—We present an actuator designed for untethered, lower-extremity powered-prostheses that replicates biological ki- netic and kinematic function of both human knees and ankles. An electric energy optimal hardware speciﬁcation is deﬁned by kinematically clamping walking gait data to the dynamic model of a series elastic actuator (SEA) and searching for motor, reduction ratio, and spring. The actuator is shown to achieve the required torque, angle, and velocity requirements for nominal walking conditions on level ground as well as varied terrain. The performance of the actuator is demonstrated on benchtop and as worn by a human subject with unilateral below knee amputation. The resulting design is a moment-coupled cantilever- beam reaction-force SEA (MC-RFSEA) that has a nominal torque rating of 85Nm, repeated peak torque of 175Nm, 105orange of motion, and a hardware mass of 1.6kg. Preliminary results from level-ground walking with the actuator tested in an ankle conﬁguration show an electric cost of transport of 0.053J/kg when walking at 1.5m/s. Index Terms —robotics, prostheses, actuator, ankle, knee. I. I NTRODUCTION A little more than a decade after the ﬁrst powered ankle prosthesis, research in lower-extremity rehabilitation robotics remains limited by a lack of commercial and academic hard- ware platforms capable of producing biologically relevant dynamics. The commercial off the shelf powered ankle and knee systems are not able to provide biologically accurate kinetics with kinematics, nor do they enable access to the underlying control systems [1], [2]. To improve upon the commercial options, a growing handful of academic research groups around the world have been building individualized platforms for study. Most of these academic platforms have remained within their own labs requiring each lab to build its own hardware. This paper describes the mechanical design of an autonomous, untethered, wearable, reaction-force series elastic actuator topology that aims to achieve biologically relevant kinetics and kinematics of both a human knee and ankle, while reducing hardware complexity and remaining within the mass bounds of human equivalent leg segments. Manuscript received February, 2021. Financial support: this work was supported in part by the MIT Media Lab Consortia, the U.S. Army Medical Research and Materiel Command (W81XWH-14-C-0111) and the Defense Advanced Research Projects Agency (W911NF-17-2-0043). 1MIT Center for Extreme Bionics and MIT Media Lab - Biomechatronics Group, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. e-mail: mcarney@media.mit.edu. 2Dephy, Inc., Maynard, MA 01754 USA.The ﬁrst powered ankle, published by Au, Weber, Herr, used a series elastic actuator (SEA) [3] conﬁgured with a parallel spring to improve torque bandwidth in the transition from controlled dorsiﬂexion to powered-push-off. Au et al. showed that the actuator’s ability to contribute energy during powered push-off improved the metabolic cost of walking [4]. Since then numerous actuators have been designed following a similar topology that includes ball-screw driven SEAs [5]–[8]. Some designs have used point-loaded cantilever beams as the elastic element in non-powered [9], powered [10], and variable stiffness [11] actuators. However, this loading condition leaves 2/3 of the spring material strain energy unused. Many ankle designs have focused around ﬂat, level-ground walking, where primary kinetic behavior occurs as a large power maneuver during powered plantar ﬂexion [10]. Commercial devices such as the BiOM/EmPower [1] even limit joint range to zero dorsiﬂexion in order to reduce electric energy expenditure during walking, at the expense of natural kinematics. To improve control bandwidth and electrical energetics parallel springs are frequently used, at a cost of range of motion and terrain adaptability. Though well designed for ﬂat ground, and self-selected walking speed, these powered prostheses quickly hit kinematic limits at higher walking velocities and varied terrain. At higher walking speed, stride length and joint angle excursion increase[12]. Mean data from nine subjects walking at 0.75m/s to 2.0m/s shows ankle dorsiﬂexion angle increases from 8.3 to 19.3 degrees. These range of motion limitations are