Powered prosthesis with hybrid controller for stair locomotion
Patent Information
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- THE RGT UNIV OF MICHIGAN
- Filing Date
- 2024-07-31
- Publication Date
- 2026-06-10
Smart Images
Figure US2024040356_06022025_PF_FP_ABST
Abstract
Description
[0001]POWERED PROSTHESIS WITH HYBRID CONTROLLER FOR STAIR LOCOMOTION GOVERNMENT LICENSE RIGHTS This invention was made with government support under HD094772 awarded by the National Institutes of Health. The government has certain rights in the invention. TECHNICAL FIELD This disclosure is related to powered prostheses and control strategies intended to make artificial joint movement more natural. BACKGROUND Conventional passive knee-ankle prostheses are unable to provide the net-positive work at the joints necessary for ascending stairs and other daily activities. People with above-knee amputation can still perform these activities but must rely on compensatory behaviors such as so-called “hip hiking.” Most prosthesis users are limited to performing “step-to” stair ascent, which effectively halves their locomotion rate while ascending a staircase. Step-to ascent is characterized by climbing only one stair step per gait cycle, as opposed to two stair steps per gait cycle in able-bodied “step- over” stair ascent. These compensatory behaviors, along with the lack of net-positive work from the passive device, often put extra strain on the individual’s natural leg, residual limb, and upper body and can lead to secondary conditions such as chronic back pain and arthritis in the natural leg. Able-bodied stair descent is characterized by a toe strike and an accompanying dissipation of energy by the ankle at the beginning of the stance portion of the gait cycle. Passive devices are unable to mimic this combination due to a lack of controlled plantarflexion at the ankle, which results in a heel strike at the beginning of the stance portion. To compensate for this deficiency of passive prostheses, users must heel strike at the edge of the step and use that edge as a pivot for the foot to achieve the necessary flexion at the knee. This inability to actively control joint angles affects both ascent and descent, leading to potential toe-stubbing during swing phase and loss of balance. Powered prosthetic devices can potentially address some of these challenges by contributing net-positive work during stair ascent, controlled negative work during stair descent, and / or active control of foot placement during both activities. Powered devices might also reduce joint power and strain on the contralateral side and limit hip compensation during stair locomotion. However, despite the potential benefits of powered devices, device control strategies that can accommodate the various activities and environments of day-to-day life remain elusive. One control strategy employs impedance control to attempt to emulate an able-bodied joint by controlling the corresponding artificial joint’s resistance to movement. An impedance controller controls the amount of torque ^^ applied by an actuator (e.g., an electric motor) at an artificial joint of a powered prosthesis. The torque can be determined as: ^^ ൌ ^^൫ ^^^^ െ ^^൯ െ ^^ ^^^, (1)where K, B, and ^^^^are impedance angle, respectively. But able-bodied joint characteristics such as stiffness can change drastically within a single gait cycle—i.e., it is not as simple as determining ideal average values for the impedance parameters and using those values. To address this, it has been proposed to divide the gait cycle into multiple discrete phases with a finite state machine (FSM) where each impedance parameter is given a constant value within each discrete phase. For example, the gait cycle may be divided into 3-4 phases, each with a unique set of constant impedance parameters K, B, and ^^^^. A major drawback of FSM impedance control is that researchers must experimentally tune the impedance parameters for each discrete phase within the gait cycle for each individual user. Similarly, thresholds based on sensor readings that define boundaries between sequential phases and control the switching between FSM states must also be tuned. These tunable parameters are often user- and task-specific and can become onerous and tedious to tune. FSM impedance controllers have been reported with combinations of approximately 40 tunable parameters and state-switching criteria. Moreover, staircases (even ADA-regulated staircases) can vary greatly in incline and / or step height, and able-bodied studies have shown corresponding variations in normative joint kinetics and kinematics. Because of staircase variations, the impedance parameters and switching criteria for an FSM impedance controller would also need to vary as a function of stair configuration. But the resulting tuning sessions would be infeasible in duration. Failure of the controller to adapt to variations in step height and / or inclination would likely result in improper biomechanics and issues with foot placement, compromising the performance of the powered device. Another possible control strategy is kinematic control, which involves imitation of able- bodied joint movement through active control of joint angles—i.e., controlling the actuator(s) to achieve joint angles and velocities that mimic able-bodied kinematics and kinetics. This strategy avoids the problems associated with impedance parameter tuning and FSM switching but is problematic during stair descent when thigh angle ^^௧^is used as the phase variable due to the relatively small range of ^^௧^during stair descent. In particular, small changes in thigh angle map to large changes in the desired knee joint angle ^^^and ankle joint angle ^^^. This sensitivity of the joint angle to the user’s thigh input and the resulting prosthesis joint patterns can cause swing phase oscillations or overly aggressive gait progression. Other control strategies for stair locomotion have generally failed to successfully control stair descent. In one example, an FSM fixed-impedance controller modulates knee torque during stance and terminal swing based on electromyography signals from the residual limb. This approach to incorporating volitional control by the user has been limited to stair ascent and struggles to achieve proper foot placement on the following stair step. In another example, a tuned-heuristic approach modulates prosthetic joint angles during swing and, during stance, modulates the knee joint torque– angle relationship based on the prosthesis knee position at foot contact. This approach has also been limited to stair ascent and has not demonstrated biomimicry. SUMMARY An embodiment of a powered prosthesis includes a joint and a controller that continuously varies impedance at the joint during a stance phase of stair locomotion by a user. Another embodiment of the powered prosthesis includes all of the features of the previously listed embodiment, the stance phase is defined between a foot strike event and a toe-off event, and the impedance at the joint is a continuous function of one or more impedance parameters, each impedance parameter being a continuous function of a phase variable representing the stance phase. Another embodiment of the powered prosthesis includes all of the features of the previously listed embodiment, and each continuous impedance parameter function is optimized based at least in part on able-bodied data independent from the user. Another embodiment of the powered prosthesis includes all of the features of either of the two previously listed embodiments, and each impedance parameter is additionally a function of step height. Another embodiment of the powered prosthesis includes all of the features of any one of the previously listed embodiments, and the controller kinematically controls the joint during a swing phase of stair locomotion by the user. Another embodiment of the powered prosthesis includes all of the features of any one of the previously listed embodiments, and the controller estimates gait phase in real time during stair locomotion by the user based on a phase variable. Another embodiment of the powered prosthesis includes all of the features of the previously listed embodiment, and the controller estimates gait phase during stair ascent and stair descent using the same phase variable. Another embodiment of the powered prosthesis includes all of the features of the two previously listed