Abstract:
In an artificial limb system having an actuator coupled to a joint for applying a torque characteristic thereto, a control bandwidth of a motor controller for a motor included in the actuator can be increased by augmenting a current feedback loop in the motor controller with a feed forward of estimated back electromotive force (emf) voltage associated with, the motor. Alternatively, the current loop is eliminated and replaced with a voltage loop related to joint torque. The voltage loop may also be augmented with the feed forward of estimated back emf, to improve the robustness of the motor controller.

Description:
RELATED APPLICATIONS 
       [0001]    This application claims priority to and the benefit of U.S. Provisional Patent Application Ser. No. 61/554,921 filed on Nov. 2, 2011, the disclosure of which is hereby incorporated herein by reference in its entirety. The application also relates to U.S. Pat. No. 8,074,633, U.S. patent application Ser. Nos. 12/551,845, 12/552,013, 12/552,021, 12/552,028, 12/552,036, 12/872,425, 13/079,564, 13/079,571, 13/347,443, 13/349,216, 13/356,230, and 13/417,949, and U.S. Provisional Patent Application Nos. 61/554,921, 61,595,453, 61,658,568, 61/659,729, 61/662,104, 61/649,640, 61/659,723, 61/679,194, and 61/691,684, the disclosures of which are each hereby incorporated herein by reference in their entireties. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This invention relates generally to systems and methods for lower body locomotion, and more particularly to the control of prosthetic, orthotic, and exoskeleton devices usable at various points of the leg, including the ankle, knee, and hip. 
       BACKGROUND 
       [0003]    Over 120,000 people suffer lower-extremity amputations each year in the United States, of which transfemoral (above-knee) amputations account for over 40%. Over 30,000 people in this transfemoral population require a new prosthetic limb each year—typically a passive, microprocessor-controlled knee joint, employing hydraulic damping and a passive carbon-fiber ankle-foot prosthesis. Such passive leg systems tend not to be biomimetic; instead they ten to be passive-elastic during stance and can neither perform net non-conservative work to propel the amputee upward and forward nor deliver the temporal torque response supplied by an intact knee and ankle joint during the gait cycle, and hence fail to fully restore function when integrated onto the residual limb. Researchers have hypothesized that the inability of conventional passive-elastic ankle-foot prostheses to provide sufficient positive power at terminal stance to limit heel strike losses of the adjacent leg is a key mechanism for the increased metabolic rate of walking amputees. These limitations in both ankle-foot and knee designs contribute to the severity of clinical problems experienced by transfemoral amputees. 
         [0004]    Current leg prostheses ten not to provide the balance desired by the transfemoral community. Amputees often fall, especially while traversing rough or irregular terrain. This may be at lease partially due because most ankle-foot prostheses fail to actively control a zero-moment point (ZMP) at the foot-ground interface, a balancing strategy sometimes employed in the field of humanoid robotics. In addition to balance problems, amputees tend to tire easier and walk slower than non-amputees. For example, amputees can require 10-60% more metabolic energy to walk than intact persons. The actual differences for any individual at a particular time result from differences in walking speed, physical fitness level, cause of amputation, level of amputations, and prosthetic intervention characteristics. Amputees may walk at much slower (e.g., 11-40%) slower self-selected gait speeds than do person with intact limbs. 
         [0005]    Integration of non-biomimetic ankle-foot and microprocessor-controlled knee prostheses has confounded researchers. Although some improvements in gait have been observed with variable-damper knee designs, many problems still remain for transfemoral amputees. For example, a variable-damper knee combined with a passive-elastic ankle-foot prosthesis offers little to no improvement in gait metabolism and walking speed compared to a mechanically-passive transfemoral system. Although some powered knee systems have been developed, these tend not to be biomechanically-conceived, and can take hours to fit and tune to a specific wearer. These powered knees tend to have a noisy motor and transmission system. Other powered robotic leg systems often exhibit three fundamental limitations: inefficient actuator design, non-biomimetic actuator control software, and poorly executed terrain-adaption software. Without a biologically-conceived actuator, the motor must be made larger and heavier to deliver necessary joint powers. 
         [0006]    To deliver the increased power, high gear-ratio transmissions are normally employed in powered leg prosthetic and orthotic applications, driven by high RPM brushless motors that are operated at currents in excess of 10× the rated current. The result is often a noisy transmission that dissipates battery power excessively, heating the motor windings instead of applying power to the joint. As a result, batteries must be made larger than necessary, or else the range on a battery charge is compromised unnecessarily. Further, motor heating can be excessive when extended periods of walking (e.g., hundreds of steps consecutively) are applied. The useful range of the prosthesis may be constrained by the need to “fold back” power when the motor winding get too hot. Most robots are programmed explicitly in a position-controlled or playback mode. Biophysically-conceived robots employ mono-articular and biarticular bionic muscle-tendon units that modulate joint impedance, equilibrium, torque and positive-feedback reflex during a gait cycle. The behavior of these bionic systems can be encoded in a relatively few parameters, implicitly defined rather than explicitly defined. Indeed, only a few parameters need to be changed to emulate biological behavior. In contrast, the explicitly controlled systems often require that movement as defined by joint angle trajectories is tuned to match biological behavior to create a response for every special case, driven by speed, terrain modality and wearer athleticism/payload. Even the most experienced clinicians may be unable to set up such a system. While many current robotic leg prostheses employ inertial componentry to estimate terrain modality, these are usually configured to adapt to the new terrain modality after several steps, whereas an intact person adjusts to terrain modality within each step. Though certain implementations of such a control may rely on playing back a temporal response at a particular terrain state, the desired behavior can be virtually impossible to tune. 
         [0007]    It is therefore desirable to provide leg devices that provide a biomimetic response throughout a walking cycle. 
       SUMMARY OF THE INVENTION 
       [0008]    Lower-extremity augmentation may rely on a muscle-tendon architecture employing series-elasticity as a means of amplifying available joint power, reducing motor work, and improving shock tolerance. An intact ankle-foot for instance employs a series-elastic actuator in the form of the calf muscle (motor) driving through the Achilles tendon (series-elasticity). A model of an intact human ankle progressing through various phases of a gait cycle is depicted in  FIG. 1 . Elastic energy is stored in the tendon in the controlled dorsiflexion phase and released later, like a catapult, in powered plantar flexion to augment the power applied by the calf muscle. A series elastic actuator (SEA) as described herein can provide a biomimetic response, and may be capable of amplifying power by greater than a factor of two. 
         [0009]    A transfemoral prosthesis may include the SEA, motor technology, neuromuscular-inspired actuator control, and intrinsic inertial sensing to provide quiet and efficient biomimetic mechanical behaviors across distinct walking speeds and terrains and the transitions between these ground surfaces. The prosthesis can provide the amputee with an enhanced metabolic economy when using a powered, ankle-foot prosthesis compared to the metabolic cost when using a conventional passive-elastic prosthesis, including a normalization of self-selected walking speed and improvement in metabolic cost-of-transport across a broad walking speed range (0.75-1.75 m/sec) using sensing, control and muscle-tendon unit (MTU) actuators. 
         [0010]    The prosthesis may integrate an artificial MTU that employs a high-torque, transverse-flux motor that reduces, in some instances over an order of magnitude, the normalized motor copper loss, R/k f   2 , in relation to conventional, radial flux motor topologies employed in the many existing robotic augmentation devices. The use of a direct-drive, transverse flux motor in an MTU may result in a much lower drive transmission ration (e.g., six times lower than a typical 200:1 gear-ratio transmission of a typical motor), allowing for operation at lower motor RPM to provide a more quiet and efficient device. Another result may be a higher resonant frequency for the MTU, allowing for higher fidelity joint torque control. 
