Toward Safe Wearer-Prosthesis Interaction: Evaluation of Gait Stability and Human Compensation Strategy Under Faults in Robotic Transfemoral Prostheses

Although advanced wearable robots can assist human wearers, their internal faults (i.e., sensors or control errors) also pose a challenge. To ensure safe wearer-robot interactions, how internal errors by the prosthesis limb affect the stability of the user-prosthesis system, and how users react and compensate for the instability elicited by internal errors are imperative. The goals of this study were to 1) systematically investigate the biomechanics of a wearer-robot system reacting to internal errors induced by a powered knee prosthesis (PKP), and 2) quantify the error tolerable bound that does not affect the user’s gait stability. Eight non-disabled participants and two unilateral transfemoral amputees walked on a pathway wearing a PKP, as the controller randomly switched the control parameters to disturbance parameters to mimic the errors caused by locomotion mode misrecognition. The size of prosthesis control errors was systematically varied to determine the error tolerable bound that disrupted gait stability. The effect of the error was quantified based on the 1) mechanical change described by the angular impulse applied by the PKP, and 2) overall gait instability quantified using human perception, angular momentum, and compensatory stepping. The results showed that the error tolerable bound is dependent on the gait phase and the direction of torque change. Two balance recovery strategies were also observed to allow participants to successful respond to the induced errors. The outcomes of this study may assist the future design of an auto-tuning algorithm, volitionally-controlled powered prosthetic legs, and training of gait stability.