embodiments, and the phase variable is determined based at least in part on a joint angle of the user and time. Another embodiment of the powered prosthesis includes all of the features of any one of the previously listed embodiments, and the joint is a knee joint. The prosthesis also includes an ankle joint, and the controller continuously varies impedance at both joints during the stance phase of stair locomotion by the user. BRIEF DESCRIPTIONS OF THE DRAWINGS FIG.1 is a block diagram of a hybrid walking controller. FIG.2 is a schematic side view of an example of a powered knee-ankle prosthesis during early stance (solid) and late stance (phantom) during stair locomotion. FIG.3 is a schematic illustration state transition criteria of a finite state machine (FSM). FIG.4 illustrates impedance parameter models for stair ascent. FIG.5 illustrates impedance parameter models for stair descent. FIG.6 is a photographic side view of a backdrivable powered knee-ankle prosthesis equipped with a hybrid stair-step controller. FIGS.7A-7E respectively illustrate a thigh angle phase variable for two different users over an entire stair ascent gait cycle, estimated and actual thigh angle at foot strike, estimated and actual minimum thigh angle, estimated and actual thigh angle at toe-off, and estimated and actual maximum thigh angle. FIG.8 illustrates intra-user kinematic trajectories over stance and swing during stair ascent for HKIC and PAS kinematics compared to able-bodied reference data. FIG.9 illustrates intra-user average and individual trial joint kinetic trajectories for a 102 mm step ascent. FIG.10 illustrates intra-user average and individual trial joint kinetic trajectories for a 152 mm step ascent. FIGS.11A-11E respectively illustrate a thigh angle phase variable for two different users over an entire stair descent gait cycle, estimated and actual thigh angle at foot strike, estimated and actual minimum thigh angle, estimated and actual thigh angle at toe-off, and estimated and actual maximum thigh angle. FIG.12 illustrates intra-user kinematic trajectories over stance and swing during stair descent for HKIC and PAS kinematics compared to able-bodied reference data. FIG.13 illustrates intra-user average and individual trial joint kinetic trajectories for a 102 mm step descent. FIG.14 illustrates intra-user average and individual trial joint kinetic trajectories for a 152 mm step descent. DESCRIPTION OF EMBODIMENTS Described below is a powered knee-ankle prosthesis equipped with a hybrid kinematic impedance controller (HKIC) and control framework that can produce biomimetic joint kinematics and kinetics during both stair ascent and stair descent over a continuum of stair heights. During the stance portion of the gait cycle—i.e., while the prosthesis is in contact with the ground or stair—the controller employs a joint impedance model that modulates stiffness, damping, and equilibrium angle as continuous functions of stance phase and step height. During the swing portion of the gait cycle— i.e., while the prosthesis is out of contact with the ground or stair—the controller employs kinematic control that modulates joint angles as functions of swing phase and step height. The hybrid controller employs a phase variable that accounts for the user’s specific leg geometry and better parameterizes the stance and swing portions of the gait cycle. The impedance parameters are continuously varied during stance rather than being held constant in multiple discrete subphases throughout the gait cycle. The prescribed impedance regulates the relationship between joint angle and torque rather than controlling joint angle directly and therefore addresses the above-described phase sensitivity issues experienced in purely kinematic control of stair descent due to the small thigh range-of-movement (ROM). The controller may emphasize late-stance knee damping during stair descent, thereby allowing use of a thigh-based phase variable with a small thigh ROM. The controller may also employ a unified phase variable for both stair ascent and descent that uses leg geometry to automate the user- and task-specific parameter tuning needed to obtain linear phase estimates. A powered knee-ankle prosthesis equipped with the HKIC controller, also referred to below as a “hybrid stair-step controller” or “stair-step controller” demonstrates biomimetic ascent and descent joint kinematics, kinetics, and work across multiple different step heights and users. Commonly assigned international patent application number PCT / US2024 / 016734 by Gregg, et al., filed February 21, 2024, is hereby incorporated by reference in its entirety. That application discloses a hybrid controller for use during walking movement, with continuously variable impedance control employed during stance and kinematic control employed during swing. The impedance controller uses impedance parameters that are continuous functions of stance phase, walking speed, and incline using real-time estimates of walking speed and incline to enable autonomous adaptation to changes in walking speed and incline. The controller uses global thigh angle ^^௧^as a task-invariant phase variable, estimates gait phase, walking speed, and incline in real time, and may be referred to below as the “hybrid walking controller.” A block diagram of the hybrid walking controller is provided in FIG.1, where real-time estimates of gait phase ^^̂ and conditions ^^̂—i.e., walking speed and incline—define the joint impedance parameters K, B, θeqand joint angles θdusing data-driven models. Depending on whether the user and prosthesis are in stance or swing, torque commands τ are calculated using either an impedance controller or a kinematic controller, respectively. Once configured with a user’s mass and leg segment lengths, the hybrid walking controller can operate autonomously, requiring neither manual impedance tuning nor external knowledge of the terrain. Commonly assigned international patent application number PCT / US2024 / 035847 by Gregg, et al., filed June 27, 2024, is hereby incorporated by reference in its entirety. That application discloses a “sit-stand controller” with continuously variable impedance control employed during stand-to-sit and sit-to-stand transitions among various chair heights. Impedance control in that controller is based on parameterized and optimized data-driven impedance parameter trajectories for sitting, standing, and walking with only two classification modes (walking or not walking). Stand-to-sit and sit-to-stand equilibrium angles are decoupled via a knee velocity-dependent scaling term. A prosthesis equipped with the sit-stand impedance controller produces biomimetic joint mechanics during sit-stand transitions, resulting in improved loading symmetry and reduced time to complete sit-stand tasks compared to passive prostheses. The sit-stand controller can be integrated with the above-described hybrid walking controller or another kinematic or impedance-based walking controller to facilitate sit-to-walk transitions from different chair heights. The stair-step hybrid controller discussed below can be integrated with the hybrid walking controller and / or the sit-stand impedance controller to enable biomimetic kinematics and kinetics across all common prosthesis tasks, including variable speed and / or variable incline walking, sit-stand transitions, and stair ascent and descent as well as transitions from one task to another. Similar to the hybrid walking controller, the stair-step controller relies on a novel, data-driven impedance parameter model based on able-bodied data that produces biomimetic joint torque during the stance portion of a gait cycle during stair locomotion. As used herein, “stair locomotion” includes both stair ascent and stair descent. As used herein, a “variable impedance controller” is a controller that continually varies the output mechanical impedance at a prosthetic joint. Mechanical impedance is generally a measure of resistance to movement from an equilibrium position, which in this context is resistance to rotation about a joint axis. Resistance to rotation about a joint axis is a function of joint stiffness, joint damping, and joint angle relative to an equilibrium angle according to equation (1), above. Mechanical impedance at a prosthetic joint can be provided via an applied torque in a rotational direction about the joint axis. This torque can be applied by an electric motor coupled