com- pounded when encountering sloped surfaces or stairs. During stair descent a 21 degree mean dorsiﬂexion angle is reached during stance, and up to 40 degrees mean plantarﬂexion angle in swing phase [13]. To demonstrate the difference between laboratory experiments and real-world consider: the American Disability Act (ADA) compliant wheelchair ramp slope speciﬁcation declares a maximum 7.1 degree inclination. Fast walking up such a ramp would limit proper kinematic function in all the ankles described except for the Vanderbilt legs. Powered knee actuators tend to be large and disregard clearance height that would allow for separate powered ankles; combined knee and ankle powered prostheses can enable coordinated motion at the knee and ankle allowing for more complex and bio-mimetic control techniques. However, they are frequently designed to a single speciﬁc height, restricting usability to a very limited patient group. Many also forgo full torque control throughout the entire gait cycle, and instead 2 provide closed-loop control only during speciﬁc phases. The commercially available ¨Ossur Power Knee weighs 3.1kg, has a clearance height of 270mm, and from the datasheet appears to only support limited position control in speciﬁc states, rather than provide full torque controlled impedance modes [2]. The Vanderbilt Leg 2.0 knee is a 2.7kg mass with a 85Nm max load, and no power rating. The Vanderbilt Leg 3.0 appears to have a ﬁxed height of 452mm limiting its use by smaller patients who are more well matched to the torque capability of the system [14]. The University of Utah Romeo knee sports an actively variable transmission (A VT) that can be adjusted when the system is unloaded, but is not yet not actively powered [15]; it has a mass of 1.7kg and a 290mm build height. The MIT Clutched Series Elastic Actuator ( CSEA ) was designed to conserve electric energy with a brake on the motor shaft, and asymmetric ﬂexion and extension springs; it has a 2.7kg mass and 280mm clearance [16]. The MIT Agonist-antagonist knee actuator that uses two series elastic actuators acting against each other to set the joint stiffness has substantial torque capability at 130Nm, but mass of 3kg and build height of 330mm [17]. The AMPRO 3 is a ﬁxed height combined knee and ankle prosthesis that makes use of harmonic drives, and spiral series elastic springs for torque control; the system mass is 5.95kg and peak 123Nm torque at the ankle [18]. In this study we present the mechanical design of TF81. The design is based on kinematically clamped simulation and optimization methods described in our paper examining electric energetics in prostheses [19]. In that paper we propose the possibility of a single actuator topology that achieves biologically relevant knee and ankle motions and forces, while maintaining an electric energy cost of transport that could be serviced by a reasonably sized battery for a day worth of walking. The hypothesis we propose to test here is that it may be possible to design an electrically efﬁcient, multi-purpose actuator capable of achieving the knee and ankle kinetics and kinematics required for walking, ramp, stair ascents/descents, and possibly fall recovery, while remaining within the mass constraints of equivalent leg segments, all while also reducing cost and maintenance complexity for laboratory researchers. The ﬁrst section of this manuscript explains the speciﬁcs of the chosen architecture and mechatronic system. We then present preliminary results of the actuator tested on bench- top, and worn by a human subject with unilateral below knee amputation. Finally, we end offering some guidance for future efforts. II. M ECHANICAL DESIGN A. Design Speciﬁcation The design speciﬁcation for range of motion, torque, power, and system bandwidth, are gathered from analysis of 1005 unique, mass-normalized, gait cycles of walking data from nine able-bodied subjects [20]. We set the performance target based on a 90kg user walking at a near jogging pace of 2.0m/s. Range of motion of the joints is increased beyond walking to accommodate varied terrain such as ramps and stairs [13], 1The TF8 name comes from being the eighth major design iteration of a powered transfemoral prosthesis. Fig. 1. The TF8 Actuator is designed