Traditional consensus control for multiagent systems (MASs) often suffers from excessive communication burden due to continuous control input updates. This paper presents a sampled-data event-triggered (SDET) adaptive fuzzy bipartite consensus control scheme for fractional-order MASs. A fuzzy state observer is constructed to estimate unmeasurable states and unknown nonlinearities. An SDET condition integrates event errors, fuzzy weight estimates, and bipartite consensus errors. Distinct from existing input-variation-based triggering mechanisms, the proposed SDET mechanism updates and transmits the control and adaptive laws only at aperiodic sampled-data instants, significantly reducing computational and communication load. To address the nonsmooth and piecewise constant virtual control signals induced by the SDET mechanism, a fractional-order command filter is incorporated into the backstepping design, effectively eliminating the explosion of complexity and facilitating rigorous stability analysis. Within a hybrid-system framework, the boundedness of all closed-loop signals is rigorously proven, and a strictly positive lower bound on inter-event intervals is derived to exclude Zeno behavior. Simulation results on a fractional-order single-machine infinite-bus power system demonstrate the effectiveness and superiority of the proposed scheme.

Avoiding the usage of joint accelerations during robot online identification and control is significant in improving modeling and tracking accuracy. Regressor filtering is feasible to achieve acceleration-free online identification, where the robot dynamics is linearly parameterized and filtered to obtain an acceleration-free filtered regressor. Nevertheless, existing calculation methods of the filtered regressor are either applicable only to robots with low degrees of freedom (DoFs) or restricted by robot modeling techniques. We propose an acceleration-free analytical regressor filtering (AF-ARF) method to obtain the filtered regressor without restrictions on the number of DoFs or robot modeling techniques, where joint accelerations are eliminated by integration by parts, and the filtered regressor is derived by using the skew-symmetric property of the inertia matrix and some matrix operations. An acceleration-free composite learning robot control strategy based on AF-ARF is developed for exact online identification and control, where closed-loop exponential stability with parameter convergence is established under a weakened condition of interval excitation. Simulative and experimental comparisons based on a seven-DoF industrial robot have validated the superiority of our method over state-of-the-art methods in online identification, model prediction, and tracking control under reduced computing burden.

Ensuring safety is crucial to promote the application of robot manipulators in open workspaces. Factors such as sensor errors or unpredictable collisions make the environment full of uncertainties. In this work, we investigate these potential safety challenges on redundant robot manipulators, and propose a taskoriented planning and control framework to achieve multi-layered safety while maintaining efficient task execution. Our approach consists of two main parts: a task-oriented trajectory planner based on multiple-shooting model predictive control (MPC) method, and a torque controller that allows safe and efficient collision reaction using only proprioceptive data. Through extensive simulations and real-hardware experiments, we demonstrate that the proposed framework11Code is available at https://github.com/jia-xinyu/arm-safety. can effectively handle uncertain static or dynamic obstacles, and perform disturbance resistance in manipulation tasks when unforeseen contacts occur.

Controlling articulated soft robots (ASRs) driven by variable stiffness actuators (VSAs) is challenging because they are highly nonlinear and difficult to model accurately. This paper proposes an efficient neural network (NN) learning control solution for ASRs driven by agonistic-antagonistic (AA)-VSAs to guarantee tracking performance without exact robot models. Composite learning resorts to memory regressor extension to enhance adaptive parameter estimation such that parameter convergence can be guaranteed without the stringent condition of persistent excitation. In the proposed method, an NN-based controller is constructed for the position tracking of AA-VSA-driven ASRs, and an NN weight update law based on composite learning is developed to enhance online modeling and control capabilities. Experiments are carried out on an ASR with three degrees of freedom and qbmove Advance actuators (a kind of AA-VSAs), which have validated the effectiveness and superiority of the proposed method in terms of modeling and tracking accuracy compared with existing control methods.

