^{1}

^{2}

^{2}

^{2}

^{3}

^{*}

^{1}

^{2}

^{3}

Edited by: Irina N. Beloozerova, Barrow Neurological Institute (BNI), United States

Reviewed by: Shinya Aoi, Kyoto University, Japan; Boris Prilutsky, Georgia Institute of Technology, United States

This article was submitted to Neuroprosthetics, a section of the journal Frontiers in Neuroscience

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

A hybrid walking neuroprosthesis that combines functional electrical stimulation (FES) with a powered lower limb exoskeleton can be used to restore walking in persons with paraplegia. It provides therapeutic benefits of FES and torque reliability of the powered exoskeleton. Moreover, by harnessing metabolic power of muscles via FES, the hybrid combination has a potential to lower power consumption and reduce actuator size in the powered exoskeleton. Its control design, however, must overcome the challenges of actuator redundancy due to the combined use of FES and electric motor. Further, dynamic disturbances such as electromechanical delay (EMD) and muscle fatigue must be considered during the control design process. This ensures stability and control performance despite disparate dynamics of FES and electric motor. In this paper, a general framework to coordinate FES of multiple gait-governing muscles with electric motors is presented. A muscle synergy-inspired control framework is used to derive the controller and is motivated mainly to address the actuator redundancy issue. Dynamic postural synergies between FES of the muscles and the electric motors were artificially generated through optimizations and result in key dynamic postures when activated. These synergies were used in the feedforward path of the control system. A dynamic surface control technique, modified with a delay compensation term, is used as the feedback controller to address model uncertainty, the cascaded muscle activation dynamics, and EMD. To address muscle fatigue, the stimulation levels in the feedforward path were gradually increased based on a model-based fatigue estimate. A Lyapunov-based stability approach was used to derive the controller and guarantee its stability. The synergy-based controller was demonstrated experimentally on an able-bodied subject and person with an incomplete spinal cord injury.

Paraplegia in persons with spinal cord injury (SCI) impairs walking function and lowers their quality of life. Functional electrical stimulation (FES) and powered exoskeletons are two potential technologies that aim to reanimate lower-limb function in these persons. FES is an artificial application of electrical potential across a muscle group to produce a desired limb function and is prescribed as an intervention to rehabilitate or restore gait function in individuals with mobility-impairements (Peckham and Gray,

Powered exoskeletons by their virtue of generating high, rapid, and reliable torque are actively being used to provide gait therapy or restoration (Farris et al.,

In Quintero et al. (

In our previous research, a dynamic optimization method was used to optimize a hybrid walking system (FES + passive orthosis) (Sharma et al.,

Aforementioned research papers in hybrid neuroprosthesis control focused primarily on coordinating FES and the motors at a single joint, even though some of these papers provided pioneering evidence of its benefits. Motivated to provide a general framework that coordinates stimulation of multiple muscles and exoskeleton actuators at multiple joints, a muscle synergy-inspired controllers were presented in Alibeji et al. (

Motivated to extend the synergy-based controller, in this paper, dynamic postural synergies were used in a control scheme to generate walking with a hybrid exoskeleton. The dynamic postural synergies are artificial synergies designed to drive the system to key dynamic postures when activated. Then sequential activation of these dynamic postural synergies drive the system to produce gait motions. An adaptive update law was used to modify the synergy activation profiles to compensate for parametric changes in the model. A PID-based feedback component was used to make the controller robust to uncertainity and disturbances. The controller uses dynamic surface control (DSC) (Alibeji et al.,

Figure

where ^{4×4} is the combined inertia of the hybrid neuroprosthesis and human limbs, ^{4} is the gravity vector, _{W}), and

where μ(^{4} is the intermediate normalized activation vector containing activation states for the actuators, and is defined as

where, μ_{kfx} ∈ ℝ is knee flexor muscle activation, μ_{kex} ∈ ℝ is knee extensor muscle activation, μ_{km} ∈ ℝ is normalized current for the knee motor and μ_{hm} ∈ ℝ is normalized current for the hip motor. In (2), ϕ(^{4×4} is the fatigue matrix that contains the fatigue factor corresponding to each stimulated muscle and is defined as

and

A 4-link gait model is used to represent a subject taking a step in a hybrid neuroprosthesis while using a walker.

In (3), ψ_{ifx}, ψ_{iex} are the torque-length and torque-velocity relationships of the flexor and extensor muscles and the conversion constants (current to torque) of the electric-motor drives is κ_{i}.

The activation state is governed by the following first order differential equation

where subscripts _{ij} is the normalized input, and τ_{ij} is the input delay.

