From a biological template model to gait assistance with an exosuit

By invention of soft wearable assistive devices, known as exosuits, a new aspect in assisting unimpaired subjects is introduced. In this study, we designed and developed an exosuit with compliant biarticular thigh actuators, called BAExo. Unlike common method of using rigid actuators in exosuits, the BAExo is made of serial elastic actuators (SEA) resembling artificial muscles (AM). This bioinsipred design is complemented by the novel control concept of using the ground reaction force to adjust these AMs’ stiffness in the stance phase. By locking the motors in the swing phase the SEAs will be simplified to passive biarticular springs, which is sufficient for leg swinging. The key concept in our design and control approach is synthesizing human locomotion to develop assistive device, instead of copying the outputs of human motor control. Analysing human walking assistance using an experiment-based OpenSim model demonstrates the advantages of the proposed design and control of BAExo, regarding metabolic cost reduction and efficiency of the system. In addition, pilot experiments with the recently developed BAExo hardware support the applicability of the introduced method. Author summary Aging and mobility of elderly people are of crucial concern in developed countries. The U.S. Census Bureau reports that by the middle of the 21st century, about 80 million Americans will be 65 or older. According to the group’s research, medical costs resulting from falls by the elderly are expected to approach $32.4 billion by 2020. Therefore, assistance of elderly people and making the assistive devices more intelligent is a need in near future. However, this is not the only application of assistive devices. Exosuits, as soft wearable robots, introduced a new aspect in assisting a large range of population, even healthy young people. We introduce a novel design and control method for a new exosuit. As the research in the field of wearable assistive devices is growing in recent years and its application in daily life becomes more evident for the society, such studies with a unique view in design and control could have a significant impact. Our proposed biologically inspired approach could be potentially applied to other exosuits.

devices are also helpful for other categories of potential users, like firefighters, laborers 4 and soldiers [4,5]. They reduce the risk of injuries during work and improve the 5 ergonomics of the work conditions. Also, recent studies show a huge societal concern 6 about aging. For example, by aging, muscle force and power decrease and to reduce the 7 cost of elderly and patients locomotion, assistive devices are demanded [6,7]. 8 One of the common goals of assistive device designers is to reduce the metabolic cost 9 of locomotion [8]. This feature is important in all above-mentioned cases and situations. 10 In the last couple of years researchers have succeeded in significantly improving the 11 metabolic cost reduction in human gaits using powered exoskeletons [1, [9][10][11]. 12 Powered exoskeletons can be categorized as (1) traditional ones with rigid structures 13 which are connected to the body in parallel to the biological skeletal system (limb) [12], 14 and (2) recently introduced exosuits using soft materials such as textiles [13,14]. The 15 ability to produce high torques, stabilize gaits in people with severe injuries (e.g., spinal 16 cord) and apply such systems in rehabilitation are of the main advantages of the first 17 group [15,16]. In comparison, having light weight and low inertia, portability and the 18 bioinspired design are of important features of the wearable exosuits. This later 19 property results in more comfort and less constraints in movement by resolving 20 misalignment between the subject's and robot's joints and the joints of the 21 exoskeleton [13,17]. Therefore, one can argue that soft exosuits are more appropriate 22 than the rigid exoskeletons to be used by unimpaired human subjects for daily activities. 23 Because of tight interaction between humans and robots, control of the assistive 24 devices becomes very crucial. Control strategies can be divided into model based and 25 model-free approaches. Model-free control methods include (but not limited to 1 ) 26 time-based (predefined trajectory tracking based) approaches [20][21][22][23], predefined 27 gait-pattern based control [24,25], and EMG-based control [26]. These so-called black 28 box methods [27] will have a high variance in walking economy among participants for 29 fixed control strategies [11]. This problem can be solved by using a 30 human-in-the-loop-optimization (HILO) [11,28]. However, HILO is a time consuming 31 and difficult process to optimize the accurate parameters for each individual. 32 1 For more information about control of assistive devices see [18,19].
Potentially, similarity in design and control of human and the robot locomotor systems 48 can provide more synergistic behavior. A brief overview of the potential advantages of 49 these lines of thoughts in the literature is presented in the following. 50 Template-based control concept of GRF feedback: In [36], the force 51 modulated hip compliance (FMCH model) was introduced as a template for posture 52 control in which the GRF (ground reaction force) was used to tune the hip joint 53 compliance. This method was later implemented in the LOPES II exoskeleton to assist 54 human walking [37,38]. The results revealed the advantages of using the force feedback 55 in reducing the human metabolic cost of walking. From biological point of view, studies 56 on normal and pathological gait demonstrated that humans also use proprioceptive 57 feedback signals (e.g., detecting load as a complex parameter, recorded by very different 58 types of receptors) in locomotion control [39,40]. In addition to ability of measuring the 59 load (e.g., body weight) in humans, high dependency of compensatory leg muscle 60 activation was demonstrated experimentally [41]. 61 Facilitating control with compliant biarticular actuators: Studies on 62 biomechanics of human gaits and robotics show that biarticular muscles help to 63 generate motions in a more energy efficient way [34,42]. In fact, these muscles actuate 64 two joints simultaneously, transfer the energy towards distal joints and further control 65 the output force direction [34,43], [35]. Given these features, biarticular assistive devices 66 can be more effective in reducing energy consumption during walking. Several examples 67 for successful applications of the biarticular elements in designing assistive devices can 68 be found in the literature [10,37,44,45]. Different aspects of analyzing biarticular 69 muscles from template modeling and biological locomotor systems to legged robot and 70 assistive devices are reviewed in [35]. Moreover, adding compliance in a serial elastic 71 actuation mechanism provides further advantages against the common method of using 72 direct-drive motors for exosuit. Some of these advantages are (not limited to) recoiling 73 energy, increasing robustness (e.g., at impacts), reducing peak power and required 74 torques of the electric motors. In biarticular compliant actuators, the returned energy of 75 one joint can be stored in the elastic element in part of the gait and returned in another 76 joint in the following phase of gait [46,47]. 77 In this study, we introduce a new biarticular exosuit called BAExo that actuates hip 78 and knee joints simultaneously. We investigate a white box model-based control in 79 a novel actuator design with compliant biarticular actuation which was not 80 employed in exosuits before. Our bioinspired white-box model is a simplified version of 81 the reflex control [48] and is originated from the GRF-based control, supported by biarticular artificial muscles are tuned based on the GRF signal in the stance phase and 85 2) passive biarticular springs in the swing phase. Here, the advantages of using such a 86 design and control of an exosuit are shown by analyzing human walking experimental 87 data with an OpenSim model. The main advantages of the proposed design and control 88 are demonstrated based on these experiment-based modeling outcomes. In addition, we 89 performed pilot experiments on our recently developed BAExo hardware setup. The 90 preliminary out comes support the applicability of the proposed method in real world.