To enhance robustness against noise resulting from velocity measurement and acceleration estimation in robot online identification and adaptive control, the robot dynamics should be filtered and parameterized to generate a filtered regression matrix regarding identifiable parameters. However, generating a filtered regression matrix is complicated for robots with high degrees of freedom (DoFs). The power balance model (PBM) of robots with spatial notations stands out as an effective option for online applications owing to its simplicity in generating an easily computed and acceleration-free filtered regression vector. This paper proposes a PBM-based recursive composite learning robot control (RCLRC) method to enhance parameter convergence so as to boost tracking control. Based on the PBM, a filtered regressor with a computational complexity of O(n) (instead of O(n2) to O(n4) for its dynamic model-based counterpart) is employed to calculate an excitation matrix, and a generalized regression equation for composite parameter update is normalized to provide more uniform convergence rates across all parameter components. Experiments on a 7-DoF robot manipulator have shown that the proposed PBM-RCLRC outperforms state-of-the-art methods on parameter estimation and tracking control.

Articulated soft robots (ASRs) driven by variable stiffness actuators (VSAs) are challenging to control well due to their highly nonlinear dynamics and difficulties in accurate modeling. The paper proposes a locally weighted learning (LWL)-based robust composite learning control (RCLC) solution for ASRs with agonistic-antagonistic (AA)-VSAs to enable the favorable tracking of both joint position and stiffness without exact robot models. In our solution, two LWL models are adopted online to estimate uncertainties in the link-side and stiffness dynamics, respectively, a nonlinear disturbance observer (DOB) is applied to improve tracking robustness at the link side, and a composite learning law is developed to achieve parameter convergence under a condition of interval excitation strictly weaker than persistent excitation so as to improve online modeling speed and accuracy. A distinctive feature of the proposed LWL-RCLC framework lies in the fact that the estimation of the DOB and the learning of LWL are independent yet work in a synergistic manner, which enables exact robot modeling online while improving tracking robustness. Experiments on a multi-DoF ASR with AA-VSAs have verified the superiority of the proposed method.

To achieve high-accuracy manipulation in the presence of unknown disturbances, we propose two novel efficient and robust motion control schemes for high-dimensional robot manipulators. Both controllers incorporate an unknown system dynamics estimator (USDE) to estimate disturbances without requiring acceleration signals and the inverse of inertia matrix. Then, based on the USDE framework, an adaptive-gain controller and a super-twisting sliding mode controller are designed to speed up the convergence of tracking errors and strengthen anti-perturbation ability. The former aims to enhance feedback portions through error-driven control gains, while the latter exploits finite-time convergence of discontinuous switching terms. We analyze the boundedness of control signals and the stability of the closed-loop system in theory, and conduct real hardware experiments on a robot manipulator with seven degrees of freedom (DoF). Experimental results verify the effectiveness and improved performance of the proposed controllers, and also show the feasibility of implementation on high-dimensional robots.

Parameter convergence in adaptive control is crucial for improving the stability and robustness of robotic systems. Nevertheless, a stringent condition named persistent excitation (PE) needs to be satisfied to ensure parameter convergence in the conventional adaptive robot control. Composite learning robot control (CLRC) is an innovative methodology that guarantees parameter convergence under a condition of interval excitation (IE) that is strictly weaker than PE. This paper puts forward a time-division multi-channel (TDMC) CLRC strategy such that parameter convergence is achieved even without the IE condition. In the TDMC mechanism, a filtered regressor is integrated with multiple time intervals to generate a generalized prediction error for parameter update, such that excitation information of regressor channels at different instants is exploited more effectively and efficiently to achieve fast and accurate parameter estimation. Global exponential stability with parameter convergence of the closed-loop system is achieved under a partial IE condition that is much weaker than IE. Experiments on a collaborative robot with 7 degrees of freedom have demonstrated the superiority of the proposed approach in both parameter estimation and trajectory tracking compared to start-of-the-art approaches.

Robot visual servoing gives the possibility of exact pose control in unstructured environments, and homography-based visual servoing (HBVS) enables 3-D control over robot end-effectors using 2-D data from cameras. However, existing methods of visual servoing usually depend on the exact information of camera and robot models. This work put forward a dynamics-based HBVS control method to achieve 3-D visual tracking under both unknown camera extrinsic and robot dynamic parameters, where exact parameter estimation is performed online by using a composite learning technique. The proposed method achieves exponential stability along with the convergence of both camera extrinsic and dynamic parameters when a weak condition known as interval excitation is satisfied. Experiments conducted with a 7-degree-of-freedom robot manipulator known as Franka Emika Panda have provided evidence that the proposed method is effective concerning parameter estimation as well as 3-D robot tracking.