         [0011]    The device may also include neuromuscular-inspired control software to emulate the biological response of an intact limb, aiding in the normalization of metabolic walking economy and biomechanical response. Intrinsic inertial sensing can enable in-situ, real-time reconstruction of hip, knee and ankle trajectory throughout the gait cycle. Pattern recognition algorithms may be applied to these reconstructed trajectories for intra-step terrain discrimination and adaptation, thereby enabling seamless terrain transitions across walking speeds. 
         [0012]    A wearer of the biomimetic prosthesis may experience and improved walking speed, metabolic economy, gait symmetry, and gain stability across level, sloped, and stair ground surfaces when compared to conventional prostheses. This restored function by objective metabolic and biomechanical measures can provide profound improvements in the quality of life of a wearer. While the device is often described with respect to a prosthetic for an amputee population, the robotic augmentation platform described here may be useful to researchers and educators focused on humanoid robots. Open interfaces may be provided to configure, refine, and deploy new applications. 
         [0013]    According to one aspect, the invention relates to a method for controlling a motorized, artificial limb having an actuator. The actuator includes a motor coupled in series with an elastic element to apply a torque characteristic to a joint. The method includes applying a voltage to windings of the motor, measuring the torque characteristic at the joint, computing a torque characteristic error as a difference between a target torque characteristic and the measured torque characteristic, and controlling the applied voltage independently of motor current to reduce the torque characteristic error. 
         [0014]    In some embodiments, the torque characteristic is a joint torque, a joint impedance, or a joint equilibrium. The applied voltage may be controlled solely based on the target torque characteristic and the torque-characteristic error. In certain embodiments, the controlling step avoids computation of motor current and/or computation of an adjustment to the motor current supplied to the motor to achieve the target torque characteristic, and may avoid measurement of motor current and using the measured current for adjusting the motor current (at least in part). 
         [0015]    In other embodiments, the limb control method is independent of a resonance frequency associated with the coupling of the motor and the elastic element. The step of measuring the torque characteristic at the joint may include measuring an angular position of the motor and/or an angular position of the joint. The method may also include measuring motor speed, estimating voltage corresponding to back electromotive force related to the motor speed, and controlling the applied voltage based on, at least in part, the estimated voltage corresponding to the back electromotive force. In certain embodiments, the artificial limb is a prosthetic limb and/or an orthotic limb. The joint may be an ankle joint or a knee joint. 
         [0016]    In another aspect, the invention relates to an artificial limb system. The system includes an actuator coupled to a joint for applying a torque characteristic thereto, the actuator having a motor coupled in series with an elastic element. The system also includes a power source for applying a voltage to winding of the motor, at least one sensor for estimating the torque characteristic at the joint, and a controller for: (i) computing a torque characteristic error as a difference between a target torque characteristic and the torque characteristic measured by the sensor, and (ii) controlling the applied voltage independently of motor current, to reduce the torque characteristic error. 
         [0017]    In some embodiments, the torque characteristic comprises a joint torque, a joint impedance, and/or a joint equilibrium. The controller may be adapted for controlling the applied voltage solely based on the target torque characteristic and the torque-characteristic error. In other embodiments, the controller is adapted for controlling the applied voltage without using a computation of motor current and/or an adjustment to the motor current supplied to the motor to achieve the target torque characteristic. The controller may be adapted to avoid at least partially using a measurement of motor current for an adjustment thereof. The controller may be adapted such that a controller response is independent of a resonance frequency associated with the coupling of the motor and the elastic element. 
         [0018]    In certain embodiments, the artificial limb system is a prosthetic limb system and/or an orthotic limb system. The joint may be an ankle joint or a knee joint. The sensor may be a joint encoder, a torque sensor, a deflection sensor disposed on the series elastic element, a joint angle sensor, or a motor angle sensor. In some embodiments the system includes a motor encoder for measuring motor speed with the controller adapted to: (i) estimate voltage corresponding to back electromotive force related to the motor speed, and (ii) control the applied voltage based on, at least in part, the estimated voltage corresponding to the back electromotive force. The system may include an observer to estimate voltage corresponding to back electromotive force with the controller adapted to control the applied voltage based on, at least in part, the estimated voltage corresponding to the back electromotive force. The system may include a linkage having a plurality of links where the linkage is coupled to the joint, the motor is coupled to a first link in the linkage, and the elastic element is coupled to a second link in the linkage. 
         [0019]    In yet another aspect, the invention relates to a method for controlling a motorized, artificial limb. The artificial limb has an actuator with a motor coupled in series with an elastic element to apply a torque characteristic to a joint. The method includes computing target motor current required to achieve substantially a target torque characteristic at the joint, measuring motor current and motor speed, and computing a current error as a difference between the target motor current and the measured motor current. The method also includes estimating voltage corresponding to back electromotive force related to the motor speed and controlling voltage applied to motor winding based on, at least in part, (i) the estimated voltage corresponding to the back electromotive force, and (ii) the current error, to reduce the current error. 
         [0020]    In certain embodiments, the torque characteristic is a joint torque, a joint impedance, and/or a joint equilibrium. The artificial limb may be a prosthetic limb and/or an orthotic limb. The joint may be an ankle joint, a knee joint, and a hip joint. 
         [0021]    In still another aspect, the invention relates to an artificial limb system. The system includes an actuator with a motor coupled in series with an elastic element coupled to a joint for applying a torque characteristic a power source for applying a voltage to windings of the motor, a current sensor for measuring motor current, and a motor encoder for measuring motor speed. The system also includes a controller for computing a current error as a different between a target current and the measured motor current, estimating voltage corresponding to back electromotive force related to the measured motor speed, and controlling voltage applied to motor winding based on, at least in part, (i) the estimated voltage corresponding to the back electromotive force, and (ii) the current error, to reduce the current error. 
         [0022]    In some embodiments, the artificial limb system is a prosthetic limb system and/or an orthotic limb system. The joint may be an ankle joint, a knee joint, or a hip joint. The controller may be adapted to determine the target motor current to achieve the target joint torque characteristic. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0023]    Other features and advantages of the present invention, as well as the invention itself, can be more fully understood from the following description of the various embodiments, when read together with the accompanying drawings, in which: 
           [0024]      FIG. 1  is a diagram of a healthy ankle throughout the phases of a walking cycle; 
           [0025]      FIG. 2  is a schematic perspective view of an ankle device, in accordance with one embodiment of the invention; 
           [0026]      FIG. 3  is a graph depicting the power output of the ankle device, in accordance with one embodiment of the invention; 
           [0027]      FIG. 4A  is a schematic cross-section view of a knee device, in accordance with one embodiment of the invention; 