91
Further comprehensive experiments with more subjects and physiological signals (e.g., 92 metabolics and EMG) measurement will be the future step. Our control approach stems from template-based modeling of posture control in human 101 locomotion. Therefore, first, we describe the VPP (virtual pivot point) concept [50] as a 102 backbone of the FMCH model [36]. Then, we explain how to use the FMCH template 103 model for control of exosuit in the stance phase (when the leg is in contact with the 104 ground). For extension of this model for the segmented leg we use biarticular actuators 105 with adjustable stiffness [51]. Then, control of the exosuit in the swing phase of walking 106 (when the leg is moving freely in the air to take a step) will be described. The control 107 scheme for the swing phase is also based on (passive) biarticular compliance, introduced 108 in [52]. As both of these control strategies use biarticular thigh muscles, we can easily 109 switch between them when the gait phase is changing (from stance to swing and vice 110 versa). This hybrid design and control approach will be called as ABC (Adaptable 111 biarticular Compliance), hereafter.

112
Legged locomotion can be described by three fundamental locomotor 113 subfunctions [53]: 1) Stance: the axial function of the stance leg, 2) Swing: rotational 114 movement of the swing leg and 3) Balance: posture control of the upper body. Here, we 115 focus on the last two subfunctions for design and control of our exosuit. This is because 116 the stance subfunction is mainly well (efficiently) supported by the human body in 117 walking at normal speed.  In order to describe our ABC method, first we explain the basic concept and developed 120 control method for the balance locomotor subfunction which is based on the VPP 121 March 21, 2020 4/24 concept, developed by Maus et al. [50].

122
The VPP model: The VPP which is observed in human and animal gaits is a point 123 on the upper body above the CoM (center of mass) at which the ground reaction forces 124 are intersecting during the stance phase [50]. This concept was already applied to 125 predict hip torque required for posture control using template modelling for different 126 gaits [54][55][56]. Template models are simple conceptual models using basic mechanical 127 elements (e.g., mass, spring) which can explain some important features of 128 locomotion [33]. One of the common templates for modeling walking and running is the 129 SLIP (spring-loaded inverted pendulum) model [57][58][59]. This model consists of a point 130 mass describing CoM, attached on top of a massless spring which represents the stance 131 leg. For describing posture control, a rigid trunk can be added to the SLIP model 132 resulting in the TSLIP (Trunk+SLIP) model [54][55][56]. Using this model, the required 133 hip torque τ V P P (see Fig. 1A) to redirect the GRF to a determined VPP can be 134 calculated by in which, f l , l, ψ, r V P P and r h are the leg force, leg length, hip angle, the distance from 136 CoM to VPP and from VPP to hip joint, respectively. The VPP angle is defined by γ, 137 the angle between body axis and the vector from CoM to VPP, as shown in Fig. 1A.

138
For more details about derivation of VPP formulation please see [50].

139
The FMCH model: In [36] Here, c h and ψ 0 are the normalized stiffness (to body weight and leg length) and the 147 rest angle of the adjustable hip spring, respectively (Fig. 1B).

148
The FMC model, an extension for segmented leg: Due to the segmentation of leg in 149 humans, for using the GRF-based control (e.g., to control the exosuit) the FMCH model 150 was extended to a biarticular level [51]. Since we use the GRF for controlling biarticular 151 muscles and not the hip spring, we will use FMC standing for force modulated 152 compliance and skip the "H(hip)" in FMCH. For this, a virtual leg was defined by a line 153 from the hip to the ankle and the virtual hip torque was defined between the virtual leg 154 and the upper body. To control this virtual hip torque both hip and knee joints should 155 be controlled in coordination. In [43] it has been shown that with appropriate design of 156 the thigh biarticular actuators in a bioinspired bipedal robot (BioBiped3), GRF direction can be controlled with minimum interference to GRF magnitude. For as much 158 as the VPP concept is based on GRF direction control, the thigh biarticular muscles 159 (simplified as adaptable springs in Fig. 1C) can be used to mimic human-like balance 160 control in the segmented leg. Thus, the force of biarticular (artificial) muscle, given by 161 this so called FMC controller, will be in which f F M C is the force applied by the biarticular actuators (adaptable springs for 163 RF or HAM artificial muscles), f l , is the axial leg force, and c, l AM and l F 0 are the 164 normalized stiffness, length and rest length of the artificial muscle, respectively. For the 165 two biarticular thigh muscles, c, l F 0 are the tunable control parameters which will be 166 March 21, 2020 5/24 determined by the optimization method described in the following section. The max 167 function represents the (muscle-like) unidirectional force generation of the actuators.