Cartesian impedance control plays a significant role in improving the safety and compliance of robot end-effectors when executing collaborative tasks with humans or environments. However, achieving target impedance is challenging under uncertain robot dynamics. In this study, we raise a composite learning-based Cartesian impedance control method to ensure exact Cartesian trajectory tracking in free motion and Cartesian target impedance in interaction under uncertain robot dynamics. Introducing a composite learning update to precise robot modeling online, so the exponential convergence and passivity of the closed-loop robot dynamics are guaranteed under a weak condition known as interval excitation. The efficacy and superiority of this method have been demonstrated through experiments on a collaborative robot with 7 degrees of freedom known as Franka Emika Panda.

The ability to handle contact makes robots qualified for many complicated tasks, such as welding, hammering, and wiping. Robot cameras facilitate position planning and control without the geometric knowledge of contact surfaces since they can project contact surfaces onto a 2-dimensional image plane. However, existing hybrid vision-force control (HVFC) methods still rely on this knowledge to project the force on the constraint subspace and do not adequately leverage the redundant degrees of freedom (DoFs) for redundant robots with contact tasks. This paper proposes an enhanced HVFC solution for redundant robots equipped with an eye-to-hand camera to unify HVFC in the Cartesian space and impedance control in the joint nullspace into one closed-loop dynamics with rigorous stability guarantees. Any geometric knowledge of contact surfaces is not required by projecting the force into the redundant space of the visual task rather than the surface’s normal space. Experiments on a seven- DoF collaborative robot have verified that the proposed method is qualified for simultaneous contact tasks in the Cartesian space and compliant interaction in the joint nullspace.

In the traditional constrained control of nonlinear systems, the controller design usually requires that the initial value of the system meets certain strict conditions, and generally only considers static constraints. This article concentrates on the issue of adaptive fuzzy echo state network decentralized control for fractional-order (FO) large-scale nonlinear systems with strong interconnections and time-varying deferred constraints. With the backstepping technique, an FO fuzzy echo state network is constructed to approximate unknown nonlinear functions and interconnected terms in each step, which greatly removes some additional assumptions on unknown functions and provides a higher degree of design freedom and stronger robustness. A shifting function and an error transformation scheme are introduced to handle constraints against the unknown initial tracking condition. Moreover, the constraint conditions are satisfied within a specified time even if they are violated initially by using a time-varying barrier Lyapunov function. Especially, an equivalent definition of the bivariate convex function is given, and an inequality is constructed, which can be used to analyze the stability of FO systems by constructing a bivariate Lyapunov function. According to the FO Lyapunov stability theorem, the proposed adaptive controller can ensure that all the signals involved remain bounded and the tracking error possesses a fast convergence. Finally, an example of the FO single-machine-infinite bus power system illustrates the effectiveness of the proposed control strategy.

Time-variant quadratic programming (QP) with multi-type constraints including equality, inequality, and bound constraints is ubiquitous in practice. In the literature, there exist a few zeroing neural networks (ZNNs) that are applicable to time-variant QPs with multi-type constraints. These ZNN solvers involve continuous and differentiable elements for handling inequality and/or bound constraints, and they possess their own drawbacks such as the failure in solving problems, the approximated optimal solutions, and the boring and sometimes difficult process of tuning parameters. Differing from the existing ZNN solvers, this article aims to propose a novel ZNN solver for time-variant QPs with multi-type constraints based on a continuous but not differentiable projection operator that is deemed unsuitable for designing ZNN solvers in the community, due to the lack of the required time derivative information. To achieve the aforementioned aim, the upper right-hand Dini derivative of the projection operator with respect to its input is introduced to serve as a mode switcher, leading to a novel ZNN solver, termed Dini-derivative-aided ZNN (Dini-ZNN). In theory, the convergent optimal solution of the Dini-ZNN solver is rigorously analyzed and proved. Comparative validations are performed, verifying the effectiveness of the Dini-ZNN solver that has merits such as guaranteed capability to solve problems, high solution accuracy, and no extra hyperparameter to be tuned. To illustrate potential applications, the Dini-ZNN solver is successfully applied to kinematic control of a joint-constrained robot with simulation and experimentation conducted.