The fatigue dynamics of the muscles, ϕ_{ij} ∈ ℝ is generated from the first order differential equation (Riener et al.,

where ϕ_{min} ∈ (0, 1) is the unknown minimum fatigue constant of a muscle, and _{f}, _{min}, _{max}] for muscles, it can be shown that ϕ ∈ [ϕ_{min}, 1], where ϕ = 1 when the muscle is fully rested, and ϕ = ϕ_{min} when the muscle is fully fatigued. The fatigue state for the motors in the fatigue matrix are set to one because the motors do not fatigue.

The stimulation applied to the muscle is bounded by two stimulation levels _{min} and _{max} to avoid under/over stimulating the muscles. This allows the normalization of the input function ^{4}, which is modeled by a piecewise linear recruitment curve (Schauer et al.,

where ^{4} is the input to the system. Based on (4) and (6), a linear differential inequality can be developed to show that μ ∈ [_{min}, _{max}]. The _{min}, _{max} values are [0, 1] for muscles because they are unidirectional and [−1, 1] for electric motors because they are bidirectional actuators.

The purpose of muscle synergies in human motor control is to reduce the complexity of the system by reducing the input space and redundant DOF. In this paper, an alternative form of synergies called dynamic postural synergies are introduced. Unlike other methods which identify synergies by using statistical analysis tools on collected EMG data or simulation results, this form of synergies is computed independently to create a reduced input space for a system that can be used to more efficiently control a system. The dynamic postural synergies generated in this paper are artificial synergies that are designed to drive the system to key dynamic postures, which are defined as the joint positions at any moment during a movement pattern. Then motions such as walking can be segmented into a finite number of dynamic postures and a dynamic postural synergy can be computed for each dynamic posture. These artificial synergies can then be activated sequentially to drive the system from one dynamic posture to the next to create the original motion.

In Bajd et al. (^{4×2}, that produce these dynamic postures were computed using dynamic optimizations. Then, another set of dynamic optimizations were used to find the optimal activation of these artificial synergies, defined as _{d}. Below, the dynamics, excluding the fatigue factor ϕ, are written in terms of the kinematic trajectories (_{d}) and the activation state generated from the dynamic postural synergies and their optimal activation (i.e., μ_{d} = _{d}) as

where _{W}, resulting from the optimal trajectories (_{d}).

The dynamic postural synergies are computed using optimizations that use the 4-link walking model in (1). The 4-link walking model was modified to reflect the hybrid neuroprosthesis testbed, therefore, only the hip motors, knee motors, and the antagonistic muscle pairs of the knee joint are used. The parameters used for this model were taken from Popović et al. (

where dynamic posture's position error is defined as _{1} = _{dp} − _{dp} is the joint positions for the desired dynamic posture. In (8), _{l} and _{1}, the distribution of the effort from the motors or stimulation can be emphasized. These optimizations were performed by using Matlab's fmincon function (MathWorks, Inc., USA). The dynamic postural synergies computed through the optimization and the postures they produce; withdrawal reflex and knee extension, can be seen in Figure

The dynamic postural synergies computed through the optimizations and the dynamic postures they result in when activated.

Unlike the synergies extracted through statistical methods, such as principal component analysis in Alibeji et al. (

In order to consistently and easily maintain the initial condition during experimentation, the subject will start the gait process while standing upright. Therefore, two sets of dynamic optimizations are computed; one for a half step (0.2 meters) and the second for a full step (0.4 meters).

These dynamic optimizations also include the double support phase (DSP) part of the gait sequence, i.e, when the body is supported by both legs. During the DSP the load transfers from the stance leg to the swing leg and the legs switch roles, i.e., the stance leg from the previous step becomes the swing leg for the next step and vice versa. To include the DSP, the swing leg has to the reach the desired position, where the swing leg makes contact with the ground, in the allotted time, _{step} = 1 s., and maintain that position, i.e., maintain contact with the ground, for a predetermined duration, _{DSP} = 0.5 s. For these optimizations, the convex cost function's objective was to minimize the synergy activation for the full duration and the final position error from _{step} to _{DSP}. The cost function is defined as

where final position error is defined as _{f} − _{f} is the final joint positions for a complete step, _{l} and _{0} is the time in which the step begins and _{f} is the final time for the step and is defined as _{f} = _{step} + _{DSP}. The last variable in the cost function, Π_{extra} is an additional cost that is activated when certain undesirable events occur in the solution, e.g., the foot drags on the ground or the swing leg overshoots.