168
In [51], we introduced this method to be applied for design and control of an exosuit 169 with one actuator mimicking just HAM muscle (hip extensor, knee flexor). Based on the 170 same argumentation of [43] the hip to knee lever arm ratio was set to 2 which generates 171 the same effect as the FMCH with springy leg [51] and equalizes models of Fig. 1A and 172 B. In this study we extend the method by 1) adding the second actuator (for RF), 2) ground clearance similar to humans [61]. They also showed that the knee-to-hip 180 moment arm ratio has a significant effects on stability of gaits at different speeds. More 181 recently, Sharbafi and his colleagues could predict kinematic and kinetic behavior of 182 swing leg and muscle forces in human walking using a template model consisting of a 183 double pendulum with combinations of biarticular (thigh) springs [52]. The outcomes of 184 these studies are in line with former biomechanical studies, which emphasize the 185 important role of the thigh biarticular muscles in the swing phase of human walking [62]. 186 It was shown that the RF and HAM muscles contribute in the first and second halves of 187 the swing phase, respectively [62]. These evidence support the ability to provide 188 human-like swing leg motion with passive biarticular springs which also fits to our FMC 189 control in stance phase (see Fig. 1C). Therefore, we used fixed springs (with constant k) 190 for assisting hip and knee joints in the swing phase.
In this equation, f P , k, l AM , l P 0 are the force applied by artificial muscle, stiffness, the 192 length and the rest length of the artificial muscle for the passive mode, respectively. The ABC control block diagram illustrating the reference force generation and switching conditions. In the FMC mode, SEA follows reference force developed by modulating the artificial muscle stiffness with GRF feedback signal. In the passive mode, the motor is locked and the SEA acts as a passive spring. In this figure t P 2 , t T D , t T O and t F E are the moments that the second peak of GRF, touch down, toe-off and force equality (from Eq.(6)) occurs, respectively. N.C (stands for not connected) means in the passive mode, there is no reference force to be followed by the actuator.
The ABC control is composed of adjustable biarticular springs with force modulated 195 compliance for a time interval (T f ) and fixed springs (with fixed stiffness k) for another 196 time interval (T p ). The following equation presents the formulation of ABC control for 197 each leg.
March 21, 2020 6/24 Here, l AM is the length of the artificial muscle (AM) including the spring length and 199 motor displacement. The reset length of AM is set differently for FMC (l F 0 ) and passive 200 mode (l P 0 ).

201
For the HAM-artificial muscle, the time interval T p starts with the takeoff 202 (beginning of the swing phase, shown by t T O ) and ends when the force generated by 203 passive spring equals the force calculated by FMC. This moment of force equality is 204 denoted by t F E and can be found when the following equality condition is held.
Then, T f starts from t F E to the next takeoff of the same leg. This switching rule is 206 considered to generate continuous changing between the two phases of the ABC control. 207 For RF-artificial muscle, T f starts by touchdown (beginning of stance phase, 208 denoted by t T D ) and ends at a certain time t lock by locking the motor before beginning 209 of the swing phase. Consequently, T p is defined from this moment to the next shown by the (grey) dashed and solid lines, respectively. In the FMC mode, the 222 reference force is calculated using GRF, AM-length and tunable parameters (l P 0 , c), 223 then SEA follows this reference force.

224
Inspired by the positive force feedback of muscles [63], we consider about 40 ms 225 delay (t d = 0.040s) in the GRF signals. Interestingly, this biologically motivated delay 226 results in a better match of FMC force with optimal force. In fact, this delay exists in 227 the exosuit implementation duo to ground reaction force measurement and the settling 228 time in the low level force control. All in all, timing active control (T f ) is given by the 229 following equations for HAM-and RF-artificial muscles The passive time T p in which the motor is locked will be the rest of the gait cycle. Eqs. 231 (5) to (7) clearly show that the ABC control approach is independent of time, and the 232 GRF and AM forces are used to detect the switching time and required forces. searched for the optimal actuation to minimize the approximated metabolic cost. Such 245 a data-driven optimal force pattern is not generated based on a control principle, but it 246 can be considered as a reference for designing the controller. For this, we applied the 247 ABC control method to deliver forces close to the optimal ones. In the following, we 248 first describe human walking data used in the OpenSim model and then discuss the 249 optimization process and the ABC implementation on the BAExo.