           [0028]      FIG. 4B  is a schematic diagram of the knee device of  FIG. 4A ; 
           [0029]      FIG. 4C  is a schematic side view of the knee device of  FIG. 4A ; 
           [0030]      FIG. 5  is a schematic side view of a leg device, in accordance with one embodiment of the invention; 
           [0031]      FIGS. 6A and 6B  are schematic cross-section and rear perspective views, respectively, of a leg device in accordance with another embodiment of the invention; 
           [0032]      FIGS. 7A and 7B  are graphs of joint trajectories for an ankle and knee, respectively, in various modalities; 
           [0033]      FIG. 8  is a block diagram of a control system for a leg device, in accordance with one embodiment of the invention; 
           [0034]      FIG. 9  is a block diagram of signals associated with a motor and joint system, in accordance with one embodiment of the invention; 
           [0035]      FIG. 10  is a block diagram of a current feedback loop, in accordance with one embodiment of the invention; 
           [0036]      FIG. 11  is a block diagram of a system for directly controlling joint torque, in accordance with one embodiment of the invention; 
           [0037]      FIG. 12  is a block diagram of an emf feedforward with current feedback loop, in accordance with one embodiment of the invention; 
           [0038]      FIG. 13  is a block diagram of an emf feedforward with joint torque feedback loop, in accordance with one embodiment of the invention; 
           [0039]      FIG. 14  is a block diagram of a model for using motor current to compute a feedback signal to manipulate voltage to control motor torque, in accordance with one embodiment of the invention; 
           [0040]      FIG. 15  is a block diagram of a model for using motor current to compute a feedback signal to manipulate voltage to control motor torque without an inner current-feedback loop, in accordance with one embodiment of the invention; 
           [0041]      FIG. 16  is a block diagram of a model with emf feedforward, in accordance with one embodiment of the invention; 
           [0042]      FIG. 17  is a block diagram of a model for using a measurement of joint torque through a single compensator to compute a voltage signal, in accordance with one embodiment of the invention; and 
           [0043]      FIG. 18  is a block diagram of a model for using a measurement of joint torque through two compensators to compute a voltage signal, in accordance with one embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0044]    Devices for transfemoral amputees typically include at least a foot-ankle device and a knee device. The foot-ankle and knee devices described herein may be used together or separately, particularly only a foot-ankle device for below-knee amputees. While the embodiments described relate to prostheses, the concepts contained herein may also be useful in other applications, including orthoses and exoskeletons. 
         [0045]    One ankle device  200  capable of restoring ankle function as defined by objective metabolic and biomechanical measures is depicted in  FIG. 2 . The ankle device  200  is capable of varying ankle impedance during the early to mid-stance periods of walking, emulating the quasi-static stiffness of an intact biological ankle. In addition, the prosthesis  200  provides a sufficiently large instantaneous power output and torque to propel an amputee upward and forward during powered plantar flexion, while still matching the size and weight of an intact ankle-foot complex, e.g., approximately 2.4% of body weight. The ankle device  200  may be a variety of weights for different applications. For example, a device  200  weighing approximately 4.8 lbs is appropriate for wearers weighing approximately 190-250 lbs. 
         [0046]    The ankle device  200  may include several different technologies, including a series-elastic actuator (SEA)  202 , integral joint torque sensor  204 , six degree-of-freedom inertial measurement unit (IMU)  206 , battery  208 , and a controller with control firmware  210  (intrinsic within the system). The SEA  202  is capable of modulating torque, impedance and position in accordance with the gait cycle state. Such may be nuanced as a function of sensed walking speed and terrain modality. Through use of the intrinsic control firmware  210 , the SEA  202  may emulate the calf muscle/Achilles tendon reflex during late stance to achieve biomimetic operation. The SEA  202  design may be optimized to amplify peak joint mechanical output power, e.g., 2× +  amplification during fast walking, as illustrated in  FIG. 3 . The SEA  202  may have a high-RPM brushless motor  212 , a hybrid belt/ball-screw transmission  214 , and a carbon-fiber spring  216 . The transmission  214  can have an L1 design life of greater than 5 million cycles, and the SEA  202  may operate at an overall motor-joint gear ratio of about 220:1. 
         [0047]    The joint torque sensor  204  may be used to precisely sense joint angle and SEA motor  212  position. The joint torque may be computed in real-time using factory calibrated models of ankle shell and carbon-fiber spring deflection, even without strain measurement devices. The IMU  206  may measure angular rate and acceleration in each of three orthogonally-opposed directions. These measures may be used selectively to detect gait cycle state transitions and instantaneous walking speed. The batter  208  is used to power the device, and may be modular to aid in insertion and removal. This is particularly helpful when the battery  208  is replaced multiple times in a day, e.g., two or three times. Many different types of batteries  208  may be used, including a lithium polymer battery. 
         [0048]    The control firmware  210  may rely on a state machine for transitioning between various control schemes based on the phase of gait. Sensors may be used to sense the transitions while walking. For example, the firmware  210  can use intrinsic sensing to track gait cycle transitions—enabling appropriate modulation of torque (including SEA reflex), impedance and position. The device  200  may employ non-linear, positive torque feedback to simulate muscle response. This can provide a wearer with a natural (biomimetic) feel. Other models, e.g., a neuromuscular muscle model, may be used. 
         [0049]    These component technologies may be used separately or in conjunction with each other, with several possible alterations for each. For example, the SEA  202  may have a transverse-flux motor  212  that eliminates the belt transmission  214 , instead relying on a direct-drive ball-screw implementation that can reduce the gear ratio (e.g., by a factor of six). Power consumption may be reduced (in some cases by more than 50%), and acoustic noise in the 1.5-3 kHz band may be reduce by up to, and sometimes greater than, 80%. 
         [0050]    Powered prosthetic knees may use a variety of different components in different arrangements. In one embodiment, a prosthetic knee  400  depicted in  FIGS. 4A-4C  provides a biomimetic response through the use of an agonist-antagonist actuator (AAA) system  402 . The AAA-based knee prosthesis  400  may emulate the synergistic muscle activity of an intact limb by using a dual-SEA system  402  that resembles the major mono-articular muscle groups that flex and extend the human knee joint. Each SEA  404  includes a torque source  406  (e.g., a motor), an elastic element  408  (e.g., a spring) in series with the torque source  406 , and a transmission  410  (e.g., a ballscrew and ballnut drive). In some embodiments, the SEA  404 , along with additional torque sensing, inertial sensing, and intrinsic control, may be the same or similar to those used in the ankle device  200 , adapted for use in the knee  400  when necessary. A floating point  412  may be coupled to an upper leg attachment for the knee  400 . 
         [0051]    The mechanical architecture of the AAA knee  400  allows for independent engagement of flexion and extension tendon-like, series springs  408  for modulating joint impedance and non-conservative motive power during the stance period, and joint position when the prosthetic foot is off the ground. Furthermore, this architecture may permit joint rotation with near zero friction via disengagement of both SEAs  404 , allowing a controller  414  (that may be intrinsic to the system) to take advantage of the passive (ballistic) dynamics of the system  402  in the swing phase, and thus, augment the overall energetic economy of the prosthesis  400  and human wearer. By matching the stiffness of the two series springs  408  to match the biomechanical extension and flexion stiffness, modulation of the stiffness can be accomplished with approximately zero-electrical power by simply shorting the motor windings (to apply a high-degree of damping and holding torque) of the appropriate motor  406 . The clutching feature can be utilized to great advantage in a transverse-flux motor implementation due to the transverse-flux motors&#39; superior brake/clutch performance resulting from its low motor resistance, R m , in relation to the motor torque constant, R m /k t   2 , which defines the motor damping with shorted leads. Certain embodiments of the knee prosthesis  400  may have a single motor with bilateral spring elements that can be always fully engaged as in a traditional SEA, or can be configured to have a “dead zone” in which neither spring is engaged, enabling agonist-antagonist “clutch” implementations. A leg prosthesis  500  including the ankle device  200  and a knee device  502  (similar to the knee device  400 ) coupled together is depicted in  FIG. 5 . 
