ~5%, (Ferciot, 1972) investigate effectiveness of reconstructive surgeries Methods manual vGRF control target tibial kinematics and GRF recorded from 10 flat foot subjects cadaveric flat foot ligament attenuation 15,000 cycles Introduction

23 Patrick Aubin23/78 Flatfoot Simulation In vitro tibia angles matched in vivo data Results

24 Patrick Aubin24/78 Flatfoot Simulation Collapse of the medial arch Results

25 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin25/86

26 Patrick Aubin26/78 Open Loop vGRF Control Manual vGRF control was non-dynamic poorly approximates a dynamic system Improvements for dynamic simulation faster tendon force actuator rise and settling time synchronization RGS software data analysis, left and right foot, dynamic tendon force trajectory path planning Introduction

27 Patrick Aubin27/78 Open Loop vGRF Control vGRF Heuristics Methods F Achilles = G·PCSA·MST·EMG x ROB R2000 tendon actuators target tendon force cadaveric foot plantar surface tendons GRF target kinematics ground motion tendon force target GRF target tibia kinematics x G RGS operator

28 Patrick Aubin28/78 Results Open Loop vGRF Control vertical GRF video

29 Patrick Aubin29/78 Results Open Loop vGRF Control 1 stance phase (%) Force (N/ ½ BW) 100 in vivo in vitro vertical GRF

30 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin30/86 ORS, Las Vegas, NV 2009 NWBS, Pullman, WA 2009

31 Patrick Aubin31/78 Metatarsalphalangeal joint (MTPJ) arthrodesis simulations Arthrodesis indications osteoarthritis previous failed surgeries Ahmad Bayomy Collaborator UW medical student research training program Introduction Arthrodesis of the First MTPJ MTPJ Modified from

32 Patrick Aubin32/78 Arthrodesis of the First MTPJ Literature suggests 20° to 25° of dorsiflexion Above 25°: Shoe wear difficulty Below 20°: Abnormal hallux pressure Dorsal fixation plate to simulate arthodesis Vary DF measure PP Introduction

33 Patrick Aubin33/78 Arthrodesis of the First MTPJ RGS simulation at ½ body weight and 10 s Methods video

34 Patrick Aubin34/78 Arthrodesis of the First MTPJ The fusion angle that minimizes peak pressure under the hallux and first metatarsal was 24.0°. Methods

35 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin35/86

36 Patrick Aubin36/78 Fuzzy logic 1.0 vGRF Control Motivation vGRF fidelity Introduction stance phase (%) Force (N/ ½ BW) 100 in vivo in vitro manual control results

37 Patrick Aubin37/78 Fuzzy logic 1.0 vGRF Control A fuzzy logic controller can addresses four major challenges: non-linear, time variant: heel strike (contact events), material properties ill-defined: knowledge is qualitative and descriptive, not analytical underdetermined: vGRF= f (nine tendons, tibia kinematics) limited number of simulations allowed neural networks and genetic algorithms not appropriate As a model-free paradigm a fuzzy rule based controller is well suited for highly nonlinear MIMO systems, [Ross, 2004]. Introduction

38 Patrick Aubin38/78 Fuzzy logic 1.0 vGRF Control Fuzzy logic controller replaces RGS operator Introduction R2000 tendon actuators target tendon force cadaveric foot plantar surface tendons GRF target kinematics ground motion tendon force target GRF target tibia kinematics RGS operator fuzzy logic controller

39 Patrick Aubin39/78 fuzzy logic vertical GRF controller Methods Fuzzy logic 1.0 vGRF Control early late stance early late stance percent stance input variables fuzzy sets negative zero positive negative zero positive vGRF error input variables fuzzy sets large neg. … zero … large pos. large neg. … zero … large pos. F Achilles output variables fuzzy sets

40 Patrick Aubin40/78 fuzzy logic vertical GRF controller Methods Fuzzy logic 1.0 vGRF Control if stance is late and vGRF error is positive and vGRF error is positive then change in Achilles tendon force is large positive if stance is late and vGRF error is positive and vGRF error is positive then change in Achilles tendon force is large positive If…. then … rules. min implication

41 Patrick Aubin41/78 fuzzy logic vertical GRF controller Methods Fuzzy logic 1.0 vGRF Control Combine fuzzy output subsets ++

42 Patrick Aubin42/78 fuzzy logic vertical GRF controller Methods Fuzzy logic 1.0 vGRF Control Determine crisp output via center of gravity

43 Patrick Aubin43/78 Fuzzy logic 1.0 vGRF Control Fuzzy sets manually tuned RGS simulations using modified single axis prosthetic foot Methods

44 Patrick Aubin44/78 Fuzzy logic 1.0 vGRF Control vGRF tracking performance 1.7% BW RMS tracking error between % stance. Results

45 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin45/86 ORS, New Orleans, LA, NV, 2009 NWBS, Pullman, WA, 2009 ASB, College State, PA, 2009