250
Experiment-based OpenSim simulation model 251 The locomotion task in this study is walking at preferred speed (1.45 ± 0.15 m/s) for 6 252 healthy subjects (age 25 ± 5 years, height 1.86 ± 0.04, details in Tab. 2). This data-set 253 is borrowed from [5] which is available at https://simtk.org/home/assistloadwalk. 254 For each subject, we used 3 overground trials in which the kinematic data, ground 255 reaction forces (GRF) and moments were measured. Using 8-camera optical motion analysing the assistance from the exosuit and the corresponding muscles' activities. We used OpenSim software (version 3.3) for simulations [68,69]. A three-dimensional 266 musculoskeletal model with 39 degrees of freedom and 80 Hill-type muscles has been 267 used for our simulations. Eight degrees of freedom (bilateral ankle eversion, toe flexion, 268 wrist flexion, and wrist deviation) which are not necessary for our analyses has been 269 locked. The model was based on 21 cadavers and 24 young healthy humans [70]. Our 270 simulation workflow was based on [5]. At first, the musculoskeletal model was scaled to 271 match the anthropometry of each subject. Then, joint angle trajectories were calculated 272 using OpenSim's inverse kinematics (IK) tool. After that, OpenSim's residual reduction 273 algorithm (RRA) tool was used to reduce the residual forces (applied to the pelvis) 274 resulting from small discrepancy between force plate data, marker data, and the  in [5]). Reserve actuators added small torque about each joint to compensate for 298 unmodeled passive structures (e.g., ligaments) and potential muscle weakness. Residual 299 actuators apply the residual forces to minimize the effects of modeling and marker data 300 processing errors. The utilized cost function at each time instance t is given by in which w f,j denotes the constants for weighting the compensating actuator forces [5]. 302 In the assisted mode, the CMC's cost function J A includes the force f k (t) applied by 303 the exosuit actuators in addition to the previous terms. Defining E as the exosuit 304 actuator set and k ∈ E the updated cost function will be Here, w f,k weight is set to a large value (1000 N) for lowering the penalty of using 306 actuators instead of muscles. We applied the same kinematic and kinetic (GRF) dataset 307 (explained in Sec. ) to both assisted (with BAExo) and unassisted models. Thus, the 308 net joint moment in assisted and unassisted modes is conserved and the provided ). Instead, here we try 319 to use this optimal signal as a reference to tune our bioinspired ABC controller. This 320 way, a closed loop control with GRF as a feedback signal can be applied to real exosuits 321 which in principle could outperform the robustness and adaptability (e.g, perturbation 322 recovery or adapting to changed gait conditions) of the feedforward (trajectory-based) 323 control.

324
In Sec. we described the ABC control method which can prescribe the appropriate 325 force in biarticular thigh artificial muscles in both stance and swing phases. The 326 stiffness and rest length of the fixed and adaptable springs in Eq. (5) will be identified 327 by fitting the ABC forces to the optimal reference trajectories using MATLAB curve 328 fitting toolbox. Using the optimal patterns, we also found that the second peak of the 329 GRF is a perfect moment to be selected as the locking time t lock for the RF-artificial 330 muscles. This way, the dependency to time is removed by using the GRF which was 331 already measured and used in the FMC control (see Sec. for details).

332
For implementing the ABC controller in OpenSim, first, we calculated force profiles 333 with Eq. (5) using kinematic and ground reaction force of the unassisted trial. Then, 334 using OpenSim's CMC tool this force profile is applied to the model and the resulting 335 metabolic cost is calculated. The main constraining assumption of these simulation 336 studies is that subjects walked with the same kinematics and ground reaction forces in 337 both assisted and unassisted conditions. Studies on soft exosuit reported relatively 338 small changes in kinematics and kinetics with assistance [71]. Hence, assuming fixed 339 kinematic and kinetic behaviour is acceptable.  The exosuit is composed of a wearable part and an actuation system. The textile 348 components of BAExo consist of a waist brace, two thigh braces and two shank braces 349 (see Fig. 3). There are also HAM and RF serial compliance that consists of a rubber 350 band, Bowden cables and force sensors (see Fig. 3C). The portable actuation system 351 with 2 electric motors will generate assistance force during walking. The actuation 352 components (motors, gears, motor drivers, pulleys and wires) and electronic boards are 353 placed in a backpack (see Fig. 3C). Detailed specification of the BAExo design is listed 354 in Table. 3.

355
For reducing the weight of the exosuit, we used one motor (with augmented gearbox) 356 for each leg, as shown in Fig. 3B,C. These motors are used to pull two serial elastic 357 rubber bands. Therefore, using these SEA arrangements, the same motor is employed 358 for generating the required force in both biarticular thigh artificial muscles. Therefore, 359 by rotating the electric motor in different directions, HAM-or RF-artificial muscles 360 produce forces. Bowden cable is used to transmit the force from the motor to biarticular 361 elastic elements (HAM, RF ; Fig. 3B and C). On the top side, the Bowden cable sheath 362 is connected to the frame of the pulley cover and the inner cable is attached to the  limbs. These components help to concentrate the SEA force in the sagittal plane and to 368 keep the knee lever arms of both artificial muscles around 4 cm. based on the metabolic cost reduction (with respect to unassisted walking) and exosuit 384 power consumption and the comparison to the optimal solution. Since the experimental 385 data (used in OpenSim models) is collected using three force plates, part of the GRF 386 data is missing for one of the stance phases, due to miss-placement of the foot for some 387 trials. To have consistent calculations for all subjects, we removed the incomplete force 388 data and demonstrated the remaining results which included two single supports and 389 one double support (from about 20% to 100% of the gait cycle). Finally, in order to 390 demonstrate the applicability of the proposed method, the outcomes of a pilot assisted 391 walking experiment (with the BAExo) on the instrumented treadmill are presented.