I. INTRODUCTION 34 I T IS impressive that humans can maintain consistent task 35 performance reliably and repeatedly while encountering 36 environmental uncertainty and internal movement variability 37 and noise [1], [2], [3]. The ability to adapt to internal and 38 external changes/errors has been discussed in many motor 39 control theories [4], [5], [6] (e.g., minimize intervention prin-40 cipal [7]) where errors/changes that do not interfere with the 41 task goal are tolerated by the individual. That is, the individual 42 does not need to correct errors deemed insufficient to disrupt 43 the task performance. It is of interest to know if this ability 44 can be applied to a wearer-robot system. Technology has 45 advanced to the point that wearable robotic limbs, such as 46 robotic prosthetic legs, can be physically attached to humans 47 to replace or augment the human biological limb function. 48 Given that a wearer-robot system is often controlled by 49 two independent mechanisms (human motor control system 50 and machine controller), understanding how the wearer-robot 51 system reacts and adapts to internal and/or external errors of 52 the limb movement control becomes especially important to 53 ensure safe wearer-robot interactions. 54 Specifically focusing on lower limb prosthetic legs, many 55 studies have investigated the biomechanics of balance recovery 56 of humans wearing a passive prosthesis while encountering 57 external perturbations, such as, simulated uneven terrains in a 58 virtual environment [8], [9], obstacle crossing [10], [11], unex-59 pected external force impact on the pelvis [12], [13], prosthetic 60 misalignment [14] that induce gait instability due to mechan-61 ical knee-buckling, altered frictional forces and mediolateral 62 foot placement, or reduced toe clearance. These laboratory 63 tasks elicited slips or trips by inducing external disturbances 64 at specific gait phases and found that prosthetics users suc-65 cessfully adapted their walking strategy to compensate for 66 external errors. Emerging robotic prostheses provide an excit-67 ing opportunity to restore the function of a missing limb, 68 in terms of power production and intelligent control. However, 69 these robotic devices are also subject to faults in sensors and 70 control commands. For example, to enable seamless terrain 71 transition for a robotic prosthesis, researchers have developed 72 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ a locomotion mode recognition system as a high-level pros-Hence, the objectives of this study were to 1) quantify 126 the error tolerable bound that does not affect the user's gait 127 stability and 2) systematically investigate the biomechanics of 128 wearer-robot systems reacting to internal errors induced by a 129 robotic prosthetic leg. Different from our previous study [23], 130 we created an experimental design to systematically scan the 131 size of prosthesis control errors to determine the effects of 132 those errors and the tolerable bound. A prosthesis control 133 error simulator was designed to artificially create errors during 134 stance phase that modulated the finite-state machine and 135 impedance control of a powered prosthesis. We focused on 136 stance phase only because prior work established that human 137 wearers are more sensitive to prosthesis control errors during 138 this phase [23]. The effects of the errors on the powered 139 prosthesis and the gait stability of the wearer-robot system 140 were evaluated. We expect that the results of this study could 141 provide insight into wearer-robot interaction and reaction to 142 intrinsic errors of robotic prosthesis and inform the future 143 strategies to ensure the wearer's safety when walking with 144 intelligent wearable robots. We used a powered knee prosthesis (PKP) developed by 148 our research group for this study. Sensors were embedded in 149 the PKP to measure knee joint angle (potentiometer), knee 150 joint angular velocity (encoder connected with the motor), 151 and ground reaction force (GRF) ( load cell, mini 58, ATI, 152 NC, USA) mounted in line with the shank pylon). A multi-153 function data acquisition card collected all sensor measure-154 ments at 100 Hz and provided digital-to-analog control output 155 to drive the DC motor through a motor controller (RE40, 156 Maxon, Switzerland).
The PKP was controlled based on a finite-state impedance 158 controller (IC) that is an established framework for robotic 159 knee prosthesis control (Fig. 1). The gait cycle was 160 divided into four phases based on the relationship between 161 ground reaction force (GRF), knee angle(θ), and knee 162 velocity(θ) [29]: initial double support (IDS, m=1), single 163 support (SS, m=2), swing flexion (SWF, m=3), and swing 164 extension (SWE, m=4). The motion of the PKP was modu-165 lated by the knee joint torque (τ ) that was generated based 166 on a set of impedance parameters and the real-time knee 167 joint angle (θ) and velocity (θ). Within each phase, three 168 impedance parameters (IP), stiffness (K m ), equilibrium (θ em ) 169 and damping (B m ) were set at constant (Equation 1). Thus, 170 in total there are 12 IP (4 phases * 3 parameters) that are 171 needed to configure each locomotion mode.     Errors in this study were imposed on the prosthetic knee 220 joint by switching the level ground IPs to disturbance IPs. The 221 mismatch of IPs mimicked the recognition errors associated 222 with switching terrain, and added a pulse of error torque via 223 the knee controller. The error in this study is characterized by 224 1) the magnitude of errors that corresponded to the perceived 225 gait instability and 2) the onset timing of the error in a gait 226 cycle. We investigated the machine errors only during stance 227 phases (IDS and SS) because errors during these phases have 228 a larger influence on balance stability compared to errors 229 induced during swing [23]. We fixed the error pulse duration 230 to 200 msec and only varied the torque magnitude to change 231 the error size. The selection of 200 msec is based on our 232 previous studies that reported the continuous misclassification 233 in human intent generally lasted no more than 300 msec and 234 200 msec was enough to cause gait instability [23]. Error sizes 235 were scored based on the presence of small (score 1), medium 236 (score 2), and large (score 3) disturbances, based on each 237 participant's reported level of gait instability (see Table I). Considering that any IP that deviated from the current 241 locomotion mode can be regarded as an error, the selection 242 of disturbance IPs are infinite. To simplify the selection as 243 well as ensure that the disturbance IP might actually be used 244 in a real situation, the disturbance IP can be denoted as: where the K level , θ level , and B level are the IP customized for the 249 participant on level ground walking, the K dist , θ dist , and B dist 250 are the disturbance IP, W is the participant's body weight, α is 251 the weighting to scale the amplitude of disturbance level.

252
To determine the K, θ , and B, five sets of IPs tuned 253 for transfemoral amputees on ramp ascent and ramp descent 254 walking were used. The mean of IP between level ground 255 and ramp ascent/ramp descent modes were calculated in which 256 K and B were normalized to the amputees' body weight. 257 Thus, the relationship amount K, θ , and B are fixed and 258 corresponded to the ramp ascent or descent (values are shown 259 in Appendix Table I). Therefore, the disturbance IP can be 260 generated by assigning an α value to equation 2, 3 and 4.
Since the amount of mechanical change elicited by distur-262 bance IPs is unknown, the magnitude of error is estimated 263 using angular impulse around the knee joint because it reflects 264 shifts in both kinetics and kinematics when errors happen.

