Design and control approach

The design and control approach presented here is based on categorizing knee joint function during mobility activities into four behaviors: resistive stance behavior, active stance behavior, ballistic swing, and non-ballistic swing. The approach is further premised on the assumption that healthy non-perturbed swing-phase is characterized by a ballistic swing motion, and therefore, a replacement of that function should be similarly ballistic (i.e., which requires the knee joint to become essentially a free hinge with very low levels of modulated resistance). Finally, the approach assumes that power generation should only be used for (1) activities requiring net knee extension during stance-phase, such as stair ascent and sit-to-stand; and (2) activities requiring non-ballistic swing, such as swing-phase during stair ascent. When not providing power, the prosthesis should remain strictly passive. In other words, the device should be passive when possible, and powered only when necessary.

For the approach presented here, activities for which the prosthesis should function in either a passive or powered capacity are depicted in Table 1, which categorizes several common activities into one of the four stance and swing behaviors described above (note that this is not a comprehensive list and some activities are not tested in this manuscript). Active and resistive stance are analogs, wherein the knee joint primarily provides an extensive torque with knee motion either in extension (active stance) or flexion (resistive stance). Ballistic and non-ballistic swing describe the contribution of knee torque to the resultant motion of the lower leg. For ballistic swing, inertial torques (i.e., gravity and thigh acceleration) dominate knee motion, with the knee providing relatively low resistance to control motion; for non-ballistic swing, active knee torque overcomes inertial forces to reposition the lower leg. Note that resistive stance and ballistic swing are behaviors provided by current commercially available passive MPKs, while active stance and non-ballistic swing are not, since they require net power generation at the knee. Note that the approach taken here therefore requires that the powered prosthesis be capable of operating both as an MPK (i.e., in a strictly passive mode that spans both very low variable impedance for cadence-adaptive swing-phase, and also high torque and power dissipation for stance knee flexion in stair and slope descent), and also capable of providing power during non-ballistic swing and stance-knee extension. Various approaches could potentially be employed for the implementation of such behaviors. For the work presented here, a knee design that incorporates a two-speed transmission in combination with both passive and active motor control is employed in order to broaden the range of achievable impedances and torques. The resulting device is able to match (or exceed) the span of passive behaviors, impedances, and torques provided by current MPKs, and is also able to provide power for non-ballistic swing movements, and stance-knee extension, as subsequently shown.

Table 1. Generalized stance and swing behaviors of different functional activities

Prosthesis hardware

The control approach described here is implemented on a knee prosthesis prototype called the ECT knee, described in detail in Culver et al. (Reference Culver, Vailati and Goldfarb2022) and shown in Figure 1. The prosthesis is actuated using a DC brushless motor (Maxon EC-4pole 22 90 W), which is connected to the knee joint through a novel two-speed electronically controlled transmission (ECT). The motor is controlled either passively or actively, depending on the control mode (i.e., passive for resistive stance and ballistic swing, active for active stance and non-ballistic swing). When controlled passively, the motor leads are shorted via a PWM control signal, such that the battery cannot provide power to the motor. Even though the battery cannot power the motor in this passive mode of control, the motor is connected to the battery through a set of diodes, such that the motor can regenerate power to the battery during passive operation. This passive motor control approach is described in detail in Vailati and Goldfarb (Reference Vailati and Goldfarb2022). When controlled actively, the motor driver employs a standard current control technique with block commutation. The two-speed transmission of the knee provides two functional regimes of operation for the prosthesis: (1) a highly backdrivable low-gear that enables ballistic swing-phase motion in passive control mode or non-ballistic swing in active control mode, and (2) a relatively higher gear that enables high-torque stance-knee flexion in passive control mode and powered stance-knee extension in powered control mode. The ECT is based on an underdetermined planetary gear transmission that is configured (i.e., made determinate) via a pair of clutches, one unidirectional, one bidirectional, which can be engaged or disengaged in various combinations to provide: (1) a high-gear ratio appropriate for stance-phase; (2) a low-gear ratio appropriate for swing-phase; and (3) a combination that enables a low-gear ratio against extension and locks against flexion. The unidirectional clutch ensures that the knee always allows stance-knee extension during stance phases of gait.

