A combination of functional electrical stimulation (FES) and an orthosis can be used to restore lower limb function in persons with paraplegia. This artificial intervention may allow them to regain the ability to walk again, however, only for short time durations. To improve the time duration of hybrid (FES and orthosis) gait, the muscle fatigue due to FES and the fatigue in arms, caused by a user’s supported weight on a walker, needs to be minimized. In this paper, we show that dynamic optimization can be used to compute stimulation/torque profiles and their corresponding joint angle trajectories which minimize electrical stimulation and walker push or pull forces. Importantly, the computation of these optimal stimulation or torque profiles did not require a predefined or a nominal gait trajectory (i.e., a tracking control problem was not solved). Rather the trajectories were computed based only on pre-defined end-points. For optimization we utilized the recently developed three-link dynamic walking model, which includes both single and double support phases and muscle dynamics. Moreover, different optimal actuation strategies for FES and orthosis aided gait under various scenarios (e.g., use of a powered or an unpowered orthosis combined with stimulation of all or few selected lower-limb muscles) were calculated. The qualitative comparison of these results depict the advantages and disadvantages of each actuation strategy. The computed optimal FES/orthosis aided gait were also compared with able-bodied trajectories to illustrate how they differed from able-bodied walking.
The torque generation capability of muscles often reduces during a functional electrical stimulation (FES) session due to the rapid onset of muscle fatigue. Hybrid rehabilitation systems that use FES and electric motor assist may overcome this issue. The primary control challenge in such a system is how to allocate control inputs between electric motor and FES during muscle fatigue and muscle recovery. One strategy is to switch between FES and the electric motor by using an estimate of the muscle fatigue. This would allow the system to switch from using FES to using the electric motor when the muscle torque output has significantly decreased, then switch back to FES once the muscles have sufficiently recovered. This paper uses a second order sliding mode controller cascaded with a feedback linearization controller for a switched, FES and electric motor, system. The second order sliding mode is achieved through the use of a variable-gain super-twisting algorithm. A Lyapunov stability analysis was used to prove asymptotic stability of the switched control system. Simulations of the developed controller on a hybrid knee extension model illustrate that prolonged knee movements can be elicited through the switched system.
The objective of this research is to observe and characterize periodic fluctuations in friction force of ball-element bearings that occur during velocity tracking motion. It is proposed that this periodic fluctuation in friction force is caused by the motion of the balls. We hope to show this relation by demonstrating that the frequency of the periodic fluctuation is equal to the frequency of the balls passing a position in the race.
To illustrate the relation between the fluctuating friction force and the motion of the balls, a testbed has been built to measure friction force, ball passage rate, and velocity error during velocity tracking motion. The velocity error will be calculated from the measurement of position, and may show how the periodic fluctuations in friction force act like a periodic disturbance to the velocity. This paper will discuss the design and fabrication of the testbed, and the resulting measured signals that will be processed to determine their periodic content and to show how they are correlated. However, before inspecting the test results, some qualitative analysis of the system and models of the measured signals will be discussed to give insight into what we may expect from the results of the velocity tracking tests.
An optical sensor has been designed and built to detect the motion of the balls in the race. The optical sensor measures the light reflected off the surface of a ball as it passes the sensing fiber. It was necessary to make some adjustments to the initial design of the sensor to correct for an instability in the signal. These adjustments, and the cause of the instability, will be discussed in this paper.
Some ball bearings display an odd sticking behavior, where the friction force greatly increases beyond the approximated static friction force. This sticking behavior will be discussed, and how it relates to the motion of the balls in the race will be illustrated. It will also be discussed how the spectral density of friction force can be used to evaluate the performance of a bearing.
Functional electrical stimulation (FES) is prescribed as a treatment to restore motor function in individuals with neurological impairments. However, the rapid onset of FES-induced muscle fatigue significantly limits its duration of use and limb movement quality. In this paper, an electric motor-assist is proposed to alleviate the fatigue effects by sharing work load with FES. A model predictive control (MPC) method is used to allocate control inputs to FES and the electric motor. To reduce the computational load, the dynamics is feedback linearized so that the nominal model inside the MPC method becomes linear. The state variables: the angular position and the muscle fatigue are still preserved in the transformed state space to keep the optimization meaningful. Because after feedback linearization the original linear input constraints may become nonlinear and state-dependent, a barrier cost function is used to overcome this issue. The simulation results show a satisfactory control performance and a reduction in the computation due to the linearization.
Neuromuscular electrical stimulation (NMES) is a promising technique to artificially activate muscles as a means to potentially restore the capability to perform functional tasks in persons with neurological disorders. A pervasive problem with NMES is that overstimulation of the muscle (among other factors) leads to rapid muscle fatigue, which limits the use of clinical and commercial NMES systems. The objective of this paper is to develop an NMES controller that incorporates the effects of muscle fatigue during NMES-induced non-isometric contraction of the human quadriceps femoris muscle. Our previous work that used the RISE class of nonlinear controllers cannot accommodate fatigue and muscle activation dynamics. A totally new control design approach and associated stability proof is required to derive a new class of NMES control design that accounts for muscle fatigue dynamics and a first order activation dynamics, in addition to the second order musculoskeletal dynamics. Motivated from a control method for robotic systems in a strict-feedback form, a backstepping based nonlinear NMES controller was designed to accommodate for the additional muscle activation dynamics. Further, experimentally identified estimates of the fatigue and activation dynamics were incorporated in the control design. The developed controller uses a neural network-based estimate of the musculoskeletal dynamics and error due to fatigue estimation. A globally uniformly ultimately bounded stability is proven the new controller that accounts for an uncertain nonlinear muscle model and bounded nonlinear disturbances (e.g., spasticity, changing load dynamics). The developed controller was validated through experiments on the left and right legs of 3 able-bodied subjects and was compared with a proportional-derivative (PD) controller and a PD augmented with a neural network. The statistical analysis showed improved control performance compared to the PD controller.
A widely accepted model of muscle force generation during neuromuscular electrical stimulation (NMES) is a second-order nonlinear musculoskeletal dynamics cascaded to a delayed first-order muscle activation dynamics. However, most nonlinear NMES control methods have either neglected the muscle activation dynamics or used an ad hoc strategies to tackle the muscle activation dynamics, which may not guarantee control stability. We hypothesized that a nonlinear control design that includes muscle activation dynamics can improve the control performance. In this paper, a dynamic surface control (DSC) approach was used to design a PID-based NMES controller that compensates for EMD in the activation dynamics. Because the muscle activation is unmeasurable, a model based estimator was used to estimate the muscle activation in realtime. The Lyapunov stability analysis confirmed that the newly developed controller achieves semi-global uniformly ultimately bounded (SGUUB) tracking for the musculoskeletal system. Experiments were performed on two able-bodied subjects and one spinal cord injury subject using a modified leg extension machine. These experiments illustrate the performance of the new controller and compare it to a previous PID-DC controller that did not consider muscle activation dynamics in the control design. These experiments support our hypothesis that a control design that includes muscle activation improves the NMES control performance.
Hybrid neuroprostheses that use both electric motor drives and functional electrical stimulation for the restoration of walking in persons with paraplegia have a promising potential. However, the hybrid actuation structure introduces effector redundancy, making the system complex and difficult to control. In this paper we design a low-dimensional controller inspired from the muscle synergy principle. The new controller requires few control signals to actuate multiple effectors in a hybrid neuroprostheses. The development of the controller and a Lyapunov stability analysis, which yielded semi-global uniformly ultimately boundedness is presented in this paper. Computer simulations were performed to test the new controller on a 2 degree of freedom fixed hip model.
Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.