with a transmission or other suitable means. Impedance control is different from kinematic control in that impedance is a measure of resistance to movement relative to an equilibrium position in a freely rotatable joint, while kinematic control positively controls joint movement by rotating an object about the joint axis from one angular position to another with a particular angular speed function via a motor and transmission or other suitable means. FIG. 2 schematically illustrates an example of a powered knee-ankle prosthesis 10 that includes an upper leg member 12, a lower leg member 14, and a foot member 16. The upper leg member 12 is adapted for attachment to the end of the leg of an above-knee amputee user at one end and is coupled with the lower leg member 14 at a knee joint 18. The knee joint 18 is a rotational joint that provides rotational movement of the lower leg member 14 relative to the upper leg member 12 about a knee axis 20. The lower leg member 14 extends from the knee joint 18 to an ankle joint 22 at which the foot member 16 is coupled with the lower member 14. The ankle joint 22 is a rotational joint that provides rotational movement of the foot member 16 relative to the lower leg member 14 about an ankle axis 24. The prosthesis 10 includes a first actuator 26 (e.g., a motor) configured to provide a knee torque ^^^in a rotational direction at the knee joint 18 and a second actuator 28 configured to provide an ankle torque ^^^in a rotational direction at the ankle joint 22. For example, the first actuator 26 may be rigidly mounted along the upper leg member 12, and its rotational output may be converted to the torque ^^^applied to the knee joint 18 via a transmission member rigidly attached to the lower leg member 14. Similarly, the second actuator 28 may be rigidly mounted along the lower leg member 14, and its rotational output may be converted to the torque ^^^applied to the ankle joint 22 via a transmission member rigidly attached to the foot member 16. Other arrangements are possible to provide torque at one or more of the prosthetic joints. The prosthesis 10 includes at least one controller 30 configured to store and employ a control scheme 32 according to which the controller operates each actuator 26, 28 to provide the desired torque ^^^, ^^^at each joint 18, 22. The controller 30 is programable and in communication with each actuator 26, 28 to control its output torque. In this example, the controller 30 is in two-way communication with each actuator 26, 28 to receive one or more inputs from the actuators, such as a real-time encoder position which can be used to determine real-time angular velocities at each joint 18, 22, among other parameters. The controller 30 may receive additional information from one or more sensors 34 (e.g., an accelerometer) to implement the control scheme 32. FIG.2 schematically illustrates the prosthesis 10 at two different phases of the stance portion of a gait cycle. The prosthesis 10 is illustrated in solid lines at or near the beginning of stance during stair ascent—that is, just after the prosthesis has contacted the tread of one of the stairs after a swing portion of the gait cycle that began on a previous stair tread or the ground. The prosthesis 10 is illustrated in phantom lines at or near the end of stance during stair ascent—that is, with the lower leg member 14 at or near full extension before the prosthesis enters the subsequent swing portion of the gait cycle or resumes normal walking. Between the beginning and end of stance is a transient period in which the prosthesis 10 is changing and moving from one end phase of stance to the other end phase. Prosthesis movement during stair descent is similar, but with some important differences discussed below. During stair descent, the stance portion of the gait cycle generally begins with the knee joint in extension and ends with the knee joint in flexion. Each joint impedance parameter during stance is a continuous function between its end phases. The term “phase” may be used herein in two senses. In one sense, a complete gait cycle is divided into a stance phase and a swing phase. These high-level phases may also be referred to as the stance portion and swing portion of the gait cycle, or simply as “stance” and “swing.” As used in the description of the hybrid stair-step controller below, the term “phase” also specifically refers to the value of a phase variable along a continuous function between 0 and 1 during the stance portion of the gait cycle or the swing portion of the gait cycle, where 0 is the beginning of stance or swing and 1 is the end of stance or swing. During stair ascent and descent, the present “phase” of stance or swing thus represents the percentage of the entire stance or swing portion of the gait cycle that has been completed—e.g., when the stance phase variable is at 0.5, the user and prostheses are halfway through the stance portion of a gait cycle. “Phase” generally correlates to time during an uninterrupted gait. The control scheme 32 may be an impedance control scheme used by the controller 30 to provide torque commands to the actuators 26, 28 during stance. When combined with walking control or sit-stand control, any combination of controllers and control schemes may be included as part of the prosthesis 10. For example, when combined with the above-described hybrid walking controller and / or sit-stand controller, the prosthesis may include a position (i.e., kinematic) controller operable during the swing portion of the user’s gait, a first impedance controller operable during the stance portion of the user’s gait, and a second impedance controller operable during the stance portion while ascending or descending stairs or during a sit-stand transition. Or one impedance controller can control joint torque based on more than one control scheme selected based on task identification. In other words, torque control at the joints 18, 22 is not limited to any particular controller or number of controllers. Rather, one or more controllers are used to control joint torque according to each of one or more control schemes. While FIG. 2 illustrates only one controller 30 and associated control scheme 32, some implementations include multiple controllers. The prosthesis 10 may for example include an impedance controller with one or more impedance control schemes and a separate kinematic controller with one or more kinematic control schemes. The prosthesis 10 may include dedicated controllers for each joint as well. Unified Phase Estimate for Stair Ascent and Descent A phase estimation method may include independent calculation of a stance phase variable ^^^^and a swing phase variable ^^^^. The phase estimation method may also include a leg geometry- based optimization of phase variable parameters. The characteristics of the phase estimation method allow for a unified phase variable definition for all stair locomotion tasks and provide an automated way to individualize the phase variable for a particular user. In other words, stair descent does not require a different phase variable definition from the one used during stair ascent. The disclosed prosthetic and controller use a unified phase variable for both stair ascent and stair descent that defines a gait cycle between sequential foot strikes (FS). This necessarily differs from gait cycle definitions based on sequential heel strikes (HS). Foot strikes include heel strikes, which are encountered at the beginning of stance phase during stair ascent, and toe strikes, which are encountered at the beginning of stance phase during stair descent. In the phase variable described below, the stance and swing portions of the gait cycle are decoupled and defined by the stance phase variable ^^^^and the swing phase variable ^^^^. This removes the interdependence of the kinematic and impedance control frameworks on each other, allowing for modifications of phase parameters for one sub-controller to have little or no effect on the behavior of the other. The gait cycle phase variable ^^ may be defined as: ^^ ൌ ^^^^ ⋅ ^^̂^^^ ^^^^ ⋅^1 െ ^^̂^^^, (2)where ^^̂^^is the average able-bodied value of normalized time at which toe-off (TO) occurs for each stair locomotion task. As illustrated in FIG.3, a finite state machine (FSM) 40 may govern changes between phase variable definitions at biologically inspired thresholds, such as maximum hip extension (MHE) or toe-off (TO). FIG.3 