         [0052]    Another embodiment of a leg prosthesis  600  is depicted in  FIGS. 6A and 6B . The substantially fully-powered transfemoral prosthesis  600  may have a transverse flux, series-elastic ankle  602  and knee  604  to produce biological ankle and knee mechanics for steady-state level-ground walking with a prosthetic mass, shape and acoustic noise output comparable to a biological leg. For example, the prosthesis may have a mass &lt;5% body weight, a shape smaller than a 50% person, and an acoustic output of &lt;45 dB one meter from the prosthesis. Such a transfemoral prosthesis  600  may normalize metabolic economy and self-selected walking speed during ground surface ambulation in a variety of contexts, including during level-ground, sloped (e.g., up to ±10 degrees and beyond), stair ascent, stair descent, and transitions therebetween. The prosthesis  600  may be able to adapt ankle and knee mechanics within a single walking cycle to enable a transfemoral amputee to walk across these ground surface variations in a manner that emulates biological leg biomechanics. 
         [0053]    The ankle device  602  may be substantially similar to the ankle device  200 , with a transverse flux motor  606  used instead of a belt transmission. Using biomimetic, muscle-tendon-like actuators (e.g., SEAs) that employ such high-torque transverse flux motors  606  can help reduce power consumption and acoustic noise levels by significant amounts (e.g., over 50% and 80% respectively) when compared to conventional (radial flux) motor transmissions to achieve cool, quiet operation across substantially all walking speeds. High-torque transverse flux motors  606  may be available from Electric Torque Machines (Flagstaff, Ariz.). Another benefit of transverse-flux motor technology is the reduction of motor copper loss per square unit of torque production (R/k t   2 ), which may be over a factor of nearly  300  at the same gear ratio as would be employed by conventional high-RPM radial flux motors like the EC30 PowerMax motor (www.maxon.com) used in most lower-extremity augmentation systems built by the research community. This attenuation in loss can be used to reduce bath transmission gear ratio (and hence motor rotational speed) and motor temperature rise. The result is quiet and efficient operation that extends range on a battery charge and reduces or eliminates heating-related range limitations. Actuator design life may be extended because friction and travel are reduced in concert with gear ratio reduction. 
         [0054]    The knee device (or muscle tendon unit; “MTU”)  604  may employ a “buckled-beam” SEA design with a gear ratio, in this embodiment approximately 30:1. The buckled beam can be light-weight and yet store up to 30 J/kg (or more) of energy, enough suitable for running and jumping. In some embodiments, the buckled-beam SEA may have a stiffness of approximately 4 Nm/rad/kg and energy storage of approximately 8 J/kg for level ground walking. The buckled-beam SEA may also use the transverse flux motor  606  as a dynamic brake (e.g., a clutch) in early stance flexion to reduce battery energy consumption and acoustic emissions. 
         [0055]    The prosthesis  600  may have multiple MTU&#39;s (e.g., the ankle device  602  and the knee device  604 ), each with embedded SEA power electronics and servo controller(s) integrated onto the motor, networked to a State Controller/IMU assembly adapted to control and coordinate the individual MTU&#39;s in accordance with the gait cycle and terrain modality. Connectivity among the remote components may be accomplished through the use of wireless technologies, such as Bluetooth® and smart WiFi (sWiFi) control modules. A BlueTooth® port can enable remote programming by Android-based cell phone/PDA to facilitate clinical tuning and evaluation. The sWiFi may be used to promote 500 Hz logging of up to 50 floating point-state variables, enabling a modification of up to 200 (and greater) control and signal processing parameters while the biomimetic prosthesis is in use. 
         [0056]    The MTUs  602 ,  604  may be designed around biomechanical torque-displacement trajectories to ensure the MTUs  602 ,  604  can provide a biomimetic response. Through the design process, certain targets may be set, such as battery and motor power electronic requirements. In one instance, the components may be designed to work across walking speeds for a typical wearer weighing 250 lbs. Other design input parameters include motor diameter and winding characteristics; series elasticity stiffness; ball-screw transmission ratio; battery and power supply topology and switching frequency. The result is a multi-variable design output space that includes walking range; acoustic energy (torque ripple harmonics) in the 1.5 kHz-3 kHz audio band; design life and prosthesis weight. 
         [0057]    A robust design is suitable for a broad range of wearer weights, including from approximately 185 lbs. to approximately 250 lbs., as may be common amongst soldiers expected to use the device  600 . However, the device  600  is usable by wearers outside of this range. The battery may be capable of powering at least 2000 steps for a 185 lb. wearer. The device  600  may be designed to output a peak torque from the muscle tendon units  602 ,  604  of at least approximately 150 N-m, and may output a peak power of at least approximately 800 watts. The ankle  602  may have a range of rotation of at least approximately 25° and the knee  604  may have a range of rotation of at least 130°. 
         [0058]    The devices  200 ,  400 ,  600  described above may rely on processing of the IMU state to detect gait cycle state transitions and to determine intra-step estimates of walking speed, allowing for intrinsic control of reflex strength in accordance with walking speed. Further, intrinsic measures of torque can detect the difference between heel-strike first and toe-strike first gait cycles, sufficient to nuance the control for stair ascent (toe-strike first) in relation to normal walking on sloping ground (heel-strike first). Separate or complementary controls may be used to control biomimetic leg systems (ankle-foot and/or knee) for stair ascent/descent and steep sloping terrain modalities. In full leg systems, the knee prosthesis may be controlled to define the trajectory of the ankle-foot in multi-terrain environments. IMU-based kinematic reconstruction algorithms may use the IMU to determine the six degree-of-freedom (6 DOF) inertial state; the homogeneous transformation that defines the orientation and origin of a coordinate system with respect to ground of the lower extremity link that connects the ankle and knee joint. Self-calibrating algorithms, which may be considered a “zero-velocity update” (ZVUP) that occurs at a “zero moment point” (ZMP), can compute the inertial state within a gait cycle without a priori information averaged from prior steps. By combining the inertial state with ankle and knee joint encoder feedback and knowledge of wearer shoe size and the kinematic transforms between ankle, knee and hip, the trajectory of the toe, heel, ankle, knee and hip can be computed in real-time. 
         [0059]      FIG. 7A  illustrates offline-kinematic reconstructions of ankle and knee trajectory using the IMU and intrinsic sensing from the ankle device, superimposed on stair and sloping ground terrain modalities. In this manner, high-quality inertial state information can be used to discriminate between different terrain modalities in real-time. As shown in  FIG. 7B , irregular knee paths may be used to anticipate foot-strike in a wide range of terrain modalities. As shown, the folding back of knee path is a precursor to foot strike. Knowing when foot-strike is reached, ankle-foot trajectory can be used to sense the stair parameters or terrain slope and the “momentum” of the impending strike, from which appropriate pre-strike joint mechanical impedance, equilibrium and reflex characteristics can be nuanced. 
         [0060]    Trial data from the walking tests may be treated as known “test vector” inputs to the kinematic reconstruction and pattern recognition algorithms. Terrain modality discrimination to disambiguate between level ground, sloped and stair terrain modalities, both in the swing phase and the stance phase, may also be tested and validated statistically. Other reference biomechanical inputs in addition to those described above may be used to design ankle and knee reflex response characteristics. Preferred muscle models may be identified using goodness of fit and efficiency as a function of terrain slope and walking speed (e.g., for slopes of +10, +5, 0, −5, and −10 degrees for walking speeds of 0.75, 1.0, 1.25, 1.5 and 1.75 m/s). Similar techniques may be used in defining the neuromuscular model as a function of polarity (stair ascent vs. descent), stair characteristics, and stair ascent/descent rates. 