Figure 1. ECT knee prosthesis prototype with one half of the housing removed (left) displaying the novel actuator (1) and lead screw (2), and fully assembled prosthesis (center) including absolute encoder (3), battery pack (4), and custom embedded system (5). The range of motion of the crank arm (6) is limited by the hard stops for extension (7) and flexion (8). A load cell (9) is fixed to the bottom of the prosthesis and attaches to the pylon clamp. The ECT was evaluated on a subject with transfemoral amputation in several experiments (right): (a) level-ground, (b) up-slope, and (c) down-slope walking on an instrumented treadmill; (d) upstairs and downstairs walking; (e) sit-to-stand and stand-to-sit transitions; and (f) an overground walking circuit that incorporates all aforementioned activities and the transitions between them.

The transmission ratios between the low and high gears are different by a factor of 5.4, which combined with passive motor control enables two orders of magnitude variation in passive impedance, and also renders it capable of providing an appropriate range of torques for powered stance and swing behaviors. Although there are two defined gear ratios, there are four possible mechanical states of the transmission, since the two clutches each have two states. These four transmission states are outlined on the transmission truth table in Figure 2 and described below:

Figure 2. The ECT is an under-determined transmission with two clutches that ground different components and provide different reduction ratios between input and output (for more details about the mechanical design, see Culver et al., Reference Culver, Vailati and Goldfarb2022). Although the ECT has two defined gear ratios, there are four possible mechanical states of the transmission (two clutches each with two states). The transmission truth table illustrates how engaging and disengaging the ring and carrier clutches produces different functional states in flexion and extension: a low transmission ratio (low), a high transmission ratio (high), over-determined locking (lock), and under-determined motion between input and output (slip or not engaged). Functionality of the prosthesis in gear states 00, 11, and 01 is demonstrated in the Supplementary Video. The FSM for walking consists of six states and the transitions between them. The FSM operates by controlling the output torque and impedance via hardware configuration and motor torque commands. Within each state, the motor is commanded to operate passively (i.e., constrained to braking behavior) or actively (i.e., using a standard block-commutation scheme). The FSM diagram indicates the corresponding gear states of the hardware and if the motor is operated actively or strictly passively. Torque control laws within each state are outlined in Table 2; transition conditions between states are outlined in Table 3.

Embedded system

A custom embedded system was designed for sensing, actuation, and control of the prosthesis. The embedded system includes: (1) power electronics to drive a brushless motor and the two clutch solenoids; (2) sensing and signal conditioning, including current sensing for motor and solenoids, encoders at the motor shaft and knee joint for measurement of knee joint position and velocity, shank axial force load measurement, and a six-axis inertial measurement unit for measurement of the shank and thigh angles and velocities; (3) two microcontrollers which implement various control tasks; and (4) controller area network (CAN) communication hardware. The system is powered using four 18650 batteries in series, providing nominal 16.8 V with a maximum continuous current capacity of 15 A. The CAN interface is used to exchange control data (i.e., sensor values and control parameters) at 500 Hz with a computer which runs a high-level controller on MathWorks Simulink Desktop Real-Time. For the passive mode of motor control, the three low-side MOSFETs of the bridge are switched simultaneously, which guarantees smooth and strictly passive braking behavior; in the active mode of motor control, a standard block-commutation scheme is used to provide current control in either active or passive behavioral regimes, as determined by the activity control system.