schematically illustrates an example of state transition criteria, with states S1 through S3 corresponding to stance phase and states S4 and S5 corresponding to swing phase. The redundant state S2 in stance phase acts as a threshold to prevent premature MHE detection, as described later. The feed-forward state S5 is a novel addition to previous FSM configurations. The FSM begins in state S1 after FS is detected. During state S1, a stance phase estimate ^^̂^^may be defined with the descending phase definition: ^^̂^^ൌఏూ^౪^ିఏ౪^ఏ⋅ ^^^^^ୌ^౪ూ^^ିఏ౪^^ౄుfor S1 & S2, (3) where parameters ^^^ୗ, ^^ୌ^^୦^^୦, angle at MHE, This phase definition is valid until MHE but is used over two states S1 MHE detection that can occur with slow strides during thigh extension in state S1. The FSM stays in state S1 as thigh angle ^^^୦decreases until a threshold ^^^→ଶൌ 0.85 ⋅ ^^^^^ୌ^is reached, corresponding to the stance phase at which thigh velocity is expected to begin detection is performed only in state S2, where a fast (10 ms) and slow (40 ms) simple average minima detection algorithm is employed on the measured thigh angle. This approach filters out noise in the thigh angle measurement as the user approaches MHE to prevent premature detection. After MHE occurs, the FSM transitions to state S3 for the remainder of stance phase. During state S3, the stance phase estimate may be defined with the ascending phase definition: ఏ౪^ିఏ^ో ^^̂^^ൌ 1 ^౪^ఏ౪ూ^^ିఏ౪^^ ⋅^1 െ ^^^୫^^for S3 (4)where parameters ^^^^ ୫ ^୦, ^^^୦,^thigh angle at MHE, and stance phase at MHE. After the loss of foot contact (FC), the stance phase estimate is saturated at ^^̂^^ൌ 1 for the remainder of the gait cycle during states S4 and S5. Following TO, the illustrated FSM transitions from state S3 to state S4, where the ascending ^^^୦trajectory gives rise to an estimated swing phase variable: ^^̂^^ൌఏ౪^ିఏ^^ో ౪^⋅ ^^^^^ୌ^for S4, (5) where ^^^^^^୦is the measured thigh angle at TO and is the anticipated swing phase at which MHFoccurs. ^^^୦ at MFH is estimated as ^^^^ୌ^ ^^ ^^୦ ൌ max൫ ^^^^୦ , ^^^^୦ ൯ െ ^^^^ ^ୌ^^୦ ^ ^^^୦ , which enforces theminimum angular separation in the training dataset for the given task.In the illustrated example, the FSM transitions from state S4 to state S5 at a thigh velocity of ^^^^୦^ .75rad / s and a thigh angle of ^^^୦^ ^^ସ→ହ^୦. The thigh angle threshold ^^ସ→ହ1^ ^^ 3 ^ ^ୌ^^୦ൌ 4^^^୦ ^4 ^^^୦corresponds to the end of the The thigh velocity threshold may be selected to prevent an early switch to state S5 if the user has not yet left the linear portion of thigh flexion. After transitioning from state S4 to state S5, a feed-forward phase definition may be defined based on the average swing phase rate in state S4 ( ^^^^ସ^ ): ^^̂^^ൌ ^^̂^ସ^ହ ^^^௧ ସ^ ^^^^^^^ ^^ for S5 (6)where ^^̂^ସ^ହis the estimated of a feed-forward phase rate prevents premature saturation of the phase variable, due to ^^^ୌ^^୦^ ^^^ୗ^୦for all stair locomotion tasks. phase saturation before MHF is undesirable because a phase variable with a non- unity slope will temporally scale the joint trajectories at the knee and ankle, desynchronizing the user and prosthesis, which can lead to tripping and / or loss of balance. If the user is ascending or descending consistently and thigh features are estimated correctly, ^^̂^^ൌ 1 will occur simultaneously with FS, returning the FSM to state S1. However, saturation of ^^̂^^in S5 after MHF may be permitted so that the knee joint reaches the necessary flexion (ascent) or extension (descent) angles early enough to give the user confidence that the prosthesis it is ready to accept their body weight upon FS. Pilot testing has revealed that users prefer this behavior to resemble their experience with conventional prostheses. At FS, the state machine transitions from state S5 to state S1, and the process repeats for the next gait cycle and / or stair stride. During the stance phase of the gait cycle, states S1-S3, the swing phase estimate may be fixed at ^^̂^^ൌ 0. Geometry-Based Thigh Feature Estimation To calculate an accurate phase variable, correct estimation of the user’s thigh trajectory features ( ^^^ୗ ^ୌ^ ^^ ^ୌ^^୦, ^^^୦, ^^^୦, ^^^୦) is important. Some calculations assume that features extracted directly from able-bodied averages of task-specific thigh are sufficient, with either hand-tuning of feature parameters or online updates of these features over multiple steady-state strides. But hand- tuning increases acclimation and training time with each new task added to a controller. And online moving-average feature predictions require multiple steady-state strides prior to convergence, which may be feasible during treadmill or level ground walking but is prohibitively slow along the relatively short distance of a staircase. Described below is a thigh trajectory feature estimator that addresses these problems. The estimator generates user-specific features for each step height that are individualized based on lower limb geometry. Referring back to FIG.2, and treating the illustrated prosthesis 10 as a two-link planar model of a human leg, an origin O may be defined at the center of rotation of the hip joint. In FIG.2, global thigh angle is denoted as ^^^୦, and the relative knee angle is denoted as ^^୩. Here, thigh segment length ^^^୦is defined as the distance between the origin O and the center of rotation of the knee joint. Similarly, shank segment length ^^^୦is defined as the distance between the center of rotation of the knee joint and the center of rotation of the ankle joint. A vector ^^^^is defined starting at the center of rotation of the hip O and ending at the center of rotation of the ankle. This model forms the basis of the thigh feature estimation outlined below. The vector ^^^^ can be written as:^^^^^௫ ^^ sin ^ ^^ ^ ^ ^^ sin ^ ^ ^ൌ ^^௬^ ൌ ^th th sh^^thെ ^^୩^ ^ ^(7) The model can be^changes to the thigh length ^^thand shank length ^^sh, while the horizontal component ^^^௫is constrained to be the same for a given step height γ, regardless of leg geometry. This is because ^^^௫at FS is somewhat constrained by the stair geometry. For each step height γ, an optimization problem can be constructed to determine the expected thigh trajectory ^^th,γ, based on the user’s thigh and shank length. The optimization minimizes the difference between the average able-bodied ^̅^^௫and an estimated horizontal component ^^̂^௫ൌ ^^thsin ൫ ^^th ,ఊ൯ ^ ^^shsin ൫ ^^th ,ఊെ ^^^^୩,ఊ൯, given normative biological knee angles ^^^^୩,ఊ: ൌ arg mఏin ^̅௫ ௫ ଶ^୦,ఊ౪^∥^^െ ^^̂^∥ଶject to ^ ^^ గ . (8) subగ^୦^ ଶ The constraint ensures the solution is within the expected range of movement of the global thigh angle calculated from able-bodied data. This nonlinear program can be implemented in MATLAB®and solved usingfmincon. The phase variable parameters can then be calculated from the expected thigh trajectory. Stance Impedance and Swing Kinematic Controllers Joint torque during stance ^^^^is calculated with an impedance controller where the impedance parameters vary throughout the gait cycle and across step heights. The stance phase estimate ^^̂^^from above and a known step height γ can be input into an impedance model to determine the joint stiffness K, damping component B, and equilibrium angle θeqfor the impedance torque control law, which is scaled by user mass m: ^^^^ ൌ ^^൫ ^^^^^^^, ^^^൫ ^^^୯^^^^^, ^^^െ ^^൯ െ ^^^^^^^, ^^^^^^൯, (9)Derivation of the impedance model is discussed further below. During swing phase, a proportional derivative (PD) controller can be used to enforce desired time-invariant joint kinematics known as virtual constraints. For each step height γ, a Fourier series may be used to model the average able-bodied knee and ankle kinematics ^^^and ^^^as functions of gait phase ^^. Before calculating the Fourier series, the desired joint kinematics are interpolated from publicly available able-bodied data as functions of the average phase variable, based on the average thigh kinematics for the associated step height γ in the reference able-bodied dataset. This approach accounts for non-linearities in the average phase trajectory, improving the phase synchronization (and thus the fit) of the estimated joint kinematics to the reference able-bodied trajectory, on average. The commanded knee joint and ankle joint torques ^^^, ^^^, are functions of their respective desired joint positions: ^^^^^ൌ ^^୮^൫ ^^^^ ^ ^^^^, ^^^ െ ^^^൯ െ ^^^^^^^^, (10)where ^^^an^^ ୮ d ^^ are the prosthesis 10 include viscous dampers