These optimizations were performed in Matlab using a genetic algorithm particle swarm optimization (GAPSO) method to minimize the cost function. The dynamic postural synergies, their activations computed through the optimizations, the joint trajectories they produce, and the gait sequence for the half step and full step can be seen in Figures

Note that for the full step results, as the swing leg leaves the ground, the stance leg is tilted posteriorly which is not typical for normal gait. This is because this system does not currently include actuation at the ankle joints to produce push off. During normal gait the first part of the gait sequence is push off, as a result of the plantar-flexion of the ankle, to propel the body forward. The differences between gait with and without push off can be seen when comparing these results to the walking simulation results in Alibeji et al. (

The control objective is to track a continuously differentiable desired trajectory ^{4}, is defined as

To facilitate the control design and stability analysis, the auxiliary error signals

where

in order to incorporate integral control. To simplify the derivations, the following notations are used: (1) the time dependence of a function is dropped [e.g., _{τ}]. In addition, to facilitate the control development and stability analysis, the following assumptions were made.

_{d}, are bounded as |τ_{d}| ≤ ϵ_{1} where

_{d}, are bounded vectors.

The open-loop error is derived by multiplying the time derivative of (12) with

where _{d} + Γ_{ext}. This expression can be written in the form

where ^{4}, is defined as Ñ ≜ _{d}. The auxiliary signals _{d}(

The term Ñ in (15) can be upper bounded by using the Mean Value Theorem as

where ρ_{1}(||^{16} is defined as

Note that the auxiliary signal _{d} is equal to the left hand side of the desired muscle dynamics in (7). Therefore, (15) can be rewritten as

where _{d}ϕμ, and _{d}ϕμ_{f} where

where

The estimates of the activation and fatigue states in (4) and (5) are generated through the following dynamics

where

In (18), the surface error, ^{4}, is defined as

The delay compensation term, _{I}, is added to the surface error, ^{4}, for μ is defined as

The filtered desired activation μ_{f} is obtained by passing

where

To felicitate the control design the desired activation,

where ĉ ∈ ℝ^{2} is the estimate of _{d}, ^{4×4} is the feedback gain matrix that is chosen to only influence the electric motors.

In _{sf}

where ^{2×2} is a symmetric positive definite gain matrix. After using (24), (18) becomes

where

Using the Mean Value Theorem, Assumption 4, and the property of projection algorithm the following terms can be bounded as

where ρ_{2}(||

The surface error dynamics are derived by taking the time derivative of (21) and using (19), resulting in

Based on the subsequent stability analysis, the normalized input

where β ∈ ℝ^{+} is a control gain.

Therefore, the closed-loop surface error dynamics can be written as

The boundary layer error dynamics are found by taking the time derivative of (22) and using (23), which results in

where η(

where △_{max} − _{min} and △_{max} − _{min}. The desired feedback activation, _{P} = _{0} + α_{1}), _{D} = _{I} = _{0}α_{1}. The control schematic for the implementation of the overall controller is represented in Figure

The control schematic for the implementation of the overall controller.

The hybrid neuroprosthesis used for experimental demonstration uses 4 electric motors; one on each hip joint and knee joint, and 4 stimulation channels; the quadriceps and hamstrings of each leg. The hybrid neuroprosthesis is controlled using two of the adaptive synergy-based PID-DSC controller with delay compensation working in tandem to produce gait, one for each leg. The Finite State Machine, shown in Figure

The Finite State Machine determines the desired trajectories and synergy activations based on what state is activated; either half right step, full left step, or full right step. Then two controllers are used, one for each leg, which work in tandem to produce gait.

The hybrid neuroprosthesis testbed, shown in Figure

The walking hybrid neuroprosthesis and the gait support device used in the experimental demonstration of the synergy-based control system. This system uses an electric motor at the hip and knee joints of each leg and FES of the hamstrings and quadriceps muscle group of each leg.

The overall control system was experimentally demonstrated on an able-bodied subject (male; 27 years old, height: 1.80 m, weight: 90 kg) and a person with an incomplete SCI (male; 41 years old, height 1.70 m, weight 70 kg, injury: T10 AIS A). For these experiments it is assumed that the behavior of the right and left leg are similar, therefore, both States 2 and 3 use the same synergies and activations computed in the previous sections. The optimizations to compute the synergies, their activations, and the trajectories they produce were performed using the subject's height and weight, but the model used the muscle parameters reported in Popović et al. (

Prior to any experimentation, an approval from the Institutional Review Board at the University of Pittsburgh was obtained. The consent procedure for human participants was written and informed. During the experiments, the subject was instructed to relax and refrain from voluntarily interfering with the hybrid exoskeleton. The estimates of the EMD, activation time constants, and fatigue/recovery rates were estimated in system identification experiments in a leg extension machine and assumed to be the same for both legs. During the experiments, the subjects used a gait assistive device called the E-Pacer (Rifton, USA) to help support and propel themselves forward. The progression and safety buttons were operated by a separate user and were used to control the FSM. The experiments were run for 6 steps, including the half right step. In order to compare the difference in power consumption between a powered exoskeleton, just motors, and a hybrid neuroprosthesis, motors and FES, the testbed was tested with two different control systems. For the first control system for the hybrid neuroprosthesis configuration, the adaptive synergy-based PID-DSC controller was used to govern the input to the FES and motors. For the second control system for the powered exoskeleton configuration, a Robust Integral of the Sign of the Error (RISE) (Xian et al.,

The experimental results from the subject with the incomplete SCI can be seen in Figures ^{1}

The desired feedforward component of

The desired feedback component of

The fatigue estimates for the knee flexors and extensors of the right leg. The fatigue estimate ranges from 1 to ϕ_{min}, which corresponds to no fatigue to fully fatigued, respectively. It can be observed that the fatigue occurs during the swing phase, and the muscles recover during the stance phase since there is no stimulation.