         [0061]    A functional test stand may be used as a bench platform for life-testing actuators and for engineering/manufacturing calibration of SEA torque-displacement models. The test stand may employ a backdrive mechanism mounted on a precision, 6 DOF, force/torque sensor to apply torque or position input/stimulus to the prosthesis joint under test. While the ankle test configuration is described for reference purposes, similar configurations may be used for other components. One configuration may be used to verify the MTU and neuromuscular control response characteristics, including, but not limited to, joint (or motor) torque, displacement/velocity, work impedance, power, design-life and battery energy per cycle. In the tests of biomechanical capability, the backdrive mechanism will “play back” a joint displacement trajectory, θ(t), that emulates the trajectory in an intact ankle. The MTU under test may deliver a joint torque, Γ(t), or motor torque, τ(t), as appropriate in synchrony with the displacement trajectory. This way, a repetitive test can be applied corresponding to theoretical or actual gait cycles to validate MTU/Neuromuscular performance. Some testing embodiments may include an in-line, robotic calibration and verification of the IMU using a robotic work cell. For example, a Staubli (Pfäffikon, Switzerland) RX90 robot may be used to supply a calibrated motion input from which the calibration and validation can be accomplished. The kinematic reconstruction verification may use this method to verify trajectory computations, including ZVUP. 
         [0062]    Certain kinematic reconstruction validation may be accomplished by comparing results, off-line, in relation to the joint trajectories computed using stereo photogrammetric methods. Raw IMU data may be recorded simultaneously with the stereo photogrammetric acquisition during biomechanical testing. On an off-line basis, the kinematic reconstruction results may be validated with the stereo photogrammetric (gold standard) used as the reference. Terrain discrimination algorithms to be deployed may also be tested against this reference data. 
         [0063]    The MTU joint torque and displacement may be calibrated individually on the functional test stand, using an adaptor built for holding the prosthesis to permit this isolated testing and calibration. Once calibrated, the torque-displacement predictions may be compared to the backdrive stimulus reference using special stimulus trajectories designed for the purpose, thereby accomplishing sensing, calibration and algorithmic verification of the MTU torque/displacement models. 
         [0064]    In a manner consistent with the kinematic reconstruction validation above, MTU torque and displacement may be recorded during clinical evaluation. The biomechanical computations arising from the joint torque-displacement predictions from the stereo photogrammetric and force plate data can be used as a reference with which to validate the MTU torque-displacement predictions on an off-line basis. Once validated, in situ measurements of torque-displacement and mechanical work can be used to validate the tuning of the neuromuscular-derived MTU control parameter vectors and to compare, in the form of a dashboard, the measurements to predefined reference measures of joint displacement, work and power across walking speeds derived from an inverse dynamics calculation on human kinetic and kinematic walking data. Once validated, in situ measures of electro-mechanical efficiency may be collected in real-time, gait-cycle-by-gait-cycle. 
         [0065]    Sound level comparisons between the radial-flux-based and the transverse-flux-based prostheses can be made in an area with an ambient noise level of &lt;40 dB. A microphone (MIC) can be placed in a number of locations relative to the test object including: 
         [0066]    Close Proximity: MIC attached to ankle via mounting bracket such that separation distance &lt;6″. 
         [0067]    Prosthesis Wearer Perception: MIC attached to user&#39;s head/upper-torso to accurately capture perception of user. 
         [0068]    Observer Perception: MIC placed in fixed location at a 1 m distance from the wearer to accurately capture perception of observer. This step may be used to account for system specific sound projection characteristics and the frequency dependent nature of sound propagation. 
         [0069]    Preprocessing can include application of an A-frequency-weighting filter to the raw sound level measurements (per IEC 61672). The acoustic comparison may be made within the 1.5-3 kHz frequency range according to the mean/maximum sound pressure level for each step event and an equivalent continuous sound Level. 
         [0070]    The biomimetic transfemoral system  600  may also be tested in its ability to reduce the metabolic economy to walk compared to an intact limb population. The metabolic rate may be calculated from measures of oxygen consumption and carbon dioxide production while amputees and age, weight and height-matched non-amputees walk on level ground and sloped (±10 degrees) surfaces. Measures of oxygen uptake and carbon dioxide production may be obtained using a portable, lightweight, breath-by-breath telemetric system (e.g., the Cosmed K4b2 (Rome; Italy)). Study participants walk around an indoor track next to an electric vehicle programmed to move at their self-selected speed when using the biomimetic prosthesis, collecting data for a minimum of 8 minutes. The final three-minute section of the recordings may be selected after steady-state conditions have been reached. The metabolic and walking speed data confirm when a transfemoral prosthesis is capable of biological ankle and knee mechanics to normalize metabolic economy and self-selected walking speed during level-ground and sloped (±10 degrees) ground surface ambulation. 
         [0071]    To assist in measuring human and prosthetic knee and ankle mechanics, reflective markers may be positioned on the body and data may be recorded using a stereo-photogrammetric system. At each gait speed, researchers measure whole body kinematics and kinetics from the right and left sides of the body, e.g., during ten trials per subject and condition. Reflective markers may be applied to the skin, including on the following bony landmarks: bilateral anterior superior iliac spines, posterior superior iliac spines, lateral femoral condyles, lateral malleoli, forefeet and heels. Additional markers may be rigidly attached to wands over the mid-femur and mid-shaft of the tibia. For transfemoral amputees, the tibia, lateral malleoli, forefeet and heel markers may be placed on the prosthesis at appropriate locations matching the intact limb. 3D pelvic and bilateral lower extremity joint kinematics may be collected by means of an eight-camera motion analysis system, sampling at 120 frames per second. 3D whole body kinetics may be collected by means of force plates (AMTI) sampling at 1080 Hz. The following anthropometric measures may be collected, along with motion analysis and force platform measures, to calculate joint kinematics and kinetics: body weight, height, leg length (measured from medial malleolus to anterior superior iliac spine), knee width, and ankle width. 
         [0072]    Joint torque and power calculations may be based on the mass and inertial characteristics of each lower-extremity segment, the derived linear and angular velocities and accelerations of each lower extremity segment, and ground reaction force and joint center position estimates. For each trial, bilateral hip, knee, and ankle joint kinematic and kinetic data during walking may be derived. Position data recorded using the motion capture system may be computed in three planes (sagittal, coronal, and transverse) using standard software provided with the system. Ground reaction forces may be measured synchronously with the kinematic data using two embedded force platforms (AMTI). Joint kinetics in each plane may be calculated using a full-inverse dynamics model. For the transfemoral ambulation trials, the human model can be modified to accurately represent the mass distribution of the prosthesis. To evaluate the accuracy of the full-inverse dynamics model, the intrinsic sensory measurements of prosthetic knee and ankle torque and power will be compared to the torque and power calculated from the inverse dynamics model. At each gait speed and test participant, average curves for each subject&#39;s knee and ankle position, velocity, torque and power may be obtained from the collected trials. Human knee and ankle mechanics from the individuals with intact limbs may then be compared to prosthetic knee and ankle mechanics at equivalent gait speeds. 