Activity control system

The activity controller is a six-state FSM, diagrammed in Figure 2, which provides full passive and powered functionality across a wide range of activities. Each state within the FSM has a unique transmission configuration and a unique torque control law (see Table 2), providing either power dissipation (passive motor control) or generalized active and emulated-passive behaviors (active motor control). Passive and active control methods, as well as low-level motor control is discussed in detail in Culver et al. (Reference Culver, Vailati and Goldfarb2022). Within each state, the knee torque is governed by a torque control law based on sensor inputs and control parameters that produce the following behaviors in each corresponding FSM state: (1) high-torque turbulent damping; (2) low-torque cadence-adaptive viscous damping; (3) low-torque unidirectional cadence-adaptive viscous damping that increases as the knee approaches full extension; (4) low-torque cadence-adaptive flexion torque pulse; (5) high extension torque that scales with residual hip torque and velocity; (6) low-torque PD controller with a virtual linkage between the thigh and knee joint, adapted from Lee and Goldfarb (Reference Lee and Goldfarb2021). FSM transitions, shown in Table 3, are governed by onboard sensing of knee angle ( $ {\theta}_K $ ), shank angle ( $ {\theta}_S $ ), shank axial force ( $ F $ ), shank axial acceleration ( $ {a}_a $ ), the walking speed estimation ( $ \omega $ ), and a state timer ( $ t $ ). Depending on the activity, the FSM transitions produce different FSM sequences. Table 4 shows the FSM sequences for different activities. Note that the FSM provides appropriate resistive or active stance-phase behavior and appropriate ballistic or non-ballistic swing-phase behavior, depending on the activity. Regarding tunability of parameters, it is not necessary to tune any of the transition condition threshold parameters in Table 3, and it is only necessary to tune some of the torque command parameters in Table 2 (e.g., individual users will not require tuning of $ {C}_{3\alpha } $ , $ {C}_{3\beta } $ , $ {C}_{5\alpha } $ , or $ {C}_{5\beta } $ ).

Table 2. Finite state torque control laws

Table 3. Finite-state machine transition conditions

Finite-state machine transition conditions depend upon measured sensor inputs (see caption for Tables 2 and 3) and several threshold parameters: knee angle ( $ {\theta}_{k, th} $ ), shank angle ( $ {\theta}_{S, th} $ ) and angular velocity ( $ {\dot{\theta}}_{S, th} $ ), shank axial force ( $ {F}_{th} $ ) and yank ( $ {\dot{F}}_{th} $ ), walking speed estimation ( $ {\omega}_{th} $ ), shank axial acceleration ( $ {a}_{a, th} $ ), and time ( $ {t}_{th} $ ).

Table 4. Controller sequence for different activities

Within each FSM state, knee torque is governed by a unique control law based upon a combination of sensor inputs: knee angle ( $ {\theta}_K $ ) and velocity ( $ {\dot{\theta}}_K $ ), thigh angle ( $ {\theta}_T $ ), shank axial force ( $ F $ ), and walking speed estimation ( $ \omega $ ). Each torque control law ( $ {f}_n $ ) has between one and three tunable parameters ( $ {C}_m $ ). For $ {f}_3 $ , $ {b}_{max} $ is a system parameter that indicates the maximum achievable motor braking impedance (i.e., when the motor leads are connected at 100% duty cycle). For $ {f}_2 $ and $ {f}_4 $ , $ {\omega}_0 $ is a tunable parameter that indicates the crossover walking speed, which is the walking speed where the motor provides neither assistance nor resistance and swing-flexion motion is governed by passive dynamics alone. For $ {f}_6 $ , $ {\theta}_{EQ} $ is the equilibrium position of the virtual spring, which is a function of the thigh kinematics, as described in Lee and Goldfarb (Reference Lee and Goldfarb2021). For $ {f}_5 $ , $ t $ is time as relevant for the filter term.