acting on the knee and ankle joints 18, 22 to limit vibrations that may naturally arise from a derivative tracking term due to the inherently minimal viscous losses of the actuators 26, 28. Time-based interpolation between ^^^^and ^^^^may be performed at each foot strike and toe-off to ensure a smooth transition as in the above-described hybrid walking controller. Stance Impedance Model Described below is a polynomial-based piecewise-linear impedance model for both the knee joint 18 and the ankle joint 22 during stair ascent and descent and the methodology used to generate the model. The model is parameterized by the user’s completion fraction of the stance phase ^^^^and the stair step height γ. In this example, the stair step height γ is defined over the range ±(102 ≤ γ ≤ 178) mm, where negative step height represents stair descent, but this methodology can be employed with other step height ranges. The model may defined by: ^^^^^^^, ^^^^^^^ ^^^ୃ ^^^^^^ ^^^^, ^^^^^ ^^ ൌ ^ ^^^^ ^^^ୃ^ ^⋮^, (11) where each task function ^^^^ ^^^ ∈ ℝௗା^ൈ଼and an interpolation vector ^^^ ^^^ ∈ ℝ଼ൈ^, ∥ ^^^ ^^^ ∥ൌ 1. For example, ^^^^ ^^^ is as ^^^,ି^^଼… ^^^,^^଼^^^^ ^^^ ൌ ^ ⋮ ⋱ ⋮ ^ ^^^ ^^^, (12) ଼ᇥ where, for example, ^^^െ178^ ൌ^1 0 … 0^ୃand ^^^178^ ൌ^0 … 0 1^ୃ. The taskfunctions for damping and equilibrium angle are defined similarly. The model is fully defined when the three parameter matrices XK, XB, and Xθare chosen. In the example presented here, model polynomial orders d = 9 and d = 4 are chosen for the knee and ankle, respectively, to balance model flexibility with overfitting risk. An optimization-based approach leveraging a dataset of able-bodied steady-state stair ascent and descent can be used to fit the model. The dataset used here contains kinematic and kinetic joint information from 22 able-bodied participants ascending and descending stairs at four step heights in the range γ = ±(102 ≤ γ ≤ 178) (J. Camargo et al., “A comprehensive, open-source dataset of lower limb biomechanics in multiple conditions of stairs, ramps, and level-ground ambulation and transitions,” J. Biomech., vol.119, p.110320, 2021). First, the inter-participant average kinematics and kinetics for each joint at each step height are calculated. For this average, right and left leg joint data are combined with an assumption of symmetry, and only the second full stair stride (where a force-plate was available to detect FS and TO) is used. The inter-participant average stance phase variable trajectory is also calculated at each step height. In principle, the objective of model fitting is to identify the optimal impedance parameter coefficient matrices ^^^∗, ^^^∗, and ^^∗ఏ that best reproduce the average mass-normalized joint torque trajectories ^^ in the dataset given the dataset kinematics. Because each column of the parameter matrices only affects the impedance for a single step height, each row can be solved independently and reassembled for the final model. Optimization Cost Function Let ^^^∗,^, ^^^∗,^, and ^^∗ఏ,^be the ith columns of ^^^∗, ^^^∗, and ^^∗ఏ, respectively. Similarly, let ^^^, ^^^, and ^^^^be vectors of length ^^ of the average dataset torques, joint angles, and joint velocities for the respective step height. Let ^^^be a vector containing the average stance phase variable trajectory based on the dataset thigh kinematics and the definitions given above in the section entitled Unified Phase Estimate for Stair Ascent and Descent. Then, the following optimization problem can be solved for each step height ^^^based on a modified squared error metric: ^ ^^^∗,^, ^^^∗,^, ^^ఏ∗,^^ ൌ arg ^^ ^^ ^^∥ ^^^െ ^^̂∥ଶଶ ^ ^^∥ ^^^^^̂ଶ^∥ଶ, (13) where ^^̂^ ൌ ^^^^^^, ^^^^൫ ^^^୯^^^^, ^^^^െ ^^^൯, Here, ^^^∈ ℝ^ൈ^is a constant diagonal weighting matrix that penalizes the spring torque ^^̂^in late stance during stair descent. This matrix ^^^ൌ diag^^^^^is defined by a piecewise-linear-in-phase weight vector ^^^∈ ℝ^ൈ^. For stair ^^^ൌ ^^^ൈ^. For stair descent, each data point ^^ is defined as ^^^^ ^^^ ൌ max ^0,1 െ^ି^^, (14) where ^^ denotes the dat mida point at the midpoint torque during descent. This spring torque penalty is added to the cost function to encourage the optimization to select solutions where late stance torque is provided mostly through damping. This behavior may be desirable because, in late stance, the thigh angular velocity is small compared to relatively larger angular velocities at the knee and ankle joints. Due to the thigh-based phase variable, low thigh velocity results in slowly changing impedance parameters, which could inhibit the desired joint progression rates if dominated by spring-like behavior. However, the optimization problem of equation (13) is non-convex, meaning that globally optimal solutions cannot be guaranteed or solved efficiently. By making the substitution ^^^^^^^^^^^^, ^^^^^^୯^^^^^, ^^^ൌ ^^^^^^^, ^^^ൌ ^^^ ^^^ୃ^^ ^^ (15) and treating the ^^ఋ∈ be reduced to a convex quadratic program. Specifically, if a decision vector ^^ ∈ ℝସௗାଷൈ^ൌ ^ ^^^ୃ,^, ^^^ୃ,^, ^^ఋୃ,^൧ୃcan be defined, where ^^ఋ,^are the columns of ^^ఋ, such that the cost function defined in equation (13) becomes linear in the unknown parameters. Let the jth column in ^^ ∈ ℝସௗାଷൈ^be defined as ^^^ ^^^ ൌ െ^ ^^^^^^^^^, … , ^^^^ ^^^ௗ^, ^^^^^ ^^^^^, … ,(16) where subscript j denotes the ∈ ℝସௗାଷൈ^be defined as: ^^^ ^^^ ൌ ^^^^^^െ ^^ୃ^^ ^ ^^ୃ^^ ^^, (18) where ^^ ൌ ^^ ^^ୃ^ ^^ ^^^^^^^^ୃ, ^^ ൌ 2 ^^ ^^^. (19) Optimization Constraints To prevent overfitting, a diagonal regularization matrix Λ ∈ ℝସௗାଷൈସௗାଷmay be added to penalize the L2 norm of x. In this example, the diagonal entries in Λ corresponding to the regularization weights on ^^^,^and ^^^,^were 1e−4for ascent and 1e−5for descent. For weights on ^^ఋ,^, the diagonal entries were 1e−10for ascent and 1e−7for descent. These hyperparameters were chosen during model fitting to produce a smooth model to capture general behavior without overfitting to the training data. Regularization also limited undesirable solutions such as an excessively large spring torque balanced by an excessively large damping torque in the opposite direction. Constraints were placed on x such that ^^ ^^ ^ ^^ where ^^ ∈ ℝ^ൈସௗାଷand ^^ ∈ ℝ^ൈ^to ensure that stiffness ^^^ ^^^^, ^^^ and damping ^^^ ^^^^, ^^^ remained within ranges that were both physiologically realistic and feasible for the prosthesis to perform. The details of the construction of ^^ are omitted for brevity, but can be reviewed in the above-noted Gregg, et al. application related to the hybrid walking controller. Due to differences in the desired joint behavior for the ankle and knee over both ascent and descent, a different set of constraints was used for each activity and joint combination as listed in TABLE I, below. TABLE I Ascent Descent i e In this c pilot trial feedback, as users were accustomed to the stiff behavior of their take-home device at the start of the gait cycle. Across both ascent and descent, torque from damping was constrained to a maximum of 0.14 Nms / rad / kg due to limitations of velocity filtering methods used in the powered prosthesis. Minimizing the cost function ^^^ ^^^ along with the regularization penalty ^^ୃΛ ^^ subject to the inequality constraints yields the final quadratic program (QP): mini ୃ௫mize ^^^ ^^ ^ Λ^ ^^ െ ^^ୃ^^, subject to ^^ ^^ The positive offset ^^^^^^originally in equation (18) is neglected without loss of generality. This QP can be solved for each step height and joint using the MATLAB®Optimization Toolbox (R2022b). To recover the original model’s equilibrium angle function ^^^୯^^^^^, ^^^in equation (11), a least- squares fit of ^^൫ ^^^, ^^^^൯ / ^^൫ ^^^, ^^^^൯ can performed to a d-th order polynomial at each incline. The polynomial to prevent significant approximation error. FIG.4 illustrates the impedance and FIG.5 illustrates the impedance models for stair descent from the training step heights γ = ±{102, 127, 152, 178} mm. To quantify the impedance parameter model’s reconstruction error, ^^̂ was calculated for the knee and ankle joints over the inter-participant average kinematic data for each training step height in the able-bodied dataset using the fit impedance model. The root mean squared error (RMSE) in joint torque was then calculated for each step height. Note that the RMSE is distinct from the cost function minima. Across all tasks, the average RMSEs were ek = 0.11 ± 0.1 Nm / kg and ea = 0.06 ± 0.03 Nm / kg. Experimental Examples The biomimicry of a working prosthesis equipped with a hybrid stair-step controller consistent with the above description and employing the impedance parameter models of FIGS.4 and 5 has been experimentally assessed with two amputee participants whose details are listed in TABLE II. TABLE II Sex Age Weight (kg) Height (m) Years as amputee Etiology l l Board (HUM00166976). The above-described control framework was implemented on a backdrivable powered knee-ankle prosthesis, a photographic image of which is shown in FIG.6. This prosthesis features a quasi-direct drive, low-inertia actuation design that allows for open-loop joint impedance control and high-bandwidth position control. A licensed prosthetist fit the robotic prosthesis to the participants, ensured proper alignment, and supervised the experiment for participant safety. Participants also wore a ceiling-mounted safety harness. Each participant each completed the experimental protocol once with the robotic prosthesis. For comparison, participant two (P2) completed the same experimental protocol on a separate testing day with their passive device (Ottobock.