265
Several sets of disturbance IPs were calculated by assigning 266 α from −10 to 10. The level ground IP, disturbance IPs, the 267 mean θ and meanθ from eight gait cycles were applied to 268 equation 1 to estimate the change of angular impulse ( L). 269 The change of angular impulse is defined as:   walking speed. Fifteen 3D Inertial Measurement Unit (IMU) 317 sensors (MTw Awinda, Xsens, USA), setting a rigid body 318 model with 12 or 13 segments, were used to obtain the 319 kinematics for head, trunk, upper arms, forearms, upper 320 legs, prosthetic lower leg, prosthetic feet, participants' shank, 321 participants' feet, and the segments that supported by the 322 L-shaped socket for non-disabled. During walking, the con-323 troller switched the level ground IP to the disturbance IP 324 at the targeted gait phase with 200 msec duration during a 325 randomly selected gait cycle. The mismatch of IP induced an 326 error to the human-machine system. The order of conditions 327 for 2 ramp IP and 2 phases were counterbalanced, and the 328 3 error sizes and ± L were randomized within a trial. Each 329 condition was repeated 7 times, resulting in 168 disturbances 330 for each participant. Rest periods were allowed between trials 331 to avoid fatigue. The effect of errors on gait instability was evaluated both 334 subjectively and objectively. After walking to the end of the 335 pathway, participants were asked to report a score regarding 336 any perceived gait instability based on a four-scale question-337 naire (see Table I). If the disturbance was rated larger than 2, 338 the error was considered to cause gait instability.

339
To quantify the safety boundary, the mean of L from 340 errors that received a perceived gait instability score = 2 was 341 reported. The mean change of prosthetic knee angle was also 342 calculated using equation 6.

390
The rotation from segment to global frame of reference was 391 given from the Xsens file using the quaternion vector (q0, q1, 392 q2, q3) with q0 as a real value and q1, q2 and q3 as complex 393 numbers. Hence, we can calculate the rotation matrix (R G P ) 394 describing the orientation of the pelvis segment as: The rotation of H from global to pelvis orientation can be 398 denoted as: where R G P T is the transpose of R G P , H is angular momentum 401 from global frame of reference and the H PG is the rotated 402 angular momentum from global to pelvis frame of reference. 403 Because the PKP errors would cause the irregular knee flexion 404 or extension, the full-body angular momentum in the sagittal 405 plane (": + " posterior and ": -" anterior) was used.

406
The peak magnitude of anterior angular momentum (-|H|) 407 was calculated to quantify the error that resulted from irregular 408 knee flexion, and the magnitude of posterior angular momen-409 tum (+|H|) was calculated to quantify the error resulting from 410 irregular knee extension. To reduce the variation between par-411 ticipants, H was normalized in a dimensionless form divided 412 by the participant's weight, height, and average walking speed. 413 Step length and width were calculated using the position of 414 the prosthetic heel and intact heel to evaluate if the participant 415 regulated these gait parameters as a compensation strategy to 416 recover gait balance. The ground reaction force (GRF) was 417 used to investigate if the participant applied a strategy to 418 avoid the error by delaying the loading of body weight on 419 the prosthetic leg. Delayed loading was defined as the GRF of 420 the prosthetic leg being less than 40% of body weight during 421 the initial 200 msec of the gait cycle. The angular momentum 422 of the trunk and intact leg during the stance phase were also 423 calculated to investigate the regulation of whole-body angular 424 momentum.

G. Statistical Analysis 426
Correlation analyses were performed to investigate the error 427 effects on mechanical change and gait instability. Due to non-428 normal and heteroscedastic data distributions, Spearman's rank 429 correlation coefficient was performed. Correlation between |H| 430 and kneeangle was tested to investigate if the change of 431 prosthesis knee angle propagated to the whole -body level and 432 influenced the overall gait instability. The potential correlation 433 between magnitude of |H| and step length/width was tested 434 to investigate if gait instability led to a compensatory step 435 associated with an increased base of support. The significance 436 level was set as α = 0.05.    Error: 0.47± 0.12). However, no significant correlation was 489 found in TF01. Fig. 6B shows that TF01 controlled the trunk 490 angular momentum close to zero and was not perturbed by 491 the errors. In addition, we also observed that the angular 492 momentum of the intact leg demonstrated a faster change from 493 posterior to anterior to compensate for the oscillation of whole-494 body angular momentum in both groups (See Fig. 6A). Participant's step length and step width were highly variable 497 and showed weak or no significant correlation between the 498 peak anterior and posterior H and step length and width in 499 both groups. A weak significant correlation was found that 500 the participants had the tendency to increase step width when 501 errors were applied at IDS resulted in irregular knee extension 502 (Step width: ρ = 0.12, p = 0.016) and increase both step 503 width and length when errors applied at SS resulted in irregular 504 knee flexion (Step width : ρ = 0.144, p = 0.007; Step 505 Length ρ = 0.213, p < 0.001 :). From the GRF data, 506 we found that three out of eight participants in the non-507 disabled group hesitated to load their body weight on the 508 PKP. Fig. 7 illustrates a case that the ground reaction force 509 was less than 40% of the participant's body weight during 510 the initial 200 msec of the gait cycle. The percentage of 511 such an occurrence within all the error cases was 14.88% 512 for participant 4, 7.14% for participant 6, and 8.93% for 513 participant 7. This study aims to investigate the biomechanics of wearer-516 robot interaction in responding to the errors applied by a 517 powered prosthetic leg and identify the safety boundary of 518 errors that impact the safe and confident use of powered arti-519 ficial legs. The effects of errors due to unmatched impedance 520 parameters was quantified based on 1) mechanical change 521 described using angular impulse, and 2) overall gait instability 522 quantified using human perception and angular momentum.