The inputs to all of the system inputs, including feedback and feedforward, for this experimental trial. Note that there is no stimulation occurring during the stance phase of each leg.

The root mean squared of the input voltage to the motors.

Incomplete SCI | Right Hip | 1.35 | 2.25 | 1.68 | 2.49 |

Right Knee | 1.68 | 3.10 | 3.52 | 3.36 | |

Able Bodied | Right Hip | 1.56 | 3.22 | 2.70 | 3.39 |

Right Knee | 0.92 | 2.50 | 3.03 | 3.70 |

As researchers, we often analyze biological systems to devise innovative solutions to real world applications. To overcome the challenge of actuator redundancy, we studied how scientists believed the human body solves its high degree of freedom and actuator redundancy problem to achieve fluid and coordinated movements such as gait. It is hypothesized that the human central nervous system (CNS) activates multiple muscle fibers in groups or patterns called muscle synergies, or motor primitives, to efficiently perform complex movements such as reaching, hand manipulations, or posture control (Sherrington,

In this research, a synergy-based control system is used to distribute the control effort to the multiple actuators of a walking hybrid neuroprosthesis. This approach is inspired from the human motor control concept of muscle synergies. In most studies, muscle synergies are proposed as a basis employed during human motor control and found by decomposing recorded EMG signals (collected from multiple muscles) to extract muscle synergies. Unlike these studies, in this paper dynamic postural synergies are designed, using dynamic optimizations, to be used as a basis for the control system for the walking hybrid neuroprosthesis. This synergy design approach, using optimizations to distribute the control effort among the available actuators, offers multiple advantages and convenience such as allowing for the incorporation of external inputs, i.e., electric motors and FES. Another benefit for this method of designing dynamic postural synergies is the ease of adding additional restrictions on the synergies, i.e., no co-activation or no negative stimulation. Based on the synergy principle, fewer control signals are used to control multiple actuators in a hybrid neuroprosthesis, therefore the use of synergies will not only solve the actuator redundancy problem similarly to how the body is hypothesized to do so, but it will do it in a more computationally efficient way. However, there are still other remaining challenges that could hamper the effectiveness of a closed-loop synergy-based control system if not addressed. These remaining challenges are EMD, actuator dynamics, and muscle fatigue. Therefore, Lyapunov-based control design approaches were used to derive this class of synergy-based controllers that are robust to EMD and compensate for activation dynamics and muscle fatigue. While the developed control system was capable of reproducing gait, the finite state machine can still be scaled-up to achieve motions other than gait such as sitting/standing and ascending/descending.

In this paper, the adaptive synergy-based DSC controller is developed and experimentally tested on an able-bodied subject and person with an incomplete SCI using a walking hybrid neuroprosthesis. This control system used dynamic postural synergies designed to reproduce the key dynamic posture; the withdrawal reflex and knee extension, which have been shown to be able to reproduce gait. Dynamic optimizations were then used to compute the optimal synergies' activation to produce a half step and full step. A finite state machine was developed to switch between the trajectories and synergy activations depending on three states; half right step, full right step, and full left step. The control system then used two of the synergy-based DSC controller, one for each leg, working in tandem to reproduce gait. The overall control system was able to recreate gait using the hybrid neuroprosthesis and the gait assistive device.

NA designed the controller, developed dynamic postural synergies, performed experiments, and wrote the paper. VM performed optimizations, BD recruited subjects for the study and supervised and provided advise on conducting experiments with subjects with SCI, and NS designed and conceptualized the control design, study, experiments, and edited the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work was funded in part by the NSF award numbers: 1462876 and 1511139. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Research reported in this article was also supported in part by Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health under award number: R03HD086529. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. NA is with the Department of Biomedical Engineering at Case Western Reserve University, Cleveland, OH, USA. VM and NS, Ph.D. are with the Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, USA 15261. BD, MD, is with the Department of Physical Medicine and Rehabilitation Science, University of Pittsburgh, Pittsburgh, PA.

The Supplementary Material for this article can be found online at:

^{1}The video footage of testing of the dynamic postural synergy-based controller on a subject with an incomplete SCI can be seen in the