®Genium X3) due to their unusual ability to perform step- over stair ascent. The experimental protocol investigated the performance of the hybrid stair-step controller and passive device during stair ascent and descent at four step heights on an adjustable staircase. Step heights of 102 mm (4 in.), 127 mm (5 in.), 152 mm (6 in.), and 178 mm (7 in.) were chosen in compliance with the Americans with Disabilities Act. Ten trials were performed at each step height. Each trial included one ascent and one descent of the staircase. A one-minute break was provided between trials, and a five-minute break was provided after the fifth trial to mitigate any fatigue effects. Joint kinematics and kinetics were recorded from the robotic prosthesis. An infrared motion capture system (Vicon Ltd., Oxford, UK) collected kinematics from each participants natural limb and passive device. Each participant attended an acclimation session on a day before the experiments, during which they were provided an overview of the high-level functionality of the controller and given time to acclimate to stair ascent and descent at a moderate step height of 152 mm (the nominal ADA- compliant step height). On the day of the experiments, each participant was given time to acclimate to the controller at each step height before performing a set of trials. Participants were encouraged to limit body weight support on the handrails to maximize the load on the prosthesis and to ascend and descend the stairs at a consistent, comfortable pace. No hand-tuning of controller parameters was performed for either participant. Participant P1 completed all step height configurations with the powered prosthesis. Participant P2 completed all step height configurations except the 178 mm configuration. A similar experimental protocol followed on a different day with participant P2’s passive device. Since participant P2 was already familiar with the stair ambulation behavior of their own prosthesis, no acclimation session was provided prior to those trials. Trials with this prosthesis in which the device failed to trigger stair ascent mode and caused the participant to kick the stair were discarded. Kinematic and kinetic data were compared between the robotic prosthesis using the above- described hybrid controller, the passive device (PAS), and the able-bodied reference data. The reference data represents the inter-subject average steady-state stride at each step height configuration from the open-source biomechanics dataset used to train the impedance model. The second full stair stride was designated as the steady-state stride for both the HKIC and PAS trials. FIGS. 7A-7E illustrates the resulting phase variable for each participant, demonstrating its ability to parameterize the gait cycle and the effectiveness of the geometry individualization. The phase variable for both participants (FIG. 7A) showed demonstrated behavior with little to no saturation for the majority of the gait cycle, though phase saturation occurred for P1 toward the end of the gait cycle. The measured thigh angle features for both participants at foot-strike (FIG.7B) and MHF (FIG.7E) closely matched the predicted feature angles from the geometry individualization. The thigh angles at MHE (FIG.7C) and TO (FIG.7D) were smaller than the predicted values and showed larger variability for both participants. FIG.8 illustrates intra-participant kinematic trajectories over stance and swing for the HKIC and PAS kinematics compared to the able-bodied reference. The kinematic trajectories at both the knee joint and ankle joint produced by the HKIC at steady-state resembled that of the inter-participant able-bodied kinematics at each step height tested. The PAS kinematics at the knee resembled the able- bodied reference in both shape and trend but reach levels of extension and flexion that are not observed in biological data. While this extreme knee ROM likely contributed to the larger amount of toe-clearance exhibited by the PAS device to prevent toe-stubs, a non-biomimetic thigh motion was required to achieve this. Throughout the gait cycle, the PAS ankle had a limited range of motion and was unable to provide biomimetic plantarflexion and dorsiflexion. TABLE III lists the kinematic ROM of the HKIC, PAS, and AB joints across step heights. At the nominal step height of 152 mm, the HKIC achieved average peak knee flexion angles of 94.13° for P1 and 93.58° for P2, allowing step clearance during swing without toe stubbing. While the PAS knee reached an excessive peak flexion angle of 122.39°, peak knee flexion for both participants with the HKIC were within one standard deviation of the AB peak of 96.31°±5.4°. At foot strike, the HKIC produced average knee angles of 69.42° and 69.21° for P1 and P2, compared to the PAS knee angle of 59.93° and AB knee angle of 68.86° ±4.33°. At the ankle joint, the HKIC achieved dorsiflexion angles of 24.04° and 26.87° during stance. In contrast, the PAS showed a reduced ankle dorsiflexion angle of 11.57°, compared to the AB dorsiflexion angle of 25.42°±4.01°. Ankle plantarflexion at the end of stance, which is important for achieving push-off, was -7.6° and -5.83° for the HKIC compared to the AB reference of -4.35°±7.12°. The PAS ankle was unable to plantarflex, remaining in a dorsiflexed configuration with a minimum ankle angle of 5.78°. TABLE III Step Metric Hei ht AB P1 HKIC P2 HKIC P2 PAS 8 7 9 1 0 9 7 2 2 0 9 FIGS. 9 and 10 illustrate the intra-participant average and individual trial joint kinetic trajectories for the 102 mm and 152 mm step heights, respectively, representing shallow and steep staircase configurations. The focus is on the stance period where the impedance controller torques determine the environmental interaction experienced by the user. The individual trials were included to showcase how the HKIC was able to accommodate changes in stride timing while providing joint torques that are similar in shape and magnitude to the AB reference. Pertinent features of the joint kinetics across all step heights are shown below in TABLE IV. TABLE IV MetricStep HeightAB P1 HKIC P2 HKIC8 6 7 4 6 8 At e sep eg o . , e ea ee e c ajectories of both participants resembled that of the AB references, achieving peak moments of -0.84 and -0.81 Nm / kg for P1 and P2. At the ankle, both participants match the AB reference in torque magnitude in early- to mid-stance but applied less torque during push-off (-1.03 and -0.72 Nm / kg for P1 and P2). At the step height of 152 mm (FIG.10), the mean HKIC knee torque trajectories of both participants were similar to that of the AB reference trajectory. The average peak knee torques for each participant were within a standard deviation of the AB average with peaks of -1.22 and -1.21 Nm / kg. Similar to the 102 mm step height, ankle torque for both participants matched that of the AB reference throughout the majority of stance but fell short at push-off. However, the push-off torque on the 152 mm configuration increased relative to the 102 mm configuration to help facilitate the larger stair rise with -0.96 Nm / kg for P2, while remaining consistent for P1 at approximately -1.02 Nm / kg. At both step height configurations, P2’s HKIC torque trajectories showed varying stance progression and peak torque timings, whereas P1’s results showed more consistent stance progression and peak torque