to operate as either a knee or ankle powered prosthesis. Shown here are two TF8 actuators stacked into a combined powered knee-ankle prosthesis. [21]. The velocity requirements are set for fast walking. A reach design criteria would increase knee velocity capability to 9.5 rad/s for trip recovery [22]. The allowable mass is based on the mass of a human calf and foot segment [23], [24]. For maximum ankle mass we assume the mass of a foot and one third of the calf mass, or 2.9% of body mass. Table I summarizes the design targets and the resulting performance of the actuator. B. System Design To ﬁnd the main design parameters of the mechatronic design (motor, transmission ratio and series stiffness) we apply a gradient descent optimization with non-linear constraints to a model of mechanical and electrical systems dynamics. The process is similar to methods in [16], [25], [26], where joint mean torque, velocity and angle trajectories aggregated from [20] are mass normalized, scaled and clamped to the dynamic equations for a series elastic actuator. The performance re- quirements of the motor are then evaluated by the optimization 3 TABLE I ACTUATOR DESIGN SPECIFICATION 2m/s Ankle Knee Target Result Units Range of Motion121-0-40 72 45-0-65 35-0-75*Deg Velocity 6.0 8.6 9.5 6.8**rad/s Max Torque2160 118 175 175 Nm Max Power 552 313 550 350**W Bandwidth Magnitude 82 73 82 82 Nm Bandwidth Frequency 4.8 6.0 6.0 6.2 Hz Segment Mass 2.6 2.6 2.0 1.6 kg 1Range of motion as shown: dorsiﬂexion - neutral - plantar ﬂexion . 2Fatigue limit for repeated torques. *The knee conﬁguration is biased to make use of a total 110 degree ROM. **Limited by current instantiation of power electronics. procedure. Constraints include deﬁned maximum allowable motor phase voltage and current as well as torque and velocity limits of the motors. The procedure steps through a database of motors to evaluate optimal conﬁgurations for each motor. In our paper [19] we demonstrate this optimization proce- dure and deﬁne a search objective to minimize the electric Cost of Transport (eCOT) for a gait cycle. The results of this simulation is the driving force for the design here presented. The eCOT overlays in Fig. 2 deﬁne a design point that satisﬁes both knee and ankle kinetics and kinematics while requiring acceptable electric energy to perform 3000 steps/charge. This performance is achieved, in simulation, at least, by storing nearly 14J of energy in an elastic element. In order to package such a high energy-density spring we narrow the design to use a ball-screw and linkage drive train. We then implement secondary tiered optimization searches to identify energy optimal joint linkage geometry and a mass optimized spring that can accommodate operating as both a knee and ankle. 1) Drivetrain: Joint torque is generated by a linear actuator that acts on a moment arm about the joint axis. The linear actuator is composed of a ball-screw with ball-nut integrated directly into the motor rotor. The rotation of the screw is constrained by a push-rod end afﬁxed to one end that pivots around an orthogonal axis located a projected distance from joint axis. To tune the linkage geometry to match the power- stroke of an ankle gait cycle, we used a gradient descent search and set the search objective to minimize eCOT. The linkage parameters we searched for f,fk,t,tkare deﬁned in Fig. 3. The moment arm across which the screws applies a torque about the joint is deﬁned as: Cθ=π−θl−(T+F) (1) c=/radicalbig a2+b2−2·a·b·cos(Cθ) (2) r=b·/radicalBigg 1−/parenleftbigga2−(c2+b2) −2bc/parenrightbigg (3) where,ris the instantaneous projected distance of the screw force along screw length c, about the joint pivot deﬁned at angleθ. The overall gear ratio is nominally 52 : 1±3.5during level ground walking. At high ﬂexion the gear ratio can sweep as Ankle & Knee eCOT: Level-ground, 90kg, 1.5m/s 20 40 60 80 100 120 140 160246Ks [N/m]105 -0.0500.050.1 0 20 40 60 80 100 120 140 160 Overall Transmission Ratio-0.0500.050.10.15COT -0.0500.050.1 COT COT Overall Transmission RatioFig. 