         [0073]    The use of neuromuscular-inspired MTU control software may emulate the biological response of an intact limb, thereby normalizing metabolic walking economy and biomechanical response, as depicted in  FIG. 8 . The implicit control architecture may be complementary or separate from the control architecture previously described, including the use of non-linear positive force feedback to achieve a reflex behavior. To create the more complex reflex dynamics in a multi-axis leg prosthesis, the control structure may be more generalized and aligned to real muscle activation models. A metasensor that measures the ground reaction force and ZMP may be created by combining the force-torque and the IMU-based kinematic reconstruction. 
         [0074]    Intrinsic inertial sensing, signal processing and pattern recognition may be used to achieve intra-step terrain adaptation—thereby enabling seamless terrain modality transitions. The kinematic reconstruction described above may be applied to the multi-dimensional leg system  600 . Pattern recognition of both ankle and knee trajectories may be used to discriminate between steep slope and stair ambulation. 
         [0075]    Closed-loop torque control algorithms may be designed using the calibrated, SEA, torque-displacement models as the primary feedback. The first SEA resonant frequency may fall in the range of 45-50 Hz, enabling a feed forward-enabled closed loop bandwidth of 25 Hz—sufficient to make the MTU response substantially invariant with transmission friction variation. Other feedback systems are described in detail below. Motor torque cogging compensation firmware can also be designed. Various neuromuscular models may be embedded in the MTU to test torque-reflex and impedance response characteristics across walking speeds (e.g., at 0.75, 1.0, 1.25, 15, and 1.75 m/s). 
         [0076]    Known prosthetic and/or orthotic devices typically employ a current-feedback system to control the operation of the motor in an SEA. Generally, in such a system voltage applied to the motor is manipulated so as to produce a desired results, e.g., to deliver the required motor torque. In order to guide the voltage manipulation the known systems only use the motor current in a feedback control system.  FIG. 9 , however, depicts other signals in addition to motor voltage and current that may also be associated with a feedback system for the device. These signals include motor torque, joint torque, and motor speed. In various embodiments described below one or more of these other signals are used instead of or in addition to motor current to control the motor voltage so to produce a desired torque characteristic, e.g., a joint torque, impedance, and/or equilibrium. Various combinations of the signals may or may not be available for measurement over a period of time. High fidelity joint torque control may be difficult in SEAs, particularly those where the series-elastic element is used as a catapult to amplify motor power at the joint. In these SEAs, the spring stiffness is relatively low (e.g., 350 Nm/rad in an ankle joint). In such a case, the first SEA resonance, which arises from the reflected motor inertia reacting with the series-spring, can be as low as 8 Hz. In conventional joint torque controllers, the bandwidth may be limited to a frequency less than this first resonance, resulting in an often underdamped response that cannot emulate biological muscle-tendon units. 
         [0077]      FIG. 10  depicts one such system that controls motor current as a surrogate for joint torque, creating a command current signal, and applying feedback compensation that drives motor voltage so as to make the motor torque track the command. In this open-loop joint torque control, motor cogging, motor ripple, SEA transmission friction, backlash, and other non-linear dynamics will influence the degree to which the joint torque can track the commanded value. An outer joint torque compensator may be applied to address this issue. One known system uses joint torque in addition to motor current to compute motor voltage. However, the manipulation of the command current signal in such a system often makes the control system very hard to control or even unstable as shown in the sequel, due to resonance characteristic of the associated physical device, allowing only a limited joint torque bandwidth for controller operation in this configuration. These problems often exist when the inner current loop is closed and joint torque error due to the SEA resonance dynamics is not eliminated by the addition of an outer joint torque loop. As described with reference to  FIG. 12 , the instability and/or bandwidth control problems may be overcome by measuring motor speed and using this variable in an EMF feedforward compensator. 
         [0078]      FIG. 11  depicts a system where joint torque is measured and the corresponding signal used instead of the measured current to compute a voltage that produces desired results. In addition to fewer limitations on the bandwidth of the compensator, this configuration more easily enables the joint torque to follow a joint torque command signal that produces desired results, in contrast with the current command signal described above. The joint torque is the most naturally commanded signal, while a current signal tends only to be related to usual performance objective through complicated interactions with other variables. 
         [0079]      FIGS. 12 and 13  illustrate configurations where voltage is computed using two components: a component that is a scaled measurement of a measurement of the motor speed and a feedback component. Feeding back a scaled measurement of the motor speed is called EMF feedforward, as the signal can provide an estimate of the electromotive force produced within the motor while canceling the effect of this force. Measuring motor speed is one way of producing this estimate of the EMF, though other methods for producing the estimate that are known to those of skill in the art are considered within the scope of this disclosure. These other methods could include the use of Kalman-filter based observer to estimate the EMF from motor winding voltage and phase current. 
         [0080]    When using the EMF estimate, the resulting system may become easier to control, such as by enabling the use of other signals in conjunction with the EMF estimate to produce desired results.  FIG. 12  depicts a current feedback loop in conjunction with the EMF feedforward. The EMF feedforward allows an improved performance in the current feedback loop.  FIG. 13  depicts a joint torque feedback loop as in in conjunction with the EMF feedforward. The use of other feedback in conjunction with the EMF feedforward, or using the EMF feedforward alone, is also contemplated. 
         [0081]    A representative dynamic model of a typical SEA that illustrates the challenges inherent in designing a controller that achieves a torque loop bandwidth not limited by the first resonance is described below. To model a foot and spring, a motor may be attached to an imaginary member which represents the foot position if the spring were in neutral. Thus the angle β associated with this member is the motor angle divided by the gearing constant. k g , with k g  in one embodiment being approximately 220. 
         [0082]    Variable and coefficient list: 
         [0083]    θ Angle of the foot (rad) 
         [0084]    β Angle of the imaginary member associated with neutral spring (rad) 
         [0085]    k g {dot over (β)} Angle of the motor shaft (rad) 
         [0086]    k g  Gearing multiplier (approx. 220) 
         [0087]    L f  Length of foot from ankle (0.28 meters) 
         [0088]    J f  Moment of inertia of foot 
         [0089]    In an embodiment, the foot may be assumed to weigh 1.5 lbs, which acts as a point mass halfway down the foot. A force of 1.5 lbs corresponds to 6.67 Newtons or kg*m/(sec) 2 . Dividing by acceleration of gravity 9.8 m/(sec) 2  gives a mass of 0.68 kg, resulting in a value of J f  of 0.68*(0.14) 2 =0:013 kg*m 2  (0.14 is L f /2). 
         [0090]    J M  Moment of inertia of the motor shaft 
         [0091]    K S  The spring constant. 
         [0092]    When β&lt;θ the spring is stretched and pulling with K S =350 N*m/rad, and when β&lt;θ the spring is compressed and pushing with K S =1200 N*m/rad. 
         [0093]    τ E  External torque on the foot. If a person of weight W steps onto the toe of the foot, τ E =−W*L f . The negative sign indicates the torques work to decrease θ. A person weighing 225 weighs 1000 Newtons. With a foot measuring 0.28 m, the torque applied would be 280 N*m. 
         [0094]    B f  The damping in the ankle joint. Due to friction, it creates a force opposing the angular velocity of the foot. 
         [0095]    B M  The damping in the motor due to friction. 
         [0096]    The basic kinematic equation τ=j*{umlaut over (θ)}  applied to the foot around the ankle joint gives: 
         [0000]      τ E   +K   S (β−θ)− B   f   {dot over (θ)}=J   f {umlaut over (θ)}  (1)
 
