From sensing to control of lower limb exoskeleton: a systematic review

As a typical application of the human-computer interaction device, the lower limb exoskeleton has attracted many researchers' attention in recent years in an attempt to improve its functionality in human body assistance, augmentation, treatment, and protection. Essentially, the interaction between the lower limb exoskeleton and the subject is mainly realized through its sensing and control system. The sensing and control of lower limb exoskeletons will significantly affect the subject's actual wearing effect in lower extremity assistance or enhancement. However, due to the limitations of sensing and control techniques, the lower limb exoskeleton is still challenging to achieve a large-scale popularization and application. Therefore, this paper investigated the literature regarding the sensing and control of lower limb exoskeletons in recent years and studied the influences of different sensor signals and controller modeling on the exoskeleton performance. In addition, the current research challenges of insufficient stability and comfort in lower limb exoskeleton control are discussed, and possible innovative insights of functional material-based actuation, invasive and epidermal electronic sensing, and data-driven deep learning are analyzed in-depth. Some future research directions of the exoskeleton control are also provided to facilitate the further development of the exoskeleton control.     

Nonlinear controls for a class of discrete‐time bilinear systems

For a discrete‐time neutrally stable bilinear system, a nonlinear state feedback control based on the passivity design has been proposed to stabilize the system globally and asymptotically. This paper shows that the decay rate resulting from the passivity control is not exponential, and the system's response speed becomes very sluggish asymptotically. A ‘normalized’ nonlinear control is therefore proposed to achieve exponential stability. The new exponentially stabilizing control not only improves the system's response speed, but also enhances the system's robustness against small parametric perturbations. Copyright © 2003 John Wiley & Sons, Ltd.     

Distributed Tracking Control for Networked Mechanical Systems

This paper investigates the distributed tracking control problems for a group of networked mechanical systems. We describe three scenarios that motivate these problems. Firstly, under the conditions that the desired time‐varying trajectory is available to a portion of the networked mechanical systems and that the available signals from the neighboring mechanical systems include the position and velocity information, a distributed tracking control strategy is proposed. Next, we remove the requirement for the neighboring mechanical system's velocity information and propose a control method so that the coupling signals among the networked mechanical systems can be only position information. In the third scenario, we assume that only positions are measured for each mechanical system. Distributed nonlinear observers are proposed to estimate the local mechanical system's velocity and acceleration. Based on the estimated states, the distributed controllers are designed to achieve the tracking control. Simulation results are provided to show the effectiveness of the proposed control laws.     

Backstepping Control for Flexible Joint with Friction Using Wavelet Neural Networks and L2‐Gain Approach

In this study, a new backstepping control scheme is proposed to deal with the high accuracy flexible joint servo system's position control. Based on the introduction of non‐consecutive friction, the cascade dynamics equations of flexible joint are established. The macroscopic controller is designed using a backstepping design technique to suppress the flexibility and external disturbance based on the L₂ property. To identify the non‐consecutive function, the wavelet neural networks (WNN) are utilized in the microscopic controller to compensate for nonlinear friction and uncertainties. The combined strategy of macro and micro controller can overcome the derivation explosion problem and avoid the joint acceleration measurement and upper bound forecast. Finally, stability analysis and mathematical simulations are presented to verify the effectiveness of this new controller.     

Simple Recurrent Neural Network‐Based Adaptive Predictive Control for Nonlinear Systems

Making use of the neural network universal approximation ability, a nonlinear predictive control scheme is studied in this paper. On the basis of a uniform structure of simple recurrent neural networks, a one‐step neural predictive controller (OSNPC) is designed. The whole closed‐loop system's asymptotic stability and passivity are discussed, and stable conditions for the learning rate are determined based on the Lyapunov stability theory for the whole neural system. The effectiveness of OSNPC is verified via exhaustive simulations.     

Hybrid‐impulsive second‐order sliding mode control: Lyapunov approach

Dynamic system of relative degree two controlled by discontinuous‐hybrid‐impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive‐twisting control exhibits a uniform exact finite time convergence to the second‐order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid‐impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second‐order sliding mode in the presence of bounded perturbations. Only ‘snap’ knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybrid‐impulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid‐impulsive‐discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.     

Passivity‐based sliding mode controller/observer for second‐order nonlinear systems

A passivity‐based sliding mode control for a class of second‐order nonlinear systems with matched disturbances is proposed in this paper. Firstly, a nonlinear sliding surface is designed using feedback passification, in which the passivity is employed to guarantee the closed‐loop system's stability. The passivity‐based controller comprising a discontinuous term guarantees globally asymptotical convergence to the sliding surface. A sliding mode‐based control law that satisfies the reaching and sliding condition is also developed. Moreover, the passivity‐based sliding mode observer is also developed to effectively estimate the system states. Compared with conventional sliding mode control, the proposed control scheme has a shorter reaching time; and hence, the system performance is less affected by disturbances, thus eliminating the need to increase the control input gain. Finally, simulation results demonstrate the validity of the proposed method.     