2. Overlaying the knee level-ground energetic map with that from the ankle there is a compromise region where both systems can operate with the same hardware conﬁguration. The dotted lines show the as built overall gear ratio and expected eCOT performance, evaluated with a 90kg person walking at 1.5m/s. L f fk tk t (a) c r CѲ Ѳl a b (b) Fig. 3. (a) The actuator geometry parameters t,tk,f,fk,Lare found through optimization. The objective was ﬁnding moment arm geometry with the most efﬁcient conﬁguration of the power stroke as speciﬁed by the load trajectory and actuator dynamics. (b) Parameters used for calculating instantaneous moment-arm length for control. low as2 : 1 as the actuator approaches limits to its controlled range of motion. An alternative output arm is used in the knee conﬁguration in order to bias the joint range of motion to remain fully controllable. The total range of controllable motion is 110 degrees. Mechanically, the system can reach 120 degrees to enable the additional range of motion for passive tasks such as when used as a knee actuator and a user wishes to sit cross-legged. Fig. 4(a,b) shows the actuator conﬁguration, (c) shows the range of motion of the actuator as an ankle. The linear motion is achieved with a Thomson Linear 5mm lead 4 ball-screw (BSPRM012L05M) and nut (KGM-N-1205-RH). The ball-nut is mounted directly in the rotor of a customized motor. Though not tested in these experiments the rotor is designed to accommodate two other lead ball-screws: a 2mm and a 10mm lead. The 5mm lead screw is chosen for these experiments due to its ability to perform as both a knee and an ankle. Optimal performance for each joint can be achieved by swapping the appropriate ball-screw and nut into the respective joint actuator. 2) Motor: The motor is a high pole-count frameless motor built into a custom rotor and stator, based on the T-Motor U10 Plus KV100 outrunner motor [27]. The rotor is designed to house the ball-nut directly inside the motor, without the need or external couplings. Thin-section, angular contact bearings support the rotor and the high axial load imparted from the ball-screw. Axial pre-load of the bearings is generated by a retaining nut that also supports a magnetic motor encoder rotor disk. The motor bearing stack with ball-nut and its associated load path can be seen in Fig. 4(d). Due to the nature of the bearings, compressive and tensile load paths differ and are shown in dotted and solid lines, respectively. The motor stator is mounted to the actuator spring frame by polymer bushings, while the pivot-rod end of the screw mounts to the output arm by way of a single needle bearing. The motor choice is based on the performance of the motor when simulated as a complete actuator clamped to the speciﬁed output trajectory. Fig. 5 shows the expected motor torque speed and power speed trajectory when applied to an (a) ankle and (b) knee for a 90kg person walking at a nominal 1.25m/s. The nominal motor limits are shown as dotted lines and the absolute peak capacity are shown in solid lines. Due to the ”peaky” nature of walking we choose an actuator and motor combination that can achieve nearly all required waypoints, allowing trajectories outside of the nominal limits, but within the maximum current limited peak torques. To note there is velocity saturation expected for 3% of knee waypoints, yet headroom for torque capacity. These motor capacity plots show that the 5mm lead chosen is a compromise between ankle and knee trajectories; more ideally tuned combinations to maximize motor capacity would be a lower lead screw for the ankle, and higher lead screw for the knee. 3) Structure: The architecture of TF8 is deﬁned as a moment-coupled, cantilever-beam, reaction-force series elastic actuator (MC-RFSEA). The reaction-force from the linear actuator induces a moment on a cantilever-beam spring by way of the motor stator being pinned to a moment arm that is clamped to the spring, thus creating a moment inducing force-couple. The spring serially grounds the output load to the frame of the actuator. Four bolts attach the spring, enabling its quick replacement to tune the performance of the actuator for a given application: such as users of different mass, to match the dynamics of either an ankle or knee, or enabling the equivalent of a sport or economy mode of operation for the actuator. In this RFSEA conﬁguration the actuator unloaded and high-impedance behavior differ from a traditional