         [0097]    The basic kinematic equation τ=J*{umlaut over (θ)} is now applied to the motor shaft, representing the motor angle as k g *β. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       τ 
                       M 
                     
                     - 
                     
                       
                         
                           K 
                           S 
                         
                         
                           k 
                           g 
                         
                       
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                         ( 
                         
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                           - 
                           θ 
                         
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                         k 
                         g 
                       
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                   2 
                   ) 
                 
               
             
           
         
       
     
         [0098]    The system may be changed to average-angle and difference. New variables may be defined as follows: 
         [0099]    φ A =0.5(β+θ); the average position between the foot and the imaginary member 
         [0100]    φ D =0.5(β−θ) the difference position between the foot and the imaginary member 
         [0000]        J=J   f +( k   g ) 2   J   M   ; B=B   f ⇄( k   g ) 2   B   M ;
 
         [0101]    The two equations become: 
         [0000]      τ E   +k   g τ M   −B{dot over (φ)}   A +( B   f   {dot over (−)}B   M   k   g   2 ){dot over (φ)} D   =J{umlaut over (φ)}   A +( J   f −( k   g ) 2   J   D ){umlaut over (φ)} D   (3)
 
         [0000]      τ E   +k   g τ M −2 K   S φ D   −B{dot over (φ)}   D +( B   f   {dot over (−)}B   M   k   g   2 ){dot over (φ)} A   =J{umlaut over (φ)}   D +( J   f −( k   g ) 2   J   D ){umlaut over (φ)} A   (4)
 