Stabilizing Control of an Underactuated 2‐dimensional TORA with Only Rotor Angle Measurement

One dimensional translational oscillation with a rotational actuator (TORA) system has been used as a benchmark for motivating the study of nonlinear control techniques. In this paper, a novel underactuated 2‐dimensional TORA (2DTORA), which has one actuated rotor and two unactuated translational carts, is presented. The analysis of controllability around the system's equilibriums yielded the controllable equilibriums and the constraint on physical parameters. To stabilize the system to its controllable equilibriums from any initial conditions, we propose a simple linear controller containing the rotor angle and angular velocity. The controller was derived from a proper Lyapunov function, including the system's total energy, that was used to show the passivity property of the system. In addition, a high pass filter was adopted to approximately differentiate the rotor angle so that an estimated angular velocity was used in the controller rather than measuring the actual rotor angular velocity. As a result, only the angle measurement is required for the designed feedback controller to stabilize the underactuated system. Finally, simulation results verify our control design and analysis.     

Neural network-based asymptotic tracking control of unknown nonlinear systems with continuous control command

ABSTRACT

This paper proposes a robust tracking controller for a class of nonlinear second-order systems with time-varying uncertainties. The controller is mainly based on the robust integral of the sign of the error (RISE) control approach to achieve an asymptotic stability result with a continuous control command in the presence of additive uncertainties. An adaptive feedforward neural network control term is blended with a new RISE controller to improve the system's transient performance. The proposed RISE controller is a modified version of the existing saturated RISE controller such that only sign of the derivative of the output is needed. The stability of the closed-loop system is well studied, where a local asymptotic stability is proven. The controller performance is validated through simulations on a two-degree-of-freedom lower limb robotic exoskeleton.     

Task-space fully distributed tracking control of networked uncertain robotic manipulators without velocity measurements

This paper investigates the task-space synchronised tracking problem of uncertain networked manipulators interconnected on directed graphs, where the dynamic leader is available to only a subset of followers and followers have only local interaction. A fully distributed tracking controller is proposed, which is composed of a distributed desired trajectory estimator, a joint-space velocity observer and an adaptive cooperative control algorithm. Specifically, the proposed controller allows each manipulator to track the dynamic leader solely using local task-space position measurements. Besides, in the presence of both dynamic and kinematic uncertainties, the adaptive cooperative control algorithm indeed improves the system's robustness. Furthermore, it is strictly proved that the proposed control scheme ensures that both task-space position and velocity tracking errors converge to zero as time tends to infinity. In the end, simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Guidance and nonlinear control system for autonomous flight of minirotorcraft unmanned aerial vehicles

Small unmanned aerial vehicles (UAVs) are becoming popular among researchers and vital platforms for several autonomous mission systems. In this paper, we present the design and development of a miniature autonomous rotorcraft weighing less than 700 g and capable of waypoint navigation, trajectory tracking, visual navigation, precise hovering, and automatic takeoff and landing. In an effort to make advanced autonomous behaviors available to mini‐ and microrotorcraft, an embedded and inexpensive autopilot was developed. To compensate for the weaknesses of the low‐cost equipment, we put our efforts into designing a reliable model‐based nonlinear controller that uses an inner‐loop outer‐loop control scheme. The developed flight controller considers the system's nonlinearities, guarantees the stability of the closed‐loop system, and results in a practical controller that is easy to implement and to tune. In addition to controller design and stability analysis, the paper provides information about the overall control architecture and the UAV system integration, including guidance laws, navigation algorithms, control system implementation, and autopilot hardware. The guidance, navigation, and control (GN&C) algorithms were implemented on a miniature quadrotor UAV that has undergone an extensive program of flight tests, resulting in various flight behaviors under autonomous control from takeoff to landing. Experimental results that demonstrate the operation of the GN&C algorithms and the capabilities of our autonomous micro air vehicle are presented. © 2009 Wiley Periodicals, Inc.     