46 Patrick Aubin46/78 Long Second Metatarsal Crossover toe deformity second metatarsophalangeal joint (MTPJ) proposed etiology: long second metatarsal Hypothesis: second metatarsal length is positively correlated with increased plantar pressure Joel Weber Collaborator MSRTP Introduction MTPJ

47 Patrick Aubin47/78 Long Second Metatarsal Surgically lengthen second metatarsal Measure plantar pressure Measure second metatarsal angle Repeated measures design (6 feet, 5 lengths) Achilles tendon force from in vivo measurement Methods

48 Patrick Aubin48/78 Long Second Metatarsal RGS simulation at ½ body weight and 10 s Methods video

49 Patrick Aubin49/78 Long Second Metatarsal vGRF tracking results Results

50 Patrick Aubin50/78 Long Second Metatarsal Second met head peak pressure was significantly associated with an increase in second met length (p=0.0005) Results

51 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin51/86 NWBS, Seattle, WA, 2010 ASB, Providence, RI, 2010 iFAB, Seattle, WA, 2010

52 Patrick Aubin52/78 Fuzzy Logic 2.0 vGRF Control Motivation improve vGRF fidelity Introduction R2000 tendon actuators target tendon force cadaveric foot plantar surface tendons GRF target kinematics ground motion tendon force target GRF target tibia kinematics RGS operator fuzzy logic controller

53 Patrick Aubin53/78 Fuzzy Logic 2.0 vGRF Control Three inputs and three outputs Three controllers in parallel Heuristics based on stance phase events Methods Achilles tibialis anterior R2000 fuzzy logic controller F ACH F TA x vGRF error percent stance

54 Patrick Aubin54/78 Fuzzy Logic 2.0 vGRF Control Heel strike no fuzzy logic output Load response tibialis anterior R2000 trajectory Midstance R2000 trajectory Late stance Achilles Methods Heuristics: if vGRF error is positive and vGRF error is positive then tibialis tendon force is large positive if vGRF error is positive and vGRF error is positive then x is large positive if vGRF error is positive and vGRF error is positive then Achilles tendon force is large positive

55 Patrick Aubin55/78 Methods Fuzzy Logic 2.0 vGRF Control R2000 robot PID tendon force controller electric motor tendon actuators cadaveric foot tendons plantar surface load cell DA AD fuzzy logic vGRF controller F Ach trajectory generator vGRF target + xjxj F Ach F tendon x 7 in vivo tibial kinematics force plate vGRF actual Σ + _ vGRF F TA +

56 Patrick Aubin56/78 Fuzzy Logic 2.0 vGRF Control Statistics methods in vitro versus in vivo Linear mixed effects regression vertical GRF Two-sample t-tests tibia angles Methods min time

57 Patrick Aubin57/78 Fuzzy Logic 2.0 vGRF Control Methods six feet, three learning trials, one final trial 2.7 s ¾ BW video

58 Patrick Aubin58/78 Fuzzy Logic 2.0 vGRF Control Results mean RMS vGRF tracking error was 5.9% BW sig. diff. (p<.05) minimum (5.9%) vGRF int. (2.0%)

59 Patrick Aubin59/78 Fuzzy Logic 2.0 vGRF Control No sig. diff. between in vivo and in vitro tibial kinematics (p<0.05) Results

60 Patrick Aubin60/78 Fuzzy Logic 2.0 vGRF Control Tendon force tracking Results 3.6 N RMS 30.6% peak 3.8 N RMS 5.0% peak in vivo estimate in vitro mean

61 Patrick Aubin61/78 Fuzzy Logic 2.0 vGRF Control Close loop fuzzy logic vGRF control improvement over open loop control Increased speed to 2.7s Accurate reproduction of tibial kinematics vGRF tendon forces Discussion

62 Introduction The RGS Iterative learning vGRF control Prosthetic gait simulation. IEEE Trans. Biomedical Eng., vol. 55, Manual vGRF control Flatfoot simulation. J. of Biomechanical Engineering, in review. Open loop vGRF control Arthrodesis simulation. J. Bone & Joint Surg., vol. 94, Fuzzy logic v 1.0 vGRF control Long second metatarsal study. J. Bone & Joint Surg., submitted, Fuzzy logic v 2.0 vGRF control. IEEE T. on Robotics, submitted Bony motion study. Gait & Posture, submitted Outline Patrick Aubin62/86 NWBS, Seattle, WA, 2010 ASB, Providence, RI, 2010 iFAB, Seattle, WA, 2010

63 Patrick Aubin63/78 Bony Motion Bony motion useful to understand joint function Non-invasive and invasive methods Introduction A. Leardini et al., 2006 C. Nester et al., 2007

64 Patrick Aubin64/78 Bony Motion Study objectives Develop an anatomical multi-segment foot model Determine foot bony motion during the stance phase of gait Introduction

65 Patrick Aubin65/78 Bony Motion Six cadaveric feet RGS simulations in 2.7s at ¾ BW Multi-segment anatomical foot model Methods

