This article addresses the three-dimensional (3-D) path-following problem of underactuated autonomous underwater vehicles (AUVs) in the presence of multiple uncertainties and nonlinearities, including unmodeled dynamics, actuator hysteresis, input saturation, and oceanic disturbance. First, the AUV kinetic model is reconstructed as a second-order nonlinear system by coupling the smooth saturation function and hysteresis dynamics of actuators. Second, the 3-D tracking error is derived in a simplified manner based on the relative motion theory. Then the approach angle-based symmetrical hyperbolic-tangent line-of-sight (SHLOS) guidance and kinematic control scheme are designed to ensure the global asymptotic stability of the kinematic system. Third, two sets of kinetic control schemes are designed without prior knowledge of AUV dynamics and disturbance, where the Nussbaum gain technique is applied to deal with the unknown hysteresis parameter. The application of the reconstructed kinetic model avoids the degraded performance caused by actuator nonlinearities. The first scheme is improved by adaptively estimating the bound of the generalized disturbance-like term which lumps the unmodeled dynamics, external disturbance, and saturation approximation error. The improved scheme guarantees the global stability of the system and transient tracking performance. Finally, comparative simulation studies under dynamic oceanic environments prove the effectiveness and robustness of the proposed control schemes.

This paper addresses the problem of robust bottom following control for a flight-style autonomous underwater vehicle (AUV) subject to system uncertainties, actuator dynamics, and input saturation. First, the actuator dynamics that is approximated by a first-order differential equation is inserted into the AUV dynamics model, which renders a high-order nonlinear dynamics analysis and design in the model-based backstepping controller by utilizing guidance errors. Second, to overcome the shaking control behavior resulted by the model-based high-order derivative calculation, a fuzzy approximator-based model-free controller is proposed, in order to online approximate the unknown part of the ideal backstepping architecture. In addition, the adaptive error estimation technology is resorted to compensate the system approximation error, ensuring that all the position and orientation errors of robust bottom following control tend to zero. Third, to further tackle the potential unstable control behavior from inherent saturation of control surfaces driven by rudders, an additional adaptive fuzzy compensator is introduced, in order to compensate control truncation between the unsaturated and saturation inputs. Subsequently, Lyapunov theory and Barbalat lemma are adopted to synthesize asymptotic stability of the entire bottom following control system. Finally, comparative numerical simulations with different controllers, environmental disturbances and initial states are provided to illustrate adaptability and robustness of the proposed bottom following controller for a flight-style AUV with saturated actuator dynamics.

This paper addresses the problem of coordinated path tracking for networked nonholonomic mobile vehicles, while building and keeping a desired formation. The control laws proposed are categorized into two envelopes by integrating individual path tracking and global virtual structure approaches. One is steering individual vehicles to track virtual vehicles moving along predefined paths, generated by a formation reference vehicle (FRV) of a time-varying desired virtual structure. The other is ensuring paths to be well tracked in order to build a geometric formation, through the distributed feedback law for path parameters related to the virtual vehicles, such that the physical vehicles are on the desired placements of the formation structure. Within this framework, geometric path tracking is achieved via nonlinear control theory, where an approaching angle is injected as a heading guidance design. The distributed feedback law is analyzed under communication constraints using algebraic graph theory. It is formally shown that the path tracking error of each vehicle is reduced to zero, and vehicles in the networked team globally asymptotically converge to a desired formation with equal path parameters. Simulation results illustrate the effectiveness of the proposed control design.

Functional electrical stimulation (FES) is able to restore motor function of spinal cord injured (SCI) patients. To make adaptive FES control taking into account the actual muscle state with muscular feedback information, torque estimation and prediction are important to be provided beforehand. Evoked EMG (eEMG) has been found to be highly correlated with FES-induced torque under various muscle conditions, indicating that it can be an useful tool for torque/force prediction. To better construct the relationship between eEMG and stimulated muscular torque, nonlinear-arx-type (NARX-type) model is preferred. This paper presents and exploits a NARX-type recurrent neural network (NARX-RNN) model for identification and prediction of FES-induced muscular dynamics with eEMG. Such NARX-RNN model is with a novel architecture for prediction, with robust prediction performance. To make fast convergence for identification of such NARX-RNN, directly-learning pattern is exploited during the learning phase. Due to difficulty of choosing a proper forgetting factor of Kalman filter for predicting time-variant torque with eEMG, such NARX-RNN may be considered to be a better alternative as torque predictor. Data gathered from two SCI patients is used to evaluate the proposed NARX-RNN model. The NARX-RNN model shows promising estimation and prediction performance only based on eEMG.

Functional electrical stimulation (FES) is effective to restore movement in spinal cord injured (SCI) subjects. Unfortunately, muscle fatigue constrains the application of FES so that output torque feedback is interesting for fatigue compensation. Whereas, inadequacy of torque sensors is another challenge for FES control. Torque estimation is thereby essential in fatigue tracking task for practical FES employment. In this work, the Hammstein cascade with electromyography (EMG) as input is applied to model the myoelectrical mechanical behavior of the stimulated muscle. Kalman filter with forgetting factor is presented to estimate the muscle model and track fatigue. Fatigue inducing protocol was conducted on three SCI subjects through surface electrical stimulation. Assessment in simulation and with experimental data reveals that the muscle model properly fits the muscle behavior well. Moreover, the time-varying parameters tracking performance in simulation is efficient such that real time tracking is feasible with Kalman filter. The fatigue tracking with experimental data further demonstrates that the proposed method is suitable for fatigue tracking as well as adaptive torque prediction at different prediction horizons.

Electrical stimulation (ES) is one of the solutions for drop foot correction. Conventional ES systems deliver predefined stimulation pattern to the affected muscles. However, time-variant muscle response may influence the gait performance as they are difficult to be taken into account in advance. Therefore, closed-loop ES control is important to obtain desired gait in presence of muscle response variation. In this work, a dual predictive control, which consists of two nonlinear generalized predictive controllers, is proposed to track desired torque. The stimulated muscle dynamics are modeled by Hammerstein cascades, with one representing stimulation to activation, the other representing activation to torque. Ankle dorsiflexion torque and ES-evoked EMG of tibialis anterior were recorded experimentally for model identification. The control scheme is validated by following desired torque trajectories with the identified model. The results show that the stimulation pattern obtained from the dual predictive control can produce good torque tracking according to the current muscle condition.