393
In order to find the control parameters of the ABC approach, first, we need to identify 394 the optimal force patterns which are calculated using the method introduced in [5] (see 395 Sec. details). In this section, we separate the design process of the HAM-and 396 RF-artificial muscles. In Fig. 4, the optimal force for the HAM-artificial muscles is 397 shown by gray colour. In the late swing phase, the optimal HAM-artificial muscles 398 starts to contribute. This contribution can be provided by a passive biarticular spring. 399 The optimal stiffness in the simulation is selected according to optimization force in the 400

March 21, 2020
T P time interval. We found that 15 − 20 kN/m is an appropriate stiffness range for 401 HAM-artificial muscle approximate the optimal solution for different subjects. In the 402 stance phase, the second peak of the optimal force can be perfectly approximated by the 403 FMC (the blue curve). This result is consistent for all subjects. Combination of passive 404 biarticular spring in the swing phase and the FMC in the ABC framework (the red 405 dashed curve) nicely predicts the optimal pattern. This result is valid for most of the 406 subjects. In the proposed ABC control for HAM-artificial muscles, the motor is locked 407 during swing phase (interval T p ) and the AM behaves like a passive spring in late swing 408 as shown in Fig. 4B. From beginning of stance phase, the FMC predicts increasing force 409 which is opposite to the generated force by the passive spring. As soon as these two 410 forces are intersecting, the ABC switches to FMC which means stretching the spring by 411 moving the motor (see Fig. 4B). Interestingly, the required movement to follow the 412 FMC is small and slow which could result in low power requirement.

413
For the RF-artificial muscles, we used an SEA for force generation. Similar to 414 human RF muscles, here the optimal force starts at mid-stance (about 35% of the the 415 gait cycle, as shown in Fig. 5). By tuning the appropriate rest length and normalized 416 stiffness, the FMC can appropriately predict the optimal force in the stance phase 417 including the first peak (see Fig. 5A). The second peak in the optimal pattern is not 418 consistent with the biological evidence of humans RF muscle actuation in walking [62]. 419 This means that the RF-artificial muscles can reduce the activation of other muscles. 420 We tried to find the best fit for the optimal RF-artificial muscles force with minimal 421 effort. The blue curve in Fig. 5A, shows that with only FMC the artificial muscle force 422 will be limited to the stance phase. The green curve shows the best fitted passive design 423 (just spring, without motor) to the optimal solution which cannot contribute to the 424 second half of swing phase. In ABC control architecture, locking the motor (equal to 425 switching off the motor for non-backderivable motors), turns the FMC into a passive 426 spring which can still contribute in the swing phase. This way, part of the optimal force 427 can be provided without energy consumption (investigating the locking time t lock is 428 described in the following).

429
The movement of the motor and the spring for RF actuator in the prescribed ABC 430 control (dashed red curve in Fig. 5A) is depicted in Fig. 5B. The motor only moves from 431 mid-stance to t lock resulting in an increase in the spring stored energy. This enhances 432 forward movement of the upper body and swing leg in the late stance and swing phases, 433 respectively. The blue line in this graph illustrates the spring length if the FMC was 434 implementing completely (without locking in between). The difference between the 435 spring (l S ) and the RF-artificial muscles (l AM ) lengths is constant after t lock .

436
In order to better understand the ability of the proposed ABC control within the 437 SEA arrangement, we investigated the effect of the serial spring stiffness and motor's 438 locking time t lock in Fig. 6. The t lock influences the contribution of the motor 439 (consumed energy) and the rest length of the spring which also affects the duration and 440 the magnitude of the RF-artificial muscles contribution in the swing phase. If we lock 441 the motor shortly after it generated the peak force (the GRF second peak) (shown in 442 Fig. 6A), tracking optimal pattern with the ABC controller is improved. However, the 443 motor needs more energy and power as it works longer and needs to stop and return in 444 the opposite direction, immediately. Locking before reaching the peak force results in 445 decreasing motor energy and power, while lowering the quality of tracking the optimal 446 pattern by diminishing the first peak. Our simulations show that locking the motor 447 when the second peak of GRF occurs, is a perfect compromise between human 448 metabolic rate reduction and motor power consumption. Such timing does not require a 449 sudden change in motor movement direction and yields in providing part of the 450 RF-actuator contribution in the swing phase. This also supports the time-independent 451 control described in Sec. .