         [0102]    When the effects of the differential damping terms are considered to be negligible, the general structural elements can be seen. The dynamics of the mechanical system may be modeled as: 
         [0000]      τ E   +k   g τ M   −B{dot over (φ)}   A   =J{umlaut over (φ)}   A   (5)
 
         [0000]      −τ E   +k   g τ M −2 K   S φ D   −B{dot over (φ)}   D   =J{umlaut over (φ)}   D   (6)
 
         [0000]    The equations for the motor dynamics are: 
         [0000]                      L        dt   dx       +   Rl     =     V   -       K   s          k   g          β   .                 (   7   )               τ M =T M   i   (8)
 
         [0103]    Taking transforms: 
         [0000]        Lsi+Ri=V−K   s   k   g   sβ   (9)
 
         [0000]      τ M =T M   i   (10)
 
         [0104]    The back emf of the motor is represented by the term K s k g sB 
         [0000]      τ E   +k   g τ M   −Bsφ   A   =Js   2 φ A   (11)
 
         [0000]      −τ E   +k   g τ M −2 K   S φ D   −Bsφ   D   =Js   2 φ D   (12)
 
         [0105]    The SEA drives the joint through a spring that serves as a catapult to amplify motor power at the joint. This form of bionic muscle-tendon unit may serve as the basis for emulation of the biomechanical response of an intact limb. 
         [0106]      FIG. 14  is a block diagram of the system, as closely approximated by the equations (9)-(12).  FIG. 15  depicts a system that achieves a similar result, i.e., the required joint torque characteristic, but the inner current-feedback loop is eliminated. 
         [0107]    The open-loop joint torque system depicted in  FIG. 14  relies on use of the motor current to compute a voltage to be applied to the motor windings to control joint torque. The controlled motor torque must in itself account for the effects of the complicated transfer function between the motor torque and the joint torque. Also, the complex loop involving the back emf proportional to {dot over (β)} is not treated directly but its effect are assumed to be negated by the disturbance rejection properties of feedback. 
         [0108]    However, there are significant limitations of using current feedback in this setting. From the partially reduced system of  FIG. 15 , it can be seen that the poorly damped spring dynamics appear as poles in the return transfer function in the naturally occurring back emf feedback within the model. This means that, when the current loop is closed, as shown in  FIG. 14 , the effects of the spring element appear as a pair of zeros near the imaginary axis in the transfer function between the voltage and the motor current. When a current-loop controller with these dynamic limitations is embedded in a closed-loop torque control, as shown in  FIG. 18 , the closed loop torque response either exhibits a bandwidth far below the resonance or exhibits an underdamped response, neither of which is useful in emulation of biological muscle tendon unit response. 
         [0109]    Using a direct measurement of joint torque, a wider bandwidth and more robust closed-loop control system is possible. Here, proportional-integral compensation applied to the joint torque tracking error will generate a stable response that extends beyond the first resonance. In the system depicted in  FIG. 15 , the resonant spring dynamics appear in the forward path of the joint torque controller rather than the feedback path. Therefore, these dynamics do not appear as troublesome zeros in a loop that measures the joint torque and manipulates that signal to produce a compensating voltage input. In general, poorly damped zeros in a feedback control design limit the bandwidth and effectiveness of the control loop, as described above. Indeed, since the poorly damped poles are substantially eliminated) i.e., legitimately cancelled by the zeros arising from the same dynamics in the naturally occurring back emf loop), the transfer function between the motor&#39;s voltage and the joint torque is quite benign (without oscillatory dynamics) and amenable to a PI or PID controller. 
         [0110]      FIG. 16  depicts a further improved system with the inclusion of emf feedforward in a closed-loop torque controller with embedded current loop. Here the feedforward substantially eliminates the underdamped dynamics, enabling simple compensation in the outer torque loop. A measurement or derived estimate of the motor speed {dot over (β)} is used in a controller to cancel the effect of the back emf. As shown in  FIG. 16 , this greatly simplifies the dynamics of the system. A feedback controller measuring and feeding back either the current i or the joint torque can be used in addition to the emf feedforward to reduce sensitivity to any remnant error in the estimation of the motor speed and other modeling errors. A simple PI loop using the motor current can control the motor torque while a PI or PID loop using the joint torque may produce excellent control of the joint torque. 
         [0111]      FIG. 17  is a block diagram of a model using a measurement of joint torque through a single compensator to compute a voltage signal that produces a desired result. The blocks of  FIG. 17  have been filled with typical transfer functions for a typical joint problem; one block giving a transfer function from motor voltage v to motor current i and a second block giving, a transfer function from motor current i to joint torque τ j . For the single loop, only the product of the two blocks may be considered so that the poorly damped poll pair that originates with the spring is exactly cancelled by the zero pair in the first block that originates in the same physical element. The resulting dynamics allow for the design and implementation of a compensator C(s) to follow the command signal τ JC . C(s) may be a PT controller. 
         [0112]    By contrast, a model of the known motor controllers, described with reference to  FIG. 18 , includes two compensators arranged in an inner loop using the motor current i and an outer loop using the joint torque τ J . The inner loop may have to contend with a poorly damped zero pair in the first block, though two systems may be expected to perform similarly by setting: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                      
                     
                         
                     
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                     2 
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                       ( 
                       s 
                       ) 
                     
                   
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                           + 
                           5000 
                         
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         [0113]    Thus, the C2 compensator needed to make the systems perform the same may be more complex than systems requiring only a single compensator, in addition to the complexity of making multiple measurements and implementing multiple compensators. 
         [0114]    It should be understood that for those skilled in the art, the control architecture described here can be extended to bionic ankles that employ physical or SEA-applied virtual, unidirectional parallel elastic elements where the torque-displacement characteristics of these can be calibrated before use. Further, while the control architecture has been applied to leg prostheses, the principles can be readily extended to orthotic, exoskeletal or humanoid applications in lower-extremity augmentation of ankles, knees and hips. 
         [0115]    The terms and expressions employed herein are used as terms and expressions of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof. In addition, having described certain embodiments of the invention, it will be apparent to those of ordinary skill in the art that other embodiments incorporating the concepts disclosed herein may be used without departing from the spirit and scope of the invention. The compositions, components, and functions can be combined in various combinations and permutations, to achieve a desired result. For example, all materials for components (including materials not necessarily previously described) that are suitable for the application are considered within the scope of the invention. Accordingly, the described embodiments are to be considered in all respects as only illustrative and not restrictive. Furthermore, the configurations described herein are intended as illustrative and in no way limiting. Similarly, although physical explanations have been provided for explanatory purposes, there is no intent to be bound by any particular theory or mechanism, or to limit the claims in accordance therewith.