Resistive and active stance

FSM states 1 and 5 provide the necessary mechanical power dissipation and generation during stance-phase to accomplish a variety of functional activities. Turbulent damping via passive motor control provides knee-yielding akin to a commercial MPK, to provide appropriate knee motion during down-slope and down-stairs walking, as well as stand-to-sit (Wolf et al., Reference Wolf, Everding, Linberg, Schnall, Czerniecki and Gambel2012). The novel active stance control law, which uses the motor in active mode, generalizes powered knee extension into a single torque control law that is adaptive across a range of activities that benefit from positive joint power. The control law was developed from observations of the interaction between the biological knee and hip joints during stair ascent. As shown in Figure 3, the torque, velocity, and power of the biological knee joint lag behind those of the hip joint during stair ascent. The torque command in Table 2 was designed to input force and motion estimates of the residual hip joint and reproduce the shape and timing of the torque profile of the biological knee joint, but without commanding a desired joint angle, which would otherwise have the prosthesis, rather than the user, control knee motion. During the pull-up phase of stair ascent, the prosthetic ankle constrains the shank to be approximately vertical; as such, the real-time hip torque is estimated as the product of the load cell force and the sine of the knee angle (see Figure 3e). The thigh velocity and knee angle terms in the control law (see Table 2) provide for the bell shape of the torque command, and the filtering term provides the phase delay between hip and knee kinetics and kinematics. Ideally, the parameters $ {C}_{5\beta } $ and $ {C}_{5\gamma } $ are invariant between users, providing the torque control law a single parameter ( $ {C}_{5\alpha } $ ) that increases or decreases the magnitude of assistive torque, depending on the user’s preference.

Figure 3. Stance-phase (a) torque, (b) velocity, and (c) power of knee and hip joints during the stance-phase of stair ascent, from Riener et al. (Reference Riener, Rabuffetti and Frigo2002). Positive y-axes indicate (a) extension torque, (b) extension velocity, and (c) power generation. Values are normalized to a maximum of unity. These plots demonstrate that the phasing of the knee joint lags the hip joint for most of the stance-phase. (d) The phases of stair-ascent as described in McFadyen and Winter (Reference BJ and Winter1988), image adapted from Lee and Goldfarb (Reference Lee and Goldfarb2021). (e) When ascending stairs with a stiff prosthetic foot, the shank is constrained to be approximately vertical. The hip torque can be approximated by onboard sensors as the product of the load cell force (F) and the sine of the knee angle ( $ {\theta}_K $ ). The control system uses this approximation of hip torque to deliver knee torque that is synchronized with the user’s motion.

The unidirectional high-gear of the ECT enables the prosthesis to provide an extension torque that either passively resists flexion or actively provides extension. Additionally, due to the unidirectional clutch, there is little resistance to user-initiated stance knee-extension (i.e., the user can extend the stance leg via hip musculature without drivetrain resistance). Because the prosthetic foot is frictionally constrained to the ground during stance-phase, the stance leg is a closed kinematic chain, and therefore, the prosthesis user has control of knee joint movement during the stance-phase via movement of the hip joint. The user is therefore able to extend the knee joint without power-assistance, albeit with disproportionate hip torque input from the user, as demonstrated in Lee and Goldfarb (Reference Lee and Goldfarb2021). In the device described here, powered knee extension is activated by the user via hip torque, which initiates a knee extension movement, which in turn is identified by the controller and used to initiate power-assisted knee extension. Because the user is able to volitionally control the activation of powered stance knee-extension, intent recognition algorithms are not necessary for coordinated control; the coordination is inherent because power delivery is solely in reaction to the motion input generated by the user. Additionally, the thigh velocity term in the torque control equation scales torque delivery with estimated thigh power. Just as the biological hip and knee work synergistically to extend the leg when it is in a closed kinetic chain, the prosthetic knee is able to follow motion and force cues from the residual hip (under the user’s neuromuscular control) and provide synchronous assistive knee torque. In this manner, the user does not ride the prosthetic knee up the stairs, but rather works with it to extend the leg, similar to the manner in which an electric bicycle coordinates its power delivery with the user’s power input. While it is possible to cause controller instability using such a method, since a velocity term is used in the torque control law to add energy, instability is avoided by the combination of making the control law unidirectional, using an exponential decay as a soft saturation on the velocity term, and using the sine of the knee angle to decay the torque as the knee extends. With this control law formulation, if the user stops extending their hip, the user’s mass decelerates the knee joint, which reduces the torque and continues the deceleration. When knee velocity inflects, the FSM switches to resistive stance behavior, providing controlled support of the user’s weight as the knee flexes.

