IROS2019国际学术会议论文集 2338

Delayed Output Feedback Control for Gait Assistance and Resistance using a Robotic Exoskeleton Bokman Lim Junwon Jang Jusuk Lee Byungjune Choi Younbaek Lee and Youngbo Shim Abstract In this study we propose an interaction control framework for gait assistance and resistance using a robotic exoskeleton We defi ne a smoothed state variable that represents joint angle movements while walking Furthermore a self feedback controller is designed with the delayed output state By applying an appropriate time delay and positive or negative feedback gain to the state variable we can generate assistive or resistive torque stably without any gait phase or environment recognition The time delayed self feedback controller refl ects the movement of the wearer s joints at every moment of control thereby stably coping with sudden task transitions e g walk stop walk forward backward walking as well as walking speed or environment changes Case studies involved gait assistance with a knee exoskeleton and gait assistance and resistance with a hip exoskeleton We performed various preliminary tests including metabolic energy measurements and a comparison of the positive or negative power of the generated torque profi les The results show the fl exibility and effectiveness of the proposed interaction control method for gait assistive or resistive training I INTRODUCTION Gait training or exercises using a robotic exoskeleton can be an appropriate solution for those who need to improve their walking performance due to aging or disease Hip and ankle assistance for example is expected to lessen the problem of excessive use of the hip muscles or a bent posture to compensate for weakened distal muscle strength and balance 1 2 It is expected that knee assistance can effectively improve a gait rehabilitation and training program in patients who suffer from arthritis 3 or have joint replacements To maximize the training effect using an exoskeleton device interaction force should be applied naturally in ac cordance with the wearer s original walking pattern Because the exoskeleton device s weight and motion constraints can distort the user s original gait pattern reducing the device s weight and improving its wearability should take precedence The device s usability maintenance and manufacturing costs and ease of wear are also key factors that cannot be over looked In addition it is necessary to design an interactive con troller capable of responding robustly and stably to changes in the wearer s movement This is because of the irregular walking patterns of those who require rehabilitation such as neuropathic patients and those who have suffered strokes B Lim J Jang J Lee B Choi Y Lee andY ShimarewiththeSamsungAdvancedInstituteofTech nology Suwon Korea bokman lim jw526 jang jusuk7 lee bj81 choi younbaek lee ddalbo shim and because training programs are conducted in a wide variety of conditions 4 e g step stair walking walking over ground that entails navigating obstacles walking at a self selected fast speed walking using a rail to walk forwards and backwards and walking while completing a cognitive task Patients who underwent joint replacement surgery must also achieve the rehabilitation goal of increasing the wearer s leg joint range of motion 5 such that fi ne assist strength control is possible Existing exoskeleton control methods based on walking phase environment recognition with neural oscillators 6 7 8 9 or discrete gait events 10 11 12 can not easily overcome the above problems because accuracy with irregular gait patterns in walking phase environment recognition is more diffi cult to guarantee To overcome this drawback depending on the periodicity of the motion Nagarajan et al proposed an admittance control strategy based on modifying the dynamic response of a coupled human exoskeleton system control 13 Rehabilitation training programs are classifi ed into two methods applying assistive force and applying resistance Recently studies on the usefulness of walking resistance training have been reported 14 15 We expect that a variety of stimuli including resistive interaction forces will help balance training 16 However there are few examples of resistance torque control using exoskeletons 17 and it is diffi cult to fi nd an interaction control method that can simul taneously cover assistive and resistive torque generation Thus we present a novel interaction control framework for gait assistance and resistance to overcome many of the limitations described above The interaction controller is based on delayed output feedback control known for stabilizing oscillatory systems under certain conditions 18 19 20 By adding a time delay buffer to the self feedback control loop we can generate assistive or resistive torque stably in the interaction between the user and exoskeleton The proposed interaction controller can operate at various gait speeds and under environmental changes e g stairs up down ramps with only angular positions and without the need for gait phase or environment recognition The proposed framework can appropriately handle non uniform ground conditions such as ramp level stair sudden stopping and forward backward walking Previously we proposed a hip assistance controller based on a time delayed feedback control method 21 In this study we show that the proposed method can be applied not only to other types of exoskeletons such as knee exoskeleton control but also to resistive torque generation The charac IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE a GEMS K b GEMS H c Interaction control framework Fig 1 Hardware prototypes for gait training with the Gait Enhancing and Motivating System GEMS and an interaction control framework for gait assistance and resistance GEMS K is our knee exoskeleton and GEMS H is our hip exoskeleton teristics of the control parameters viz the time delay and feedback gain are also analyzed and discussed To my