452
Increasing stiffness of the serial spring, enlarges the magnitude of the RF-artificial 453 muscles force (consequently the peak value), as shown in Fig. 6B. With larger stiffness, 454 we need less displacement of the motor to create the same force with the FMC which 455 means less lengthening in the serial spring. This results in shorter contribution of the 456 passive spring in the swing phase. Therefore, by decreasing stiffness, the stored energy 457 and lengthening of the spring (as well as motor's displacement) are increased which 458 results in applying force for a longer period in the swing phase. Fig. 6B shows that 459 2500N/m is an appropriate spring stiffness which can approximate the optimal solution 460 the best. In this figure, the moment of reaching the second GRF peak is selected as Here, the l F M C is the prescribed length of the serial spring to apply FMC force, which is not followed after t lock . T p and T f are respectively, passive mode and FMC operation time intervals, used in ABC control method. The shaded region shows the swing phase of the gait cycle. The gait cycle starts with the touch down of the right leg. The RF-artificial muscles optimal force pattern for the right leg and its approximation by the ABC controller (using SEA) in the OpenSim walking model. (B) Displacement of the motor (l M ) and the length of the serial spring (l S ) and RF-artificial muscle (l AM ). Here, the l F M C is the prescribed length of the serial spring to apply FMC force, which is not followed after t lock . T p and T f are respectively, passive mode and FMC operation time intervals used in ABC control method. The shaded region shows the swing phase of the gait cycle. The gait cycle starts with the touch down of the right leg. Metabolic cost reduction 463 We calculated the metabolic cost by integrating the instantaneous whole-body 464 metabolic rate over one walking step (one single and one double support) using the 465 U mberger2010M uscleM etabolicsP robe in OpenSim 3.3 [5,72]. According to the 466 subsection 2.2.1, due to the quality of our data, we focused on analyzing one double 467 support and two single support phases. Thus, to estimate an average whole-body 468 metabolic rate, we averaged the instantaneous whole-body rate over half a gait cycle 469 (considering the approximate mediolateral symmetry of walking). To assess the effect of 470 this approximation on our results, we compared the percentage of metabolic energy 471 reduction of using complete gait cycle and half gait cycle in some trials in which 472 complete gait cycle's data are available. We found the negligible difference in our results 473 between using a complete gait cycle and a half-gait cycle.

474
Similar to Optimal controller, the BAExo with the ABC control can also reduce 475 required energy for walking at preferred speed. The metabolic cost reduction and the 476 exosuit energy consumption of the optimization-based and the ABC control methods 477 are shown in Fig. 7, 8. Comparison between percentage of the metabolic cost reduction 478 for different subjects in Fig. 7, shows that our control method can effectively reduce the 479 metabolic cost of walking by about 60%-80% of the optimal method. Although the 480 reduction in the ABC control is less than the optimal approach (which was expected), it 481 can provide a bioinspired white box controller, instead of black box method of giving a 482 time-based trajectory, obtained by optimizing for a specific data set.

483
To provide a basis for comparing the efficiency of different methods, we illustrate the 484 reduced metabolic energy (in Joule, not in percent) in the human subjects body versus 485 the consumed energy in the exosuit in Fig. 8A. As the ABC control also benefits from 486 compliant design of the actuators (SEA), we also used a compliant design for the 487 optimal solution to reduce the consumed energy in the BAExo. Note that, both optimal 488 DD and optimal SEA are in the actuation level of applying the same optimized force 489 patterns on the exosuit which will not affect metabolic cost reduction, shown in Fig. 7. 490 As demonstrated in Fig. 8A, the results of optimization with direct drive (DD) are all 491 below the line with a slope of one, representing 100% efficiency. By adding the serial 492 compliance, the consumed energy is reduced by 15%. The comparison between ABC 493 control and the optimal solution with SEA, shows that the ABC is in average more 494 efficient. To facilitate realizing this comparison, the efficiency (defined by the ratio of 495 the saved energy in human body to consumed energy in the exosuit) is depicted in the 496 separated graph (Fig. 8B). This graph shows that, not only the average efficiency of 497 different subjects, but also control efficiency for each subject is lower for ABC compared 498 to (SEA-equipped) optimal case. It is important to mention that the efficiency above 499 100% in Fig. 8B is not irrational as the BAExo design benefits from compliance and 500 biarticular structures (see discussions in Sec. for more details).  Metabolic energy reduction compared to unassisted mode and device energy consumption for the ABC and the optimal controllers for different subjects (showed by different marker). The mean and the standard deviation of three experimental trials for each subject are shown by the bar height and the error-bar, respectively. (B) The efficiency (defined by the ratio between metabolic cost reduction and consumed energy in the device) of the ABC and the optimal controllers for the BAExo in OpenSim. Note that, both optimal DD and optimal SEA are in the actuation level of applying the same optimized force patterns on the exosuit. Circle and square markers show the mean efficiency for each subject and the mean efficiency for each method respectively.

Exosuit control implementation 502
The ABC control approach -represented in block diagram Fig 2-is implemented in the 503 BAExo hardware setup. The control sequence (timing), the GRF and artificial muscle 504 forces are depicted in 9. In the simulations, two separate actuators were used to implement ABC control method in RF-and HAM artificial muscles (AM). The 506 employed control sequence, is shown in Fig. 9A. This is a typical pattern, developed 507 based on the double-hump GRF signal shown Fig. 9B, and might slightly change step 508 to step. In other words, this is not a fixed time-based pattern. The proposed control 509 approach will result in AM force profiles, illustrated in Fig. 9C. As can be seen in this 510 graph, the two AMs are not actuated simultaneously except in a short period around 511 40% of the gait cycle. Note that, despite activating FMC control for the RF artificial 512 muscle from beginning of stance phase, it will not generate force until mid-stance. 513 Similarly, the HAM artificial muscle will be slack in the late stance. This means that 514 both AMs can be controlled by one motor connected to the two springs (rubber bands), 515 as explained in Sec. . This simpler (and lighter) arrangement could also result in 516 simpler control protocol. By merging the RF-and HAM-artificial muscle force 517 generation in Fig. 9A, the motor control pattern for the experimental setup (with one 518 motor) will be given by the sequence shown in Fig. 9D. The electric motor will start to 519 stretch the HAM artificial muscle as soon as the generated force (measured by the force 520 sensor) is equal to the desired FMC-based desired force. This is the force equality 521 moment which was explained by Eq. (6). After passing the mid-stance, the HAM force 522 will converge to zero while the RF force will start to increase. Therefore, after 523 mid-stance the motor will rotate in opposite direction to stretch RF artificial muscle 524 and follow the FMC for this AM. This will continue until the second peak of GRF 525 (shown in Fig. 9E) which occurs slightly before take-off moment. At this moment, the 526 motor will be locked to switch to the passive mode. This simplified ABC control 527 method is developed based on the GRF, depicted in Fig. 9E and will result in AM 528 forces drawn in Fig. 9F. This figure demonstrates that the force-based control of the 529 adaptable biarticular compliance (ABC) method could nicely match simulation results 530 as well as human thigh artificial muscle patterns in walking [62].