SEA. The primary difference is the spring is serially located in the (a) (b) θd θp (c) (d) Fig. 4. (a) Spring deﬂection occurs when a torsional load (dotted arrow) is applied at the rotary output, reaction force from the motor/screw causes deﬂection of the spring. (b) Shows the load path from the applied load at the joint, through the linear actuator, the cantilever spring and to the structural frame. (c) The full range of motion of the ankle conﬁgured TF8 prosthesis. Motion is labeled as θdis dorsiﬂexion, and θpis plantarﬂexion. (d) Close- up of the ball-screw integrated into the motor. The compression load-path is shown as the dotted line, while the tension load-path is shown as the solid line through the motor bearing stack. -100 -50 0 50 100 150 Angular Velocity [rad/s]0135Motor Torque [Nm] 0 50 100 150 Absolute Angular Velocity [rad/s]0100300500Absolute Power [W]Load Requirement Nominal Limit Peak Limit (a)-400 -300 -200 -100 0 100 200 300 400 Angular Velocity [rad/s]0135Motor Torque [Nm] 0 100 200 300 400 Absolute Angular Velocity [rad/s]0100300500Absolute Power [W]Load Requirement Nominal Limit Peak Limit (b) Fig. 5. These plots are the (a) ankle and (b) knee motor trajectories and limits of a 90 kg person walking at 2.0 m/s with as designed and optimal gear ratio. Using a screw lead of 0.005 mm for a nominal gear reduction of N=52.8. Solid line is motor peak limit, dotted line is nominal continuous limit. The knee actuator would beneﬁt from a lower reduction ratio to better utilize the torque and velocity capability of the motor. ground-path of the motor, rather than the output path of the actuator. The lumped parameter assumption commonly used for a SEA is not valid for free-space motions. In the high- impedance case motor-mass is also sprung with the rotor inertia. The performance of the high-impedance condition 5 differs from the low-impedance moving-output condition by enabling an impulse load to deﬂect the spring and motor with- out rotating the motor inertia, thus improving high-frequency inertial conditions at the cost of larger sprung-mass at lower frequency [28], [29]. The spring deﬂection during loading of the actuator is shown in Fig. 4(a,b). The dotted-line arrow represents an applied joint torque, τland the solid arrow is force from motor displacement along the length of the screw, Fs. The green dotted line in Fig. 4(b) shows the load path when the structure experiences an internal compressive load that would be due to an ankle dorsiﬂexion or knee extension maneuver. The dis- placement shown is the maximum allowed deﬂection, limited by hard-stops built into the actuator structure (not shown). The conﬁguration shown is the minimum viable actuator; the three staggered holes near the output pivot are mounting holes where the frame could be grounded to a support structure. In the application of a prosthesis the structure is swept back around the spring and motor in order to mount the device to a pyramid adapter. This structural routing could be designed for alternative applications. 4) Elastic Elements: The cyclical motion of gait is well suited to leverage the energy storage and power delivery capacity of springs [30]. The goal of the series elastic element design is to maximize energy storage (low stiffness) in the spring while also maximizing system control bandwidth (high stiffness) – two opposing objectives. Increasing spring stiffness improves natural frequency, but reduces the amount of energy that can be stored for a given loading condition, and puts greater precision requirements on encoder based force sensing. Reduced spring stiffness improves energy storage but also requires the motor to travel greater distance to reverse direction at high load. The strain energy density and loading conﬁguration de- termine the total energy storage capacity of a spring. The moment-coupled load application to the series elastic element in TF8 is chosen for its bending dominated strain. In addition to the ﬂat plate spring being simple to manufacture and afﬁx, in pure bending it also exploits the material properties of composites. By aligning all tension and compression forces with a unidirectional tensile ﬁber orientation, we fully leverage the asymmetric properties of composites. In the case of