timing across trials. The HKIC was able to provide the net-positive work necessary for stair ascent (see TABLE IV), producing biological trends similar to able-bodied data as step-height varied. The knee joint imitated biological work particularly well, producing an average of 0.61 J / kg and 0.58 J / kg at the knee for both participants at the 152 mm configuration, which is within one standard deviation of the AB reference value of 0.51±0.18 J / kg. Similarly, at 102 mm, the HKIC provided 0.33 and 0.32 J / kg at the knee, within a standard deviation of the AB reference of 0.34±0.14 J / kg. The ankle joint produced, on average, lower net-positive work than the AB reference for both participants, but P1’s ankle work was within a standard deviation of the AB reference for all step heights. Despite the lower average net-positive work, the ankle joint produced biological trends similar to the knee, increasing from 0.15 J / kg and 0.06 J / kg at 102 mm to 0.24 J / kg and 0.14 J / kg at 152 mm. Stair Descent Trials FIGS.11A-11E highlight phase and thigh feature prediction results over all stair descent trials. P1’s average phase variable exhibited monotonic behavior for the majority of the gait cycle but was saturated at the start and during the last tenth of the gait cycle. This saturation at the end of the stride is likely caused by the larger MHF angle reached by P1 in comparison to the predicted phase variable parameter, as shown in FIG.11E. P2 similarly showed phase saturation for the first ten percent of the gait cycle but then exhibited monotonic behavior for the majority of the stride. At foot strike (FIG. 11B) the predicted thigh angle parameter was within a standard deviation of P2’s foot strike angle. P1’s average MHE angle similarly matched the predicted thigh angle. At TO, there was a large discrepancy between P2’s predicted thigh angle and the experimental results, implying early TO from the participant. FIG.12 illustrates the intra-participant kinematic trajectories over stance and swing for the HKIC and PAS kinematics compared to the able-bodied reference data. Across the four step heights considered in this study, the stance kinematic trajectories produced by the HKIC at both the knee and ankle joints at steady-state resembles that of the inter-participant AB kinematics. While P2’s swing kinematics resembled the AB reference, P1’s swing kinematics followed AB trends but progressed rapidly at the beginning of swing and then remained almost constant for the latter half of swing. This behavior was likely a result of the phase saturation at this point in the gait cycle, shown in FIG.11A. Both participants exhibited knee kinematics with similar profiles to the AB reference data for the majority of stance. However, P1 had less knee flexion than expected at TO. The PAS kinematics at the knee resembled the AB reference. However, the PAS ankle had a limited range of motion and was unable to provide biomimetic plantarflexion and dorsiflexion. To compensate for the minimal ankle ROM, the participant placed their foot at the end of the stair tread, using the edge as a pivot point to achieve knee flexion. TABLE V lists the kinematic ROM of the HKIC, passive, and AB joints over multiple step heights. At the nominal 152 mm step height, the HKIC was able to achieve the necessary knee flexion during swing to avoid toe-stubbing with average peak knee flexion angles of 91.38°±3.00° for P1 and 88.40°±2.39° for P2. At FS, the HKIC reached knee extension angles of 20.38° and 17.06° for P1 and P2, within one standard deviation of the AB reference of 19.96°±6.40°. The HKIC ankle reached dorsiflexion angles of 30.75° and 36.63° during stance and plantarflexion angles of -10.08° and -7.48° at FS. TABLE V Step 4 9 9 1 102 18.44±5.13 15.63±1.84 15.88±0.81 11.48±0.39 127 19.19±5.63 17.19±2.6 15.87±3.00 11.57±0.49 4 3 4 5 7 3 2 2 1 1 4 5 3 3 7 4 6 3 ed higher kinematic errors at key points in the gait cycle compared to the HKIC. The PAS ankle similarly underperformed in comparison to both the HKIC and AB reference due to its limited ROM, forcing P2 to perform compensatory lunging and edge-of-step pivot behaviors that likely negatively impacted PAS knee performance. During stair descent, the HKIC ankle and knee joint kinetic profiles for both participants resembled that of the able-boded reference data. FIGS. 13 and 14 illustrate the intra-participant average and individual trial kinetic trajectories at both joints for the 102 mm and 152 mm step heights. Kinetic performance across all step height configurations is listed in TABLE VI. TABLE VI MetricStep Height(mm) AB P1 HKIC P2 HKIC5 7 6 4 4 3 8 8 5 3 3 6 At nee extension torques of -0.83±0.06 Nm / kg for P1 and -0.77±0.05 Nm / kg for P2. The HKIC also reached biomimetic peak torques (-0.76 and -0.81 Nm / kg) at the ankle for both participants. At the nominal step height of 152 mm, the peak torques were -1.05 and -0.94 Nm / kg at the knee and -0.84 and -1.06 Nm / kg at the ankle for P1 and P2. Across these step height configurations, peak joint torques for both participants were within a standard deviation of the able-bodied reference data and increased in magnitude with step height, following biological trends. During stair descent, the HKIC provided controlled negative work at both joints. The HKIC knee joint performed -0.56 and -0.33 J / kg at the nominal 152 mm step height and -0.34 and -0.15 J / kg at the 102 mm step height, which were less than AB. The HKIC results for P2 followed biological trends of increasing magnitude of work with increased step height. Looking at trends for P1, work increased with step height from 102 mm to 127 mm to 178 mm, but did not follow this trend at the 152 mm step height. Given that the 152 mm step height configuration was the first tested, this inconsistent behavior could be an indicator of insufficient acclimation. On the other hand, the HKIC ankle provided biomimetic negative work of -0.3 and -0.39 J / kg at 152 mm and -0.22 and -0.27 J / kg at 102 mm, which are within a standard deviation of the reference AB values of -0.44±0.15 J / kg and -0.26±0.13 J / kg. These results demonstrate increased work with increased step height, following biological trends. HKIC Performance The indirect-volitional HKIC was able to handle variations in stance progression and timing differences between different trials, step height configurations, and participants. The average phase progression during stair locomotion was monotonic throughout the majority of the gait cycle for ascent and descent (Figs. 4 & 7). This monotonic behavior, along with the similarity of many observed and estimated thigh features, points to the strength of the thigh feature estimation paradigm discussed above. P1 exhibited phase saturation over the last tenth of the stair descent stride. Normally, excessive saturation or pauses in phase cause desynchronization and can lead to trips, falls, or oscillations. However, to promote user confidence at FS, the phase variable definition was intentionally biased to saturate early so the prosthetic joints would arrive at their FS configuration early as in. During stair descent trials, P1 often waited at MHF for the feed-forward behavior of the phase variable to bring the knee to an extended position before proceeding with FS. P2 exhibited a similar waiting behavior at MHF but was more consistent in synchronizing the feed-forward phase completion with FS, resulting in little to no phase saturation. This could explain why an increased FS thigh angle was observed for P1 but not for P2. The small pause in P1’s phase variable is the likely cause of their abnormal swing kinematic progression during stair descent. While these kinematics may not exactly match the progression of the AB reference data when plotted over normalized swing time due to saturation or non-linearities in phase, this behavior showcases the indirect-volitional benefits of the disclosed control scheme by allowing user stride progression to dictate leg behavior, thereby synchronizing the user and prosthesis. The discrepancies in measured vs. predicted thigh features at TO may point to premature TO by the participants due to compensatory habits they have developed from using their passive devices. This early TO relative to the predicted angles resulted in limited torque being provided at the ankle at push-off and subsequently below-nominal ankle work during stair ascent, as well as less knee flexion exhibited