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1. Cadence Tracking for Switched FES Cycling with Unknown Input Delay

   Allen, B.; Cousin, C.; Rouse, C.; Dixon, W. (January 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   Functional electrical stimulation (FES) induced cycling provides a means of therapeutic exercise and functional restoration for people affected by neuromuscular disorders. A challenge in closed-loop FES control of coordinated motion is the presence of a potentially destabilizing input delay between the application of the electrical stimulation and the resulting muscle contraction. Moreover, switching amongst multiple actuators (e.g., between FES control of various muscle groups and a controlled electric motor) presents additional challenges for overall system stability. In this paper, a closed-loop controller is developed to yield exponential cadence tracking, despite an unknown input delay, switching between FES and motor only control, uncertain nonlinear dynamics, and additive disturbances. Lyapunov-Krasovskii functionals are used in a Lyapunov-based stability analysis to ensure exponential convergence for all time. 

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2. Adaptive Trajectory Tracking During Motorized and FES-Induced Biceps Curls via Integral Concurrent Learning

   https://doi.org/10.1115/DSCC2020-3125  

   Allen, Brendon C.; Stubbs, Kimberly J.; Dixon, Warren E. (October 2020, ASME Dynamic Systems and Control Conference)

   null (Ed.)

   A common rehabilitative technique for those with neuro-muscular disorders is functional electrical stimulation (FES) induced exercise such as FES-induced biceps curls. FES has been shown to have numerous health benefits, such as increased muscle mass and retraining of the nervous system. Closed-loop control of a motorized FES system presents numerous challenges since the system has nonlinear and uncertain dynamics and switching is required between motor and FES control, which is further complicated by the muscle having an uncertain control effectiveness. An additional complication of FES systems is that high gain feedback from traditional robust controllers can be uncomfortable to the participant. In this paper, data-based, opportunistic learning is achieved by implementing an integral concurrent learning (ICL) controller during a motorized and FES-induced biceps curl exercise. The ICL controller uses adaptive feedforward terms to augment the FES controller to reduce the required control input. A Lyapunov-based analysis is performed to ensure exponential trajectory tracking and opportunistic, exponential learning of the uncertain human and machine parameters. In addition to improved tracking performance and robustness, the potential of learning the specific dynamics of a person during a rehabilitative exercise could be clinically significant. Preliminary simulation results are provided and demonstrate an average position error of 0.14 ± 1.17 deg and an average velocity error of 0.004 ± 1.18 deg/s. 

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3. Robust Power and Cadence Tracking on a Motorized FES Cycle with an Unknown Time-Varying Input Delay

   https://doi.org/10.1109/CDC42340.2020.9304066  

   Allen, Brendon C.; Stubbs, Kimberly J.; Dixon, Warren E. (December 2020, IEEE Conference on Decision and Control)

   null (Ed.)

   Functional electrical stimulation (FES) induced cycling is a common rehabilitative technique applied for those with a movement disorder. An FES cycle system is a nonlinear switched dynamic system that has a potentially destabilizing input delay between stimulation and the resulting muscle force. In this paper, a dual objective control system for a nonlinear, uncertain, switched FES cycle system with an unknown time-varying input delay is developed and a Lyapunov-like dwell-time analysis is performed to yield exponential power tracking to an ultimate bound and global exponential cadence tracking. Preliminary experimental results for a single healthy individual are provided and demonstrate average power and cadence tracking errors of -0.05 ± 0.80 W and -0.05 ± 1.20 RPM, respectively, for a target power of 10 W and a target cadence of 50 RPM. 

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4. Deep Neural Network Based Saturated Adaptive Control of Muscles in a Lower-Limb Hybrid Exoskeleton

   https://doi.org/10.1115/IMECE2023-112415  

   Ting, Jonathan A; Basyal, Sujata; Allen, Brendon C (October 2023, American Society of Mechanical Engineers)

   Hybrid exoskeletons are used to blend the rehabilitative efficacy and mitigate the shortcomings of functional electrical stimulation (FES) and exoskeleton-based rehabilitative solutions. This paper introduces a novel nonlinear controller that may potentially improve the rehabilitative efficiency of a lower limb hybrid exoskeleton by implementing four key features into the FES and exoskeleton controllers. First, the FES input to the user’s muscles is saturated based on user preference to ensure user comfort. Second, rather than discarding the excess control effort from the saturated FES input, it is redirected into the exoskeleton’s motor controller. Third, a safe deep neural network (DNN) is designed to estimate the unknown dynamics of the hybrid exoskeleton and the DNN is implemented in the FES controller to improve the control efficiency and tracking performance. Fourth, an adaptive update law is designed to estimate the unknown muscle control effectiveness to facilitate the implementation of the DNN. Lyapunov stability-based methods are used to generate real-time adaptive update laws that will train the adaptive estimate of the muscle effectiveness and the output layer weights of the DNN in real-time, ensure the effectiveness and safety of the controllers, and prove global asymptotic tracking of the desired trajectory. 

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5. Saturated Control of a Switched FES-Cycle with an Unknown Time-Varying Input Delay

   Allen, B. C.; Stubbs, K. J.; Dixon, W. E. (December 2020, IFAC Conference on Cyber-Physical Human-Systems)

   A common rehabilitation for those with lower limb movement disorders is motorized functional electrical stimulation (FES) induced cycling. Motorized FES-cycling is a switched system with uncertain dynamics, unknown disturbances, and there exists an unknown time-varying input delay between the application/removal of stimulation and the onset/removal of muscle force. This is further complicated by the fact that each participant has varying levels of sensitivity to the FES input, and the stimulation must be bounded to ensure comfort and safety. In this paper, saturated FES and motor controllers are developed for an FES-cycle that ensure safety and comfort of the participant, while likewise being robust to uncertain parameters in the dynamics, unknown disturbances, and an unknown time-varying input delay. A Lyapunov-based stability analysis is performed to ensure uniformly ultimately bounded cadence tracking. 

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