Ballistic swing

FSM states 2–4 provide walking-speed-adaptive ballistic swing phase behavior (see Figure 4). To estimate walking speed, the shank angular velocity is recorded and averaged from foot contact until the user initiates swing-phase in late-stance. The result is a linear relationship between the value of the average stance-phase shank angular velocity ( $ \omega $ ) and the walking speed. As such, $ \omega $ is a zero-parameter term that measures relative changes in walking speed within a single stride and can be used directly in control equations to provide cadence-adaptive behavior. During swing-flexion, when estimated walking speeds are above the crossover walking speed (i.e., when $ \omega >{\omega}_0 $ ), a damping torque is provided, similar to a commercial MPK. When $ \omega <{\omega}_0 $ , a feedforward assistive flexion torque is provided, which increases the peak-flexion knee angle to a biomimetic value not achievable with passive dynamics alone. This assistive torque has low amplitude and is provided unidirectionally, without trying to control knee angle directly, which enables a swing-phase motion that is still inertially coupled (i.e., ballistic swing is preserved because low actuator impedance makes the knee joint receptive to inputs from inertial forces), but with the caveat that the motor is helping the user by “pushing” the lower leg toward flexion.

Figure 4. Ballistic swing torque control laws, incorporating both assistive and resistive behaviors. (a) During swing-flexion, for walking speeds below $ {\omega}_0 $ , an assistive torque is provided; for walking speeds above $ {\omega}_0 $ , a resistive torque is provided. Both torque control laws are linearly proportional to walking speed, which provides cadence-adaptive behavior. (b) Gain scheduling of swing-flexion assistance torque. After the user has flexed the knee joint past 10°, the assistance torque begins ramping up to the commanded value as a function of knee angle. At 30° of flexion, the assistance torque has reached its commanded value. After 55° of flexion, the commanded torque is zeroed so the knee joint velocity can inflect for swing-extension. (c) The swing-extension torque control law commands a linear damping torque where the linear damping coefficient is a function of the walking speed and the knee angle (walking speeds from slow to fast are graded from blue to yellow). The commanded torque is zero until a predetermined angle that is a function of the walking speed estimation ( $ {C}_{3\alpha }+{C}_{3\beta}\omega $ ). After this point, the damping coefficient rapidly increases toward the maximum value ( $ {b}_{max} $ ). An exponential curve serves as a soft saturation of knee damping.

FSM state 3 provides cadence-adaptive ballistic swing-extension behavior (see Figure 4c), which is appropriate for the swing-extension phase of all evaluated walking activities except for stair ascent, which requires non-ballistic swing. For level and up-slope walking, swing-extension behavior is provided immediately after peak-flexion; for down-slope and down-stairs walking, swing-extension behavior is provided when the user lifts the flexed prosthetic knee, allowing inertial and gravitational forces to provide the extensive torque.