best knowledge this is the fi rst example of applying time delay control to walking resistance and knee assistance This paper is organized as follows Section II describes the interaction control framework based on delayed output feedback control for knee and hip exoskeletons Section III provides the experimental results under various walking conditions Finally we conclude with a summary of the study and suggestions on how to extend our framework into other types of exoskeletons such as single joint driven assistance e g an ankle exoskeleton device worn only on one foot II FRAMEWORK ANDALGORITHM A Interaction Control for Gait Assistance and Resistance Our interaction control framework for gait assistive or resistive training is shown in Fig 1 The interaction control method is based on delayed output feedback control DOFC The DOFC based controller design can be classifi ed into two steps Step 1 Defi ne an output state representing the current leg s motion with joint angular positions Step 2 Determine the smoothing rate delay time and feedback gain of the output state Once the value or range of the control parameters is de termined it is confi gured as a self excited feedback control loop As shown in Fig 1 c the input of the interaction con troller comprises the joint angular positions and the output is the interactive torque The original state value yraw t is calculated as a function of the joint angles yraw t f q t Noisy sensing data yraw t is fi ltered through the state smoother Delay due to state smoothing is not a problem because an additional time delay is used in the next procedure The smoothed state y t is delayed for some time by passing through the state delayer y t y t t This process is easily implemented by using a constant time delay buffer Here reducing the time delay value leads to an early assist or response while increasing the time delay value results in a late assist or response Finally interaction control torque is generated by multiplying the delayed state y t t by the feedback gain The magnitude of the gain is proportional to the magnitude of the generated interaction torque i e as the gain increases the generated torque becomes more assistive or resistive At this time amplifying the state value using positive gain generates assistive torque and conversely negative gain generates resistive torque B Assistive or Resistive Torque Generation from Knee or Hip Joint Angles The proposed interaction control framework can be ex pressed in a more detailed and concrete form as shown in Fig 2 We fi rst defi ne an output state yraw t as that representing the projected leg motion yraw t sinqr t sinql t 1 where qrand qlare the right and left joint angles respec tively We use the sinusoidal projected joint angle difference for knee and hip exoskeleton control The original noisy sensor data is smoothed by passing through a simple fi rst order low pass fi lter yi 1 yi 1 yi raw 0 0 assist mode if 0 05 for the paired t test no exo vs exo In other words there was no signifi cant change in metabolic energy expenditure due to wearing the knee exoskeleton and its assistance during TABLE I REDUCED METABOLIC COST WITH THE KNEE EXOSKELETON SubjectNo ExoExo Assist No rNMR W kg NMR W kg rNMR 14 294 43 3 4 22 773 13 12 8 33 383 62 7 3 42 952 940 3 53 873 636 3 Mean SD 3 45 0 563 55 0 52 3 4 6 5 NMR net metabolic rate rNMR reduced net metabolic rate from free walking condition No exo p value 0 4 0 05 for paired t test No exo vs Exo A negative value means that metabolic energy has increased compared to normal walking with no exoskeleton walking This means that the increase in metabolic energy due to weight and the movement restriction due to wearing the knee exoskeleton was offset by knee assistance during walking Through this preliminary test we showed that an increase in metabolic energy can be prevented through knee only assistance for the fi ve healthy subjects and furthermore that it might be possible to reduce metabolic energy by tuning the control parameters and optimizing the extension fl exion assistance ratio magnitude and timing selection Notice that three of the fi ve subjects had increased metabolic energy expenditure while two had decreased metabolic energy B Gait Assistance and Resistance with a Hip Exoskeleton The basic assistance strategy Fig 2 b can be extended for both right left hip torque generation r des l desby modifying the original torque equation in 3 Right hip fl exion left hip extension rh des t t 6 lh des t t H Left hip fl exion right hip extension lh des t t 7 rh des t t H where H denotes the hip extension fl exion torque ratio if H 1 the hip extension and fl exion torque strength is the same In this study we set the smoothing factor for the hip exoskeleton Hto 0 05 in 2 and the hip extension fl exion ratio Hto 1 This smoothing factor H like the knee exoskeleton case was manually determined to produce smooth interaction torque Fig 6 shows the joint angle and assistance torque values during walking task transitions from forward to backward walking and backward to forward walking The assistance controller and the output torque are directly affected by the hip motions as seen in Fig 6 For the forward backward forward walk transition task the resulting mean positive and negative power values were 3 85 W and 0 13 W respec tively Lower negative power value compared to relatively large positive power supports the idea that the resistive torque generation was minimal 12345 Gait speed km h 0 2 4 6 8 Mean power W Positive Negative 12345 0 2 4 6 8 12345 0 2 4 6 8 12345 0 2 4 6 8 t 0 35 st 0 25 s t 0 05 st 0 15 s a Mean positive negative power vs Time delay 12345 Gait speed km h 1 2 3 4 5 RMS torque Nm b RMS torque vs Time delay Fig 5 Generated mean positive negative power and the RMS torque changes due to time delay changes t 0 05 0 15 0 25 0 35 s 8 Positive mean positive power Negative mean negative power 68101214161820222426 60 40 20 0 20 Angle