mod- erately thick beams the Timoshenko Beam Theory estimate of beam deﬂection diverges from that of the Euler-Bernoulli (EB) bending beam model due to internal shear forces. However, for beams of slenderness ratio (h/L) less than 0.15 the deviation from the EB remains under 1.7% [31]. Thus, though the total strain in the beam includes bending, axial, and shear strains, it is heavily dominated by bending and axial forces, and can be estimated using the simpler EB form: Ubend=M2L 2EI=L(Pxt+LPy)2 2EI(4) Uaxial=P2 xL 2AE(5) Ushear=P2 yh 2AG(6) Utotal=Ubend+Uaxial+Ushear (7)where,Px,Pyare the longitudinal and transverse to the spring components of screw force Fs, deﬁned as: Px=Fscosθp, Py=Fssinθp, andθp=Fs Kxt.Ksis linear spring stiffness, andtis the moment arm length as described in Fig. 3. To deﬁne the spring geometry we numerically solve for the length, height and width of the spring, subject to a minimum mass objective, geometric constrains, and selected material properties. The target design parameters are speciﬁed from the initial clamped optimizations: stiffness Ks, and stored energy (7). The beam height is then solved from: h=/radicalBigg 6(Pxt+PyL) b·σf(8) where,bandLare beam width and length, respectively, and σfis the allowable fatigue limit of the material. Similar to The results of optimization deﬁned a nominal series stiffness Ks= 271kNm m, and an 8.6mm thick unidirectional ﬁberglass spring. Carbon ﬁber is of course optimal, but for cost reasons we went with a unidirectional E-glass ﬁberglass composite (GC-67-UCB) manufactured by Gordon Composites [32]; future iterations could beneﬁt from a thinner carbon ﬁber beam. After initial testing we adjusted to a thicker spring to compensate for an overall lower than expected structural stiffness. The conﬁguration as built has a 42 mm x 12.44 mm thickness beam with a sprung length of 86 mm and an overall measured linear stiffness of 378 kN/m. The maximum deﬂection is limited by mechanical features built into the structure; at the maximum 13mm of deﬂection the spring experiences nearly 265Nm or torque and stores 19 Joules of mechanical energy. 5) Mass and Height: The minimum working actuator con- ﬁguration as shown in Fig. 4(a) has a mass of 1.3kg. The overall hardware mass as a knee, not including electronics or battery, measures 1.6kg. The electronics and wiring harness weigh 53g and 52g, respectively. The fully equipped actuator conﬁgured as an ankle such as Fig. 6 with on-board electron- ics, ﬂex-foot, adapters and battery together weigh 2.0kg. The mass breakdown is shown in Table II. Conﬁgured as an ankle the output joint placement is de- signed to match the relative orientation of the BiOM [1] when mounted on an ¨Ossur Vari-ﬂex foot [33] – the unloaded height of the ankle is 67mm and lateral placement with respect to mounting holes in the Vari-ﬂex is matched. Matching align- ment allows direct kinematic comparisons to BiOM/EmPower. When conﬁgured as an ankle the mounting height of a pyramid adapter is at an unloaded height of 223mm with a mass of 2.0kg, and as an ankle + knee the minimum height, without medial-lateral offset is 443mm, with a total mass of of 3.7kg. 6) Mechatronics: The mechatronic system is composed of a control unit that houses a mid-level controller, motor driver, battery management system, sensor inputs and communica- tions to external peripherals. The control unit is a modiﬁed version of the Dephy Inc. FlexSEA system [34]. The mid-level controller is based on a STM32F427 180Mhz microprocessor. The block diagram of this control unit is shown in Fig. 7. The main loop in the control unit is operating at 1kHz, providing sensor updates, safety checks and controls, while 6 Load Cell 52Motor Spring 156223 15Joint EncoderControl Unit21 Motor Encoder Fig. 6. The TF8 Actuator is shown conﬁgured as an ankle powered prosthesis with the main components labeled. The actuator minimum build height is 171mm measured between standardized mounting plates, shown here with standard prosthesis components attached. All dimensions are in millimeters. TABLE II MASSDISTRIBUTION OF THE TF8 K NEE ACTUATOR HARDWARE Component Mass (g) (%) Structural Components 556 35 Motor 549 34 Spring 116 7 Ballscrew 100 6 Spring Clamping Hardware 95 6 Load Cell 54 3 Electronics 