531
Roughly speaking, in the stance phase, the desired trajectories will be followed by a 532 low level force control using the force sensors and in the swing phase the motors will be 533 locked using position control. The attached video (S1 Video) shows the motor 534 movement and the functionality of the BAExo assisting a subject in walking on an 535 instrumented treadmill. Based on the subject self explanation, he feels assistance and a 536 clear difference to the transparent (zero torque, applied by disconnecting the rubber 537 bands from shank and switching off the motors) mode. The force patterns (GRF and 538 the AM forces) look normal and as expected (Fig. 9). This experiment was to validate 539 applicability of the control and design method for walking assistance. More quantitative 540 (Oxygen consumption, EMG and kinematic) measurements with more subject are 541 required to identify the assistance level.

543
In this study, we introduced BAExo as a new exosuit with innovative contributions in 544 different levels of design and control: 1) Underlying control concept: we developed a 545 human-inspired control method instead of the common trajectory based control of the 546 assistive devices [73]. 2) Actuation level: implementing compliant biarticular 547 actuation with SEA arrangement is proposed in BAExo design. Combination of 548 biarticularity and compliance, as two bioinspired design features legged systems, are 549 rarely applied to assistive devices [35]. 3) Feedback signal: using the ground reaction 550 force as a sensory feedback for control in locomotion which was inspired by 551 biomechanical studies [41,49] is applied for the first time in a soft wearable exosuit. 552 We investigated the proposed ABC design and control idea by human 553 experiment-based simulations in OpenSim and preliminary experiments on human 554 assisted walking with our recently developed BAExo robot. In order to facilitate 555 identifying an optimal design and control for a new assistive device with respect to 556 improving metabolic cost reduction in human locomotion, neuromuscular simulation 557 models are advantageous. In simulation based analyses of gait assistance, we assume 558 that the kinematic and kinetic behavior stays the same after wearing the exoskeleton as 559 demonstrated in [71]. We accept the discrepancy between experimental and simulations 560 especially in predicting humans' reactions to external forces (e.g., from the exosuit).

561
Nevertheless, such kind of neuromuscular experiment-based models (e.g., OpenSim 562 models) are the best known software tools for proof of concept before experimental 563 investigations. Furthermore, by using such simulation models, one can examine the 564 effects of assistive devices on forces and metabolic consumption of individual muscles 565 which is extremely difficult by experiments [5]. Hence, first we used the simulation 566 model of gait assistance to evaluate our proposed approach (compared with optimal 567 solution resulting in maximum reduction in metabolic cost). To validate the 568 applicability of the method, we also implemented it on the hardware setup to show its 569 functionality in interacting with humans. In the following, we discuss the outcomes of 570 the simulations and experiments in light of the three above-mentioned contributions. 571 1) underlying control concept: Our FMCH-based control [36,51] of the BAExo 572 has a significant difference to the state-of-the-art methods of controlling assistive 573 devices. Instead of replicating the outputs of the human locomotion control system e.g., 574 joint torques, here we try to discover the underlying control principles for synthesizing 575 locomotor functions. Recently, reflex-based control (introduced by Geyer and Herr [48]) 576 was utilized for gait assistance [31,66,74]. Neuromuscular models [48] are useful 577 biologically inspired tools for developing model-based control of assistive 578 devices [30,74,75] which could potentially address the adaptability of the controller for 579 different conditions. Nevertheless, the main barrier for using such models to control 580 assistive devices is their complexity and a large number of parameters to be 581 tuned [31,74]. As the neuromuscular control in human locomotion is too complex and is 582 not well understood [32], we employed a simplified model prescribed by the Template & 583 Anchor concept [33]. Such kind of template-based control is recently employed for 584 bioinspired legged locomotion control [76] and also assistive devices [19]. In that respect, 585 we selected the FMCH model [36], which was developed to explain human balance 586 control based on the VPP concept [50]. By use of biarticular thigh actuators with 587 appropriate lever arms, an extension of the FMCH model for a segmented leg was 588 presented [51]. This way, we translated a biomechanical template model of human 589 balance control to a practical anchor level as a core concept for design and control of 590 the so called BAExo. In the here here presented approach we combined this model with 591 the passive biarticular spring model for human-like swing leg control (the DPS model 592 in [52]). Therefore, the first and maybe the most important novelty of this study is 593 introducing a new (template-based) approach for design and control of exosuits (for 594 will be reflected in the GRF patterns, our ABC control approach has sufficient sensory 602 information to adapt. 2) Actuation level: The force (GRF) modulated compliance 603 model which is based on the VPP concept was already applied for control of LOPES-II 604 exoskeleton in our previous studies [37,38]. In addition to lack of swing phase control in 605 the LOPES experiments, for implementing the FMC (GRF-based control) in such a 606 rigid exoskeleton, the two single joint actuators were used to emulate the biarticular 607 actuation. Therefore, part of the advantages of the proposed method were not met.