523
Inspired by the minimize intervention principle (MIP) in 524 human motor control [27], a different perspective was taken 525 in this study to investigate the effect of machine errors in 526 the wearer-robot system. It is common that most wearer-robot 527 studies consider errors as failure to the system and aim 528 to pursue a higher accuracy rate or methods to correct 529 the errors (i.e., increase the accuracy of terrain recogni-530 tion for the volitional controller of powered artificial legs 531 [10], [11], [12], [13], [14], [15], [16], [17]. Instead of regarding 532 all errors are "harmful", instead we have relied on the user's 533 feedback to estimate a safety boundary for errors that would 534 not affect gait stability during level-ground walking. Following 535  Moreover, the estimated safety boundary from our proposed 543 experimental protocol could be applied to auto-tune the control 544 parameter of the powered prosthetic leg [34], [35], [36].

545
During the tuning process, the control parameters will update It is noted that the estimated safety boundary quantified by 552 the change of angular impulse at the knee joint is dependent on 553 the gait phase, the direction of torque change, and was varied 554 across participants (Fig. 4). This might be due to individuals 555 having different levels of demand for balance [37], [38]. 556 Firstly, some participants showed a smaller error-tolerant range 557 (TF01, participant 2 and 6) compared to other participants. 558 These participants might be particularly sensitive to errors and 559 felt threatened even when the PKP performed a small, unex-560 pected changes. Secondly, a small change of negative impulse 561 (knee flexion torque) during the IDS phase was enough for 562 all participants to report gait disturbance compared to the SS 563 phase, and a small positive impulse change (knee extension 564 torque) during the SS phase compared to the IDS phase 565 contributed to 5 out of 8 non-disabled participants and one 566 amputee (TF02) reporting gait instability. This result indicates 567 this study [40]. Since the error tolerant range is sensitive to   (Fig. 5). In addition, the amputee group showed a smaller 589 value of |H| compared to the non-disabled group (see Fig. 5E). 590 This result aligns with previous studies that the magnitude 591 of H reflects on the level of gait instability and the ability 592 to sufficiently reduce the excessive change of H is crucial to 593 avoid a fall [41], [42], [43], [44]. In this study, two strategies 594 were observed to regulate H. When participants perceived a 595 larger disturbance, they quickly swing the intact leg forward 596 which resulted in a faster change of intact angular moment 597 from posterior to anterior direction. In addition, participants 598 who can maintain stable trunk angular momentum were able to 599 restrain the normal patterns of H, such as TF01 [37], [39], [45] 600 (see Fig. 6B) compared to other participants whose trunk 601 angular momentum oscillated with H (see Fig. 6A). Moreover, 602 the distinct double oscillation pattern of H found in some This study investigated the biomechanics of wearer-robot 664 systems reacting to internal errors induced by a powered 665 knee prosthesis, and quantified the error tolerable bound that 666 does not affect the user's gait stability. Two balance recovery 667 strategies: regulating trunk and intact leg angular momentum, 668 and delaying the loading of body weight, were observed for 669 participants to successful respond to machine errors. The error 670 tolerable bound depends on the gait phases, the direction 671 of torque change, and was variable across participants. The 672 outcomes of this study could aid future design of an auto-673 tuning algorithm, volitionally-controlled powered prosthetic 674 legs, and training of gait stability.

675
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