Experimental assessment

An experimental assessment was performed to investigate: (1) the ability of the prosthesis and control system to provide strictly passive functionality essentially identical to a state-of-the-art daily-use MPK; (2) the ability of the prosthesis to provide powered functionality for non-ballistic swing and stance-knee extension; and (3) the ability of the control system to seamlessly transition between the aforementioned activities. The experimental assessments consisted of four tests (see Figure 1): (1) treadmill walking on level-ground and ramps; (2) up-stairs and down-stairs walking; (3) sit-to-stand and stand-to-sit transitions; and (4) walking in an over-ground circuit with level-ground, ramps, stairs, and sitting/standing. The assessments were conducted on a single subject with transfemoral amputation – a 62-year-old male with traumatic amputation (50 years ago), K-4 activity level, weighing 85 kg, who used an Ottobock C-Leg 4 as his daily-use prosthesis (8 years with C-Leg). The subject completed 100 hr of testing on the prosthesis throughout the development of the control systems. In experiments 1–3, the subject first conducted the protocol wearing his daily-use MPK, then followed the same protocol wearing the ECT knee, using the same socket and prosthetic foot (a Fillauer Allpro). The ECT knee was neutrally aligned in a similar manner to his C-Leg 4 by the user’s prosthetist. Total masses of the ECT prosthesis and subject’s MPK, including prosthetic foot, shell, and shoe, were 3.50 kg and 3.25 kg, respectively. Kinematic data were recorded via a motion capture system (Vicon), and ground reaction forces were recorded via force plates integrated into either a Bertec instrumented treadmill for experiment 1, or into the floor (AMTI) for experiment 3. Data used by the embedded system to implement the control tasks was also collected and is presented when appropriate.

Experiment 1 had three treadmill walking conditions: (1) level walking at nine treadmill speeds between 0.4 and 1.2 m/s; (2) upslope walking at a slope of 8° at three treadmill speeds between 0.5 and 0.7 m/s; and (3) downslope walking at a slope of −8° at three treadmill speeds between 0.5 and 0.7 m/s. In the level-ground walking trial, speeds were ramped up from 0.4 to 1.2 m/s, incrementing by 0.2 m/s, then speeds were ramped down from 1.1 to 0.5 m/s, decrementing by 0.2 m/s. The subject was allowed to reach steady-state before motion capture data were recorded, and 15 strides of steady-state walking were recorded for each walking speed. In the up-slope and down-slope trials, speeds were ramped up from 0.5 to 0.7 m/s at 0.1 m/s increments, and data were recorded in the same manner as level-ground trials. The expectation of experiment 1 is that the ECT knee will demonstrate the same resistive stance and ballistic swing-phase behaviors as the C-Leg with improved swing-flexion kinematics at slower walking speeds (due to swing-assistance).

Experiment 2 involved ascending and descending an eight-step staircase five times using a step-over gait. Each step was 17 cm (6.5 in) high. The subject was considered to be in steady-state on each step except for the first and last steps, resulting in a total of 15 strides per device. The subject was allowed to use the staircase handrails for balance. The expectation of experiment 2 is that the ECT knee will have a knee trajectory more similar to the contralateral knee than the C-Leg, as previously demonstrated in comparisons of powered knee prostheses to MPKs (Lawson et al., Reference Lawson, Varol, Huff, Erdemir and Goldfarb2013).

Experiment 3 involved standing from and sitting to a chair 10 times with each foot placed on separate force plates. The subject did not use his arms to aid standing as to not compromise inverse dynamics. For experiments 1–3, the subject rested 5 min between trials, and all data were recorded on the subject’s daily-use MPK before the subject was fit with the ECT knee, and repeated the same experimental procedures. The expectation of experiment 3 is that the ECT knee will show significant increase in prosthetic side joint power and ground reaction force with a simultaneous decrease in intact side joint power and ground reaction force, relative to the C-Leg, as previously demonstrated in comparisons of powered knee prostheses to MPKs (Wolf et al., Reference Wolf, Everding, Linberg, Czerniecki and Gambel2012).

In experiment 4, the subject completed a single loop through a circuit that included level-ground, turns, ramps, stairs, and sitting/standing with a chair. Knee angle and controller state data were recorded using the embedded system. This circuit was only completed once to demonstrate the ability of the control system to adapt to a variety of ambulation conditions, rather than to evaluate the biomechanical efficacy of the controller (which is demonstrated with experiments 1–3). The expectation of experiment 4 is that the subject will be able to complete all tasks with biomimetic movement and without hesitation when transitioning between activities. The experimental protocol was approved by the Vanderbilt Institutional Review Board. The experimental participant provided written informed consent before his participation as required by the approved protocol.