53 3 Fasteners 48 3 Encoder Hardware 45 2 Total 1616 100 the underlying motor drive current controller is operating at 20kHz. The external sensors include an absolute on-axis joint encoder (AS5048B), incremental off-axis motor encoder, and load-cell (Futek LCM300). The load cell signal has a nine sample median ﬁlter and a 30Hz low-pass butterworth ﬁlter applied to reduce noise. Internal sensors include an inertial measurement unit, motor phase current sensor, wheat- stone bridge strain-gauge circuit, and a temperature sensor. The peripheral communications allow communication between a host computer through USB, Bluetooth and RS485 for connection to additional FlexSEA units. An I2C bus is used to communicate with an external electromyography (EMG) ampliﬁer board also designed by our research group [35]. The battery used for walking experiments is composed of two 3S 11.1V 1.0Ah lithium polymer hobby-grade batteries connected in series for a nominal operating voltage of 22.2V and a lifetime of roughly 5500 steps; the battery combined mass is 180g and is usually strapped onto the socket of a test subject to reduce distal mass. 7) Control: The torque compensator is a proportional in- tegral differential (PID) controller with integral anti-windupControl Unit System State Updates Safety Systems Mid- level Controller Impedance Controller Torque Controller Motor DriverJoint Encoder Motor Encoder Force Sensor Current Sensor Temp Sensor IMUPCBExternalSensors High -level Controller Peripheral DevicesExternal Peripherals Physical ActuatorI2C, SPI, ADCI2C, S PI, UART, USB, RS485, Bluetooth Control Unit Fig. 7. The TF8 embedded system layout is shown in schematic form. The Control Unit is based on the FlexSEA embedded system developed by Dephy, Inc. consisting of a motor driver and a STM32F427 micro- controller. The system supports external peripheral devices, sensors, and common communication protocols. and a feed-forward term. A second order low-pass butterworth ﬁlter set at 20Hz cutoff frequency adjusts the torque reference to phase align with the feedback term. The feed-forward term is a notch ﬁlter deﬁned by the inverted plant model estimated from the system identiﬁcation, and made realizable with a 30Hz low-pass butterworth ﬁlter applied to the reference torque. The notch ﬁlter helps reduce excitation around the natural frequency of the RFSEA [28]. The PID controller gain tuning is done manually with the joint output rotor statically locked in position and 50Nm step impulses applied. III. M ETHODS A. System Characterization To verify actuator load capabilities, and perform system identiﬁcation we use the high-impedance, locked-output test method [36]. The locked-rotor experiments pushed the actu- ator to its designed fatigue-limit load rating of 175Nm and to the maximum allowable spring deﬂection and hard-stop limited torque of 218Nm . To identify system characteristics of both the open-loop and closed-loop conditions of the locked rotor state we command a linear-ramping, sinusoidal chirp command of ±50Nm torque amplitude, with 2.5Nm Gaussian white noise across the frequency range of 0.1-12Hz. Equivalent mass, stiffness and damping characteristics are then extracted from these models and used in control simulations to further tune the torque compensator. B. Preliminary Clinical Evaluation Subject testing was performed at the Massachusetts Institute of Technology (MIT) Media Lab Biomechatronics Gait Lab- oratory. Participants were informed of and consented to test protocols approved by the MIT Institutional Review Board: the Committee on the Use of Humans as Experimental Subjects. All subjects self-reported to be healthy with activity levels equivalent to K3 or above: having ambulatory activity with variable cadence. 