by P2 during stair descent. Another possible explanation for this discrepancy is that the average AB data used to estimate thigh features does not fully represent the individual behavior of the participants. For both ascent and descent, the HKIC followed biological trends seen in able-bodied stair locomotion, producing knee extension and ankle plantarflexion torques during stance that increased with step height. In swing, both participants also achieved biomimetic levels of knee flexion with the HKIC that allowed for clearance of the following step without toe-stubbing or tripping. During stair ascent, the HKIC produced the necessary joint torques at the knee and net-positive work at both joints for multiple step height configurations, which follows biological trends of increasing joint work and peak torque with increasing step height. The HKIC also produced kinematics that resembled the AB reference data. The HKIC provided biomimetic plantarflexion angles in tandem with push-off torques at the ankle, which was unachievable with the PAS due to its limited ROM (Table SIII). During stair descent, the HKIC enabled biologically similar kinematics and kinetics at the ankle, producing peak plantarflexion torques within a standard deviation of the AB reference across step heights. At the nominal 152 mm step height, the HKIC provided biomimetic, controlled negative work at the ankle and allowed biomimetic levels of ankle plantarflexion at FS, exhibiting toe-strike behavior and energy dissipation. Across multiple step heights, the HKIC showed biological trends of increasing magnitude of ankle work with step height. The PAS was unable to provide the same level of ankle plantarflexion, resulting in a heel-strike behavior at the beginning of stance that does not allow for the same absorption of energy. Instead, the passive device forces users to compensate with their residual hip or contralateral limb. The HKIC also reached biological peak knee torques for both participants, which allowed for controlled negative work and support that characterize AB stair descent during mid-to-late stance. The torque provided at the knee in early stance was constrained due to hardware limitations and certain continuity requirements in the optimization. Despite this limitation, the peak knee torque and work provided by the HKIC generally followed biological trends of increasing torque and work magnitudes with increasing step heights. During the experimental sessions, both participants provided positive qualitative feedback. P1 voiced a preference for the ability of the HKIC to perform step-over stair ascent, an activity they are unable to perform with their PAS device. While P2 was already capable of a modified step-over ascent movement using their passive device, they voiced a preference for stair descent due to the support provided by the HKIC. Both participants found it helpful that the HKIC did not require them to perform the compensatory lunging behavior they are forced to use during passive device stair descent. It was noted that P1 acclimated quickly to stair ascent but struggled more with stair descent due to: 1) the tendency to perform their accustomed compensatory lunging behavior, and 2) a hesitancy to trust the device to support them as they neared terminal stance. Conversely, P2 acclimated quickly to stair descent but took more strides to acclimate to stair ascent. In particular, it took time for P2 to learn to avoid the compensatory hip whipping motion that they use to perform step-over stair ascent with their passive device. Unlike other proposed powered prosthesis control schemes, the hybrid stair-step controller disclosed above does not require hand tuning user-specific controller parameters—i.e., the control scheme is user-independent. One notable difference between the HKIC control approach and other powered prosthesis control schemes is that the HKIC extends to both stair ascent and descent, whereas prior heuristic approaches have been limited to just performing stair ascent. Various embodiments include a powered prosthesis comprising an artificial joint, an actuator, and a controller that continuously varies impedance at the joint via torque commands to the actuator during at least a portion of a user gait cycle during at least two of the following tasks: walking (other than on stairs), stair locomotion, and a sit-stand transition. The prosthesis may be a multi-mode prosthesis having a walking mode, a stair locomotion mode, and a sit-stand mode, where the controller is configured to transition from one control scheme to another when the prosthesis is changed from one mode to another. The mode change may be automated or user-selected. One example of an automated mode change is a change between walking mode and sit-stand mode as described in the Gregg et al. application noted above and related to the sit-stand impedance controller. A user-initiated mode change may involve use of a switch on the prosthesis or a remote control operated by the user or performance of a particular maneuver by the user that the controller recognizes as a request for a mode change. The controller may be a hybrid controller that continuously varies impedance at the joint during one portion of a user gait cycle and kinematically controls joint angle during a different portion of the gait cycle. Impedance control may be employed during stance phase while kinematic control is employed during swing phase across all of the listed tasks. The joint may be an ankle joint and / or a knee joint, and the powered prosthesis may be a lower leg prosthesis for use by an above- knee amputee. It is to be understood that the foregoing description is of one or more embodiments of the invention. The invention is not limited to the particular embodiment(s) disclosed herein, but rather is defined solely by the claims below. Furthermore, the statements contained in the foregoing description relate to the disclosed embodiment(s) and are not to be construed as limitations on the scope of the invention or on the definition of terms used in the claims, except where a term or phrase is expressly defined above. Various other embodiments and various changes and modifications to the disclosed embodiment(s) will become apparent to those skilled in the art. As used in this specification and claims, the terms “e.g.,” “for example,” “for instance,” “such as,” and “like,” and the verbs “comprising,” “having,” “including,” and their other verb forms, when used in conjunction with a listing of one or more components or other items, are each to be construed as open-ended, meaning that the listing is not to be considered as excluding other, additional components or items. Other terms are to be construed using their broadest reasonable meaning unless they are used in a context that requires a different interpretation.
Claims
CLAIMS 1. A powered prosthesis comprising a joint and a controller that continuously varies impedance at the joint during a stance phase of stair locomotion by a user.
2. The powered prosthesis of claim 1, wherein the stance phase is defined between a foot strike event and a toe-off event and the impedance at the joint is a continuous function of one or more impedance parameters, each impedance parameter being a continuous function of a phase variable representing the stance phase.
3. The powered prosthesis of claim 2, wherein each continuous impedance parameter function is optimized based at least in part on able-bodied data independent from the user.
4. The powered prosthesis of claim 2, wherein each impedance parameter is additionally a function of step height.
5. The powered prosthesis of claim 1, wherein the controller kinematically controls the joint during a swing phase of stair locomotion by the user.
6. The powered prosthesis of claim 1, wherein the controller estimates gait phase in real time during stair locomotion by the user based on a phase variable.
7. The powered prosthesis of claim 6, wherein the controller estimates gait phase during stair ascent and stair descent using the same phase variable.
8. The powered prosthesis of claim 7, wherein the phase variable is determined based at least in part on a joint angle of the user and time.
9. The powered prosthesis of claim 1, wherein the joint is a knee joint, the prosthesis further comprises an ankle joint, and the controller continuously varies impedance at both joints during the stance phase of stair locomotion by the user.