A Lyapunov controller for stable haptic manipulation of hydraulic actuators

A scheme for bilateral control of hydraulic actuators is developed and experimentally evaluated in this paper. The control laws are derived based on Lyapunov's feedback control design technique. Owing to the discontinuity originating from a sign function in the control laws, the control system is non‐smooth. First, the existence, continuation, and uniqueness of Filippov's solution to the system are proven. Next, the extensions of Lyapunov's stability theory to non‐smooth systems and LaSalle's invariant set theorems are employed to prove the asymptotic stability of the control system. Effectiveness of the proposed controller is verified by simulation and experimental studies. It is shown that beside stability, the system has good transparency in terms of position and force exchanges between the master and slave actuators. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method

We present an asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle using the sliding mode control method and immersion and invariance based adaptive control strategy in this paper. The control system is divided into two loops: the inner‐loop for the attitude control and the outer‐loop for the position. The sliding mode control technology is applied in the inner‐loop to compensate the unmatched nonlinear disturbances, and the immersion and invariance approach is chosen for the outer‐loop to address the parametric uncertainties. The asymptotic tracking of the position and the yaw motion is proven with the Lyapunov based stability analysis and LaSalle's invariance theorem. Real‐time experiment results performed on a hardware‐in‐the‐loop‐simulation testbed are presented to validate the good control performance of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive neural network hierarchical sliding mode control for six degrees of freedom overhead crane

This paper presents an effective control method for three-dimensional (3D) overhead cranes with six degrees of freedom (DOF). Two payload swings and an axial payload oscillation should be minimized besides driving the bridge, trolley, and hoisting drum to bring the payload to the desired position in space. First, a novel 3D-6DOF crane model is developed, where the sixth degree of freedom is axial cargo oscillation that has never been considered in previous studies. A controller is then designed using the hierarchical sliding mode control method. Moreover, a radial basis function neural network (RBFNN) is used to approximate the system's unknown dynamic model accurately. According to the Lyapunov principle, a control law and an updated law for the neural network's weight matrices are designed to ensure the stability of the closed-loop system. Simulation results on Matlab software show the proposed approach's effectiveness, such as smaller swing, minor axial oscillation, and precise position as desired.     

Hybrid Control Scheme of a Hydraulically Actuated Lower Extremity Exoskeleton for Load-Carrying

In this paper, a lower extremity exoskeleton is developed to help human beings walk and carry heavy loads. The exoskeleton is actuated by a pump-based hydraulic actuation system. The hydraulic actuation system has a high speed on/off valve and a unidirectional cylinder with embedded springs on the cylinder rod. The hybrid control scheme, including two modes, i.e., position control and following control, is proposed to drive the exoskeleton system. The position control mode is employed to support the carrying load in the stance phase. The following control mode is used to shut down the DC motor to disable the pump and open the relief valve in the swing phase. In the position control, an online Gaussian process regression algorithm is proposed to estimate the human gait trajectory using the human robot interaction signals. A general position control strategy, i.e., proportion integration differentiation (PID), is utilized to control the exoskeleton to shadow the estimated human gait trajectory. In the following control, the operator can lead the mechanical legs with the help of embedded springs on the cylinder rod. Experiments are performed on the healthy human subject, who walks on the level ground at natural speed. The experimental results demonstrate that the proposed hybrid control strategy is suitable for the pump-based hydraulically actuated lower extremity exoskeleton.     

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

This paper proposes a new state‐feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous‐bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady‐state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master–slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.     

Control‐oriented modeling and deployment of tensegrity–membrane systems

This study addresses control‐oriented modeling and control design of tensegrity–membrane systems. Lagrange's method is used to develop a control‐oriented model for a generic system. The equations of motion are expressed as a set of differential‐algebraic equations (DAEs). For control design, the DAEs are converted into second‐order ordinary differential equations (ODEs) based on coordinate partitioning and coordinate mapping. Because the number of inputs is less than the number of state variables, the system belongs to the class of underactuated nonlinear systems. A nonlinear adaptive controller based on the collocated partial feedback linearization (PFL) technique is designed for system deployment. The stability of the closed‐loop system for the actuated coordinates is studied using the Lyapunov stability theory. Because of system complexity, numerical tests are used to conduct stability analysis for the dynamics of the underactuated coordinates, which represents the system's zero dynamics. For the tensegrity–membrane systems studied in this work, analytical proof of zero dynamics stability remains an open theoretical problem. An H_∞ controller is implemented for rapid stabilization of the system at the final deployed configuration. Simulations are conducted to test the performance of the two controllers. The simulation results are presented and discussed in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition

A new approach to model order reduction of nonlinear control systems is aimed at developing persistent reduced order models (ROMs) that are robust to the changes in system's energy level. A multivariate analysis method called smooth orthogonal decomposition (SOD) is used to identify the dynamically relevant modal structures of the control system. The identified SOD subspaces are used to develop persistent ROMs. Performance of the resultant SOD‐based ROM is compared with proper orthogonal decomposition (POD)–based ROM by evaluating their robustness to the changes in system's energy level. Results show that SOD‐based ROMs are valid for a relatively wider range of the nonlinear control system's energy when compared with POD‐based models. In addition, the SOD‐based ROMs show considerably faster computations compared to the POD‐based ROMs of same order. For the considered dynamic system, SOD provides more effective reduction in dimension and complexity compared to POD.