66 Patrick Aubin66/78 Bony Motion Anatomical multi-segment foot model digitized virtual points bone pins and quad clusters Methods

67 Patrick Aubin67/78 Bony Motion RGS simulation at ¾ body weight and 2.7 s Methods video

68 Patrick Aubin68/78 Bony Motion Motion of 17 joints recorded Midfoot joints have substantial motion Results Range of motion: 23.2± 4.6 Range of motion: 12.2± 2.2

69 Patrick Aubin69/78 Bony Motion In vitro results consistent with invasive in vivo data Results indicate limitations of simplified rigid body models Better understanding of midtarsal joint midfoot motion inter-metatarsal mobility Discussion

70 Patrick Aubin70/78 Conclusion Dynamic vGRF tracking performance Stance phase (%) Force (N/ ½ BW) 100 in vivo in vitro open loop Fuzzy v 1.0 Fuzzy v 2.0

71 Patrick Aubin71/78 Conclusion vGRF controlClinical studyspeed 1.5 s prosthetic gait simulation iterative learning static flatfoot simulation manual 10 s arthrodesis of first MTPJ open loop 10 s long second metatarsal fuzzy logic s foot bony motion fuzzy logic 2.0

72 Patrick Aubin72/78 Acknowledgements Department of Veterans Affairs, Research Rehabilitation and Development Service grant numbers A2661C, A3923R, A6669R and A4843C.

73 Patrick Aubin73/78 Special thanks to: Center of Excellence for Limb Loss Prevention and Prosthetic Engineering

74 Patrick Aubin74/78 References Ferciot CF. Clin Orthop 85:7–10, Kaz, AJ. Foot Ankle Int. 28: , Nester, CJ. J. of Biomechanics 40: 3412– Leardini, A. Gait & Posture 25: , 2007.

75 Patrick Aubin75/78 Extra slides

76 Patrick Aubin76/78 Motivation Introduction scientific method Hypothesis Experiment Data (Results) Conclusion The function of A is B. Condition A causes disease B (etiology). Treatment A has a better outcome than treatment B. Gray's Anatomy of the Human Body Living subjectsComputational Cadaveric Model

77 Patrick Aubin77/78 State of the Art Dynamic cadaveric gait simulators Introduction Vertical GRF control Trial and error Tibia DOF 3 Speed 12 s Vertical GRF control Trial and error Tibia DOF 3 Speed 2 s Vertical GRF control: Trial and error Tibia DOF 3 Speed 20 s Vertical GRF control: Force control Tibia DOF 3 Speed 60 s Pennsylvania State U. U. of Salford and Iowa State U. Medical School at Hannover, Germany U. of Wisconsin-Milwaukee and Mayo Clinic Cleveland Clinic Vertical GRF control: iterative control Tibia DOF 6 Speed 3.2 s

78 Patrick Aubin78/78 Open Loop vGRF Control Achilles tendon dictates vGRF Results Achilles vGRF Force (N/ ½ BW)

79 Patrick Aubin79/78 Fuzzy logic 1.0 vGRF Control RGS Block diagram with fuzzy logic controller Methods R2000 PID tendon force controller electric motor tendon actuators cadaveric foot tendons plantar surface load cell DA AD fuzzy logic vGRF controller F Ach trajectory generator vGRF target + xjxj F Ach F tendon x 8 in vivo tibial kinematics force plate vGRF actual Σ + _ vGRF operator

80 Patrick Aubin80/78 Long Second Metatarsal second met length PP and pressure time integral (PTI) under second met head (p=0.005, p<0.0001) PP and PTI under first met head (p=0.029, p=0.024) second toe transverse plane angle (p=0.003) Results

81 Patrick Aubin81/78 Fuzzy Logic 2.0 vGRF Control Methods Stance phase events foot flat 16.6% COP under met heads 43.5% heel rise 50% peak TA force ~18%

82 Patrick Aubin82/78 Fuzzy Logic 2.0 vGRF Control R2000 trajectory optimization to increase speed Methods Vicon Plate trajectory Inverse kinematic map Motor velocity Optimization Best TIB pose ROB

83 Patrick Aubin83/78 Fuzzy Logic 2.0 vGRF Control Within subject variability Results

84 Patrick Aubin84/78 Fuzzy Logic 2.0 vGRF Control Medial/lateral and anterior/posterior GRF similar to in vivo Results medial/lateral anterior/posterior

85 Patrick Aubin85/78 Fuzzy Logic 2.0 vGRF Control Precise tibial kinematics Results

86 Patrick Aubin86/78 Conclusion Gait simulator comparison systemvGRF controlvGRF (%)speed (s) tibial DOF Pennsylvania State Univ. open loop Univ. of Salford & Iowa State Univ. open loop5023 Medical School of Hannover, Germany force control50603 Univ. of Wisconsin- Milwaukee & Mayo Clinic open loop40203 Cleveland Clinic iterative control VA RR&D fuzzy logic752.76


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