7 Fig. 8. Feedforward model based control block diagram. The low-pass ﬁlter is implemented within the feedforward term to make it realizable. To verify the ability of the actuator to replicate biologically relevant torque and velocity capabilities we test the actuator conﬁgured as a foot-ankle powered prosthesis, worn by human subjects with below knee amputation. The preliminary testing includes a 52 year old, 75kg male subject, with unilateral below knee amputation walking on a treadmill at speciﬁed speeds. Additionally, an initial experiment with a female subject aged 46, with unilateral below knee amputation was evaluated on stair climbs, and a second male subject, aged 51, with above knee leg difference was also evaluated with two TF8 actuators conﬁgured a powered ankle and knee. Ex- perimental procedures include donning and adjustment of the TF8 to match the alignment and comfort of the participant’s standard issued prosthesis. The walking controller we implemented is a ﬁnite-state machine walking controller following similar methods to [4], [37]–[39]. The state transitions are shown in Fig. 9. Joint torque is speciﬁed by the mid-level impedance controller. The impedance torque command follows the standard single-joint form:τd=Kd(θdes−θl)−B(˙θl)where,τdis desired joint torque speciﬁed to the torque controller, θdesis desired joint angle set point, θlis measured joint angle, and ˙θlis measured joint velocity. The initial impedance parameters were based on parameters in [40]. Control parameters were then tuned to match the comfort level of the subject as they acclimated to walking at self-selected speed with the powered ankle-foot system. Stance is triggered by a heel-strike transition from swing, identiﬁed by an absolute torque signal greater than a deﬁned threshold. During controlled-dorsiﬂexion a virtual unidirec- tional parallel spring is superposed onto the stance impedance settings. As the subject leans into the virtual parallel spring, joint torque rises until reaching a speciﬁed threshold at which point the powered plantarﬂexion state triggers. The joint angle set-point then ramps to a plantarﬂexed position along with a transition in virtual stiffness and damping. As the user is propelled forward and lifts their foot the measured torque drops below a threshold and the swing phase is triggered. Swing phase then rapidly moves the toe position into a dorsiﬂexed state to provide toe-clearance throughout swing. The controller then waits for the next heel strike. The parameters available to tune include virtual parallel stiffness, push-off torque threshold, push-off torque ramp rate, push-off stiffness, toe-off angle and damping. During theexperiments, on-board sensors recorded and transmitted, at a rate of 100Hz, the full actuator state across a wireless bluetooth communication protocol to a secondary computer. Data collected included joint angle, velocity, torque, ﬁnite- state, as well as motor current and voltage. IV. R ESULTS A. Control Bode plots of both open and closed-loop system response in a high-impedance state are shown in Fig. 10. The open- loop frequency response aligns well with a second order mass spring damper system as characterized by: G(s) =90 s2+20s+120. (9) The natural frequency is measured at about 1.5 Hz and calculated from the estimate in (9) at 1.6 Hz. The feed forward control, Fin Fig. 8, includes a low- pass 2nd order Butterworth ﬁlter with 30 Hz cutoff frequency applied to the inverse of the plant model G(s): F(s) =3.553e04s2+7.106e05s+4.264e06 90s2+3.393e04s+3.198e06. (10) The PID portion of the torque controller is manually tuned to achieve an under-damped response with relatively quick rise-time. The response to a 50Nm step-input applied to the locked-rotor conﬁguration is shown in Fig. 11. The rise time Tr= 0.072 s, peak time Tp= 0.096s, with a percent overshoot of OS = 20%, and settling time of Ts= 0.232s. This results in a system estimate of closed-loop natural frequency ωn= 5.9 Hz, and damping ratio ζ= 0.47. The closed-loop frequency response aligns well with a second order mass spring damper system as characterized by: G(s) =920 s2+30s+980. (11) The natural frequency is 3.9Hz. The closed-loop -3dB band- width is 6.2Hz with a phase margin of 61.5 degrees. B. Preliminary Clinical Evaluation Torque and power from a 75kg participant with unilateral below knee amputation walking with a ﬁnite-state machine controller on a treadmill at 1.5 m/s is shown in Fig. 12. 8 Stance Heel Strike Powered PlantarflexionSwing Heel Strikeτ > τpow θ < θvparτ < τswing θ ≥ θpushτ ≥ τhs θ > θdfControlled Dorsiflexion (a) (b) Fig. 9. Schematic and human subject demonstration of state transitions: (a) State transitions are triggered by torque and angle thresholds tuned to meet test subject p