608
Developing an exosuit with compliant biarticular actuators is our solution to regain 609 these benefits. With biarticularity, transferring energy from one joint to another enables 610 the system to reduce energy consumption [35]. Moreover, adding compliance in a serial 611 elastic actuation mechanism provides further advantages such as, recoiling energy, 612 increasing robustness (e.g., at impacts), reducing peak power and required torques of 613 the electric motors. OpenSim simulations demonstrated the ability of the proposed 614 mechanism to reduce metabolic cost up-to 12% with the optimized solutions. In these 615 simulations, we assumed that the kinematic and kinetic behavior of human subject did 616 not change. Definitely, adaptation of human subjects to the exosuit's force could 617 improve the control quality and may result in higher metabolic cost reduction. 618 Experimental results show that the generated force patterns in the biarticular thigh 619 actuators are similar to their biological counterparts (RF and HAM muscles). This 620 supports the control concept, and the effects on the metabolic cost in real experiments 621 could be tested in the future.

622
In our experiments, we tested 3 different stiffness values and we found that the 623 subject feels more comfortable with the lowest value for the RF-artificial muscles and 624 the highest value for HAM-artificial muscles. Since the optimal design and control 625 parameters (in Eq. (5)) are subject-dependent, we do not expect to find similar values 626 for the optimal solution in simulations and the experiments. Another important 627 difference emerges from imprecision in the position and compliance of the attachment 628 points (due to the soft tissue and movement between braces and the body which are not 629 modeled). For example, different lever arms yield finding dissimilar spring stiffness 630 values to generate the same joint torques, although we kept similar hip to knee lever 631 arm ratio (close to 2) in both cases. Therefore, the simulation study can support the 632 validity of the proposed method and the calculated parameters (e.g., spring stiffness) 633 can be used as initial guess for the experimental study. Nevertheless, the optimal design 634 and control parameters must be found separately in experiments with individual human 635 subjects. Moderating optimal values, found from modeling analyses for the developed 636 assistive devices was found in other studies. For example, in a recent study, Nucklos et 637 al., showed that the optimal ankle stiffness from the assistive device should not be more 638 than (around) 50% of the quasi stiffness of the ankle joint [77] which could be found by 639 neuromuscular models. 3) Feedback signal: The last novelty of this study is introducing the ground 641 reaction force (GRF) as a useful feedback signal. Basically, our control approach is 642 similar to impedance control while the actuator impedance (stiffness) is adjusted by the 643 GRF signal. Biological evidence supports implementation of GRF for locomotion 644 control [40,49]. Studies on locomotor disorders confirm the same concept of force 645 feedback importance from another perspective when the proprioceptive inputs can 646 adapt the locomotor pattern to external demands [78]. Dietz et al, stated that "cyclical 647 leg movements ONLY in combination with loading of the legs lead to an appropriate leg 648 muscle activation" [78]. In other words, the compensatory leg muscle activation during 649 the stance phase of the gait is load dependent [41,49]. Pathological gait analyses 650 confirm the importance of GRF in locomotion control; e.g., when there is a reduced 651 load sensitivity and respectively, decreased leg extensor activation in Parkinsonian 652 gaits [39]. Inspired by these studies, positive force feedback (PFF) in muscle 653 control [59,63] and the FMCH template model are all in line with the idea of using 654 GRF as a feedback signal for locomotion control. Although, control theory says that 655 positive feedback destabilizes controlled systems, the PFF explains how reinforcing the 656 extensor activity during the loading period of the stance phase will contribute to load 657 compensation without leading to instability [49]. It is noteworthy to mention that in 658 PFF, the constraints (limited muscle force) and hybrid dynamics of the gait (switching 659 between stance and swing phases) are of reasons to explain how positive feedback could 660 stabilize locomotion. In contrary to phase-detection-based methods (for gait assistance), 661 here, the GRF-based control indirectly synchronizes the exosuit control with human 662 movement. The GRF is considered as an informative sensory signal for control which 663 removes the need to realize gait phasing. In equations (5) to (7) we removed the 664 dependency to time, by using the GRF and the artificial muscle properties (e.g., length 665 and force). In addition, external perturbations will be reflected in the GRF patterns 666 and in the case of designing an appropriate controller, this sensory information could 667 potentially robustify the system against perturbations. Technical issues exist in the 668 implementation level such as measuring the GRF in a portable exosuit. Insole force 669 sensor would be our solution to provide the GRF for overground walking in the future. 670 Comparison between the efficiency of the ABC and the optimal solution supports 671 advantages of our bioinspired design. Although the ABC results in less metabolic cost 672 reduction, it is more efficient than the optimal solution even if it is equipped with serial 673 compliance. More interestingly, the developed device could generate efficiency above 674 100%. This phenomenon is also observed when passive exosuits can yield metabolic cost 675 reductions without consuming energy [79][80][81]. The total energy of the human body and 676 the assistive device can be decreased to less than the metabolic cost in the unassisted 677 gait because of: 1) storing and returning energy with compliant elements [79][80][81] and 2) 678 transferring energy from one joint to another with biarticular mechanisms [80,81]. This 679 is not investigated sufficiently in active devices due to influence of the actuators