deg Right Left 68101214161820222426 6 4 2 0 2 4 Velocity rad s 68101214161820222426 10 5 0 5 10 Torque Nm 68101214161820222426 Time sec 10 0 10 20 30 Power W ForwardBackwardForwardBackward Fig 6 Hip joint angle velocity torque and power trajectories for the selected task transitions from forward to backward walking and backward to forward walking The hip joint sensing data are obtained from the hip exoskeleton A forward backward forward walk t 0 25 s 8 H 1 H 0 05 is performed with exoskeleton assistance In the torque plot the gray dashed line represents the estimated torque from current sensing while the blue and red solid lines denote the generated desired assistance torque With six male subjects age 41 3 2 weight 71 5 0 kg height 174 8 2 cm we previously showed that hip assistance can reduce metabolic energy from walking by an average of 20 compared to normal walking state with out the exoskeleton 21 We also showed with same six male subjects how the proposed assistance algorithm can be generalized in assisting in various conditions speed and environment changes by showing the differently adapted torque and power profi les with fi xed control parameters t 0 25 8 21 The generated torque and power under fi xed control parameters showed a consistent trend of change in walking speed environment except for small variance due to individual hip pattern differences For this reason experiments were conducted on a single subject and on a variety of situations 1 RelationshipbetweenTime delayandGenerated Power Torque We can adjust the assistance response or timing by adjusting the time delay t Figure 5 shows the generated MP mean power and RMS root mean square torque for four selected time delay values t 0 05 0 15 0 25 0 35 s As shown in Fig 2 b the generated torque has a sinusoidal form so the RMS torque value difference denotes the generated torque difference One male subject age 40 weight 67 kg height 160 cm wore the hip exoskeleton and walked with assistance We used a fi xed gain of 8 The treadmill speed increased from 1 km h to 5 km h in 1 km h increments The torque and power generated in the hip joint were calculated with a sensor attached to the exoskeleton As shown in Fig 5 b the time delay t affects the generated torque magnitude even though it is a control variable related to assistance timing The generated torque amplitude increases as the time delay increases The positive and negative powers delivered to the subject is shown in Fig 5 a The magnitude of the positive power generated is likely to be highest at around a time delay of t 0 25 s If there is too much time delay such as when t 0 35 s this indicates that there is a problem with generating assistive positive power for high speed walking An increase in negative power generation means that the amount of work done by the wearer has increased due to a mismatch between the assist and the users movement If the time delay value is too small t 0 05 s negative power generation does not increase even at high speed gait but there is also less positive power generation and assistive torque generation It is therefore necessary to set an appro priate time delay value 2 Adjusting Transfer Power by Gain Change We can adjust the assistance resistance strength strong or weak by adjusting the feedback gain Same one male subject walked on the treadmill after wearing the device The treadmill speed was fi xed at 4 km h We set the time delay t to 0 25 s From 5 to 10 we increased the gain value by 0 2 for every two steps 1 walking cycle Fig 7 a shows the change in the torque and power profi le when the gain gradually increased from 5 to 10 The resistance torque generated at the negative gain 5 was inverted as the gain increased little by little and smoothly changed to the assistive torque 0 The generated power also shows a gradual change in response to the gain change Fig 7 b shows the gain and generated RMS torque and 020406080100 8 6 4 2 0 2 4 6 8 Generated torque Nm 020406080100 Gait cycle 10 5 0 5 10 15 20 25 30 35 Generated power W Extension resist 0 Flexion assist 0 Extension Flexion resist 0 Extension Flexion assist 0 a Torque and power 50510 2 1 0 1 2 3 4 5 6 RMS torque Nm Resist Assist 1 Resist 50510 Gain 4 2 0 2 4 6 8 10 12 Mean power W Positive Negative b RMS torque and Mean power Fig 7 Generated torque and power changes due to gain changes The feedback gain was increased from 5 to 10 t 0 25 s 4 km h walking speed Positive mean positive power Negative mean negative power TABLE II REDUCED METABOLIC COST WITH THE HIP EXOSKELETON ConditionExo generatedHuman reduced gain RMS Nm MPP W NMR W kg rNMR 1 8 03 867 483 49 3 1 2 9 54 308 293 24 10 1 3 11 04 789 303 07 14 8 4 12 55 2210 362 98 17 1 5 14 05 7011 342 85 20 9 RMS RMS torque MPP mean positive power NMR net metabolic rate rNMR reduced net metabolic rate from free walking condition No exoskeleton power relationships under given walking conditions t 0 25 s 4 km h walking speed A linear proportional rela tionship between the generated torque power and the gain is observed In the plot on the right side of Fig 7 b when the gain is positive 0 mean negative power MNP generation is inhibited compared to mean positive power MPP On the other hand when the gain is negative 0 MPP generation is effectively suppressed compared to MNP 3 Effects on Metabolic Cost by Adjusting Gain Fine control of power delivery can be extremely useful for gait rehabilitation or training This is because customized rehabil itation is possible depending on the stage of the rehabilitation and the patients condition Fig 8 and Table II show the resulting metabolic measurement for fi ve selected gains 8 9 5 11 12 5 14 Same one male subject walked on the treadmill at 4 km h Fig 8 Raw metabolic rate data The red line denotes the raw data The black line denotes the fi ltered metabolic data shown for visual purposes The horizontal black line denotes the median with respect to the last 3 minutes und