Model-based impedance learning control can provide variable impedance regulation for robots through online impedance learning without interaction force sensing. However, the existing related results only guarantee the closed-loop control systems to be uniformly ultimately bounded (UUB) and require the human impedance profiles being periodic, iteration-dependent, or slowly varying. In this article, a repetitive impedance learning control approach is proposed for physical human-robot interaction (PHRI) in repetitive tasks. The proposed control is composed of a proportional-differential (PD) control term, an adaptive control term, and a repetitive impedance learning term. Differential adaptation with projection modification is designed for estimating robotic parameters uncertainties in the time domain, while fully saturated repetitive learning is proposed for estimating time-varying human impedance uncertainties in the iterative domain. Uniform convergence of tracking errors is guaranteed by the PD control and the use of projection and full saturation in the uncertainties estimation and is theoretically proved based on a Lyapunov-like analysis. In impedance profiles, the stiffness and damping are composed of an iteration-independent term and an iteration- dependent disturbance, which are estimated by repetitive learning and compressed by the PD control, respectively. Therefore, the developed approach can be applied to the PHRI where iteration-dependent disturbances exist in the stiffness and damping. The control effectiveness and advantages are validated by simulations on a parallel robot in a repetitive following task.

This article presents a novel efficient experience-replay-based adaptive dynamic programming (ADP) for the optimal control problem of a class of nonlinear dynamical systems within the Hamiltonian-driven framework. The quasi-Hamiltonian is presented for the policy evaluation problem with an admissible policy. With the quasi-Hamiltonian, a novel composite critic learning mechanism is developed to combine the instantaneous data with the historical data. In addition, the pseudo-Hamiltonian is defined to deal with the performance optimization problem. Based on the pseudo-Hamiltonian, the conventional Hamilton-Jacobi-Bellman (HJB) equation can be represented in a filtered form, which can be implemented online. Theoretical analysis is investigated in terms of the convergence of the adaptive critic design and the stability of the closed-loop systems, where parameter convergence can be achieved under a weakened excitation condition. Simulation studies are investigated to verify the efficacy of the presented design scheme.

Traditional constraint control tends to impose indirect constraints on system states through intermediate tracking errors, so verifying the feasibility conditions is necessary, which usually results in a mismatch between actual constraint performance and constraint objectives. This article proposes an adaptive output feedback backstepping self-triggered (ST) control scheme for uncertain nonlinear fractional order systems with unilateral full state constraints and partially immeasurable states. A stable reduced-order observer is constructed to estimate immeasurable constraint system states, while ensuring that state constraints are met. Considering that event-triggered strategy requires real-time monitoring of control signals to update measurement errors, a ST scheme is proposed to avoid this drawback. Simultaneously, a new nonlinear mapping is constructed to complete the unilateral state constraint problem while satisfying the convexity condition of mapping functions. The designed controller not only avoids the Zeno behavior but also guarantees the convergence of tracking errors and the boundedness of closed-loop system signals. Finally, comparative simulation and actual case are provided to verify the validity and practical value of the proposed control strategy.

Obstacle avoidance (OA) and joint-limit avoidance (JLA) are essential for redundant manipulators to ensure safe and reliable robotic operations. One solution to OA and JLA is to incorporate the involved constraints into a quadratic programming (QP), by solving which OA and JLA can be achieved. There exist a few non-iterative solvers such as zeroing neural networks (ZNNs), which can solve each sampled QP problem using only one iteration, yet no solution is suitable for OA and JLA due to the absence of some derivative information. To tackle these issues, this paper proposes a novel solution with a non-iterative neural controller termed NCP-ZNN for joint-constrained redundant manipulators. Unlike iterative methods, the neural controller involving derivative information proposed in this paper possesses some positive features including non-iterative computing and convergence with time. In this paper, the reestablished OA-JLA scheme is first introduced. Then, the design details of the neural controller are presented. After that, some comparative simulations based on a PA10 robot and an experiment based on a Franka Emika Panda robot are conducted, demonstrating that the proposed neural controller is more competent in OA and JLA.

Zeroing neural networks (ZNNs) are powerful alternatives to solving quadratic programming (QP) for constrained control of parallel and serial robots. A recent study showed that a ZNN solver designed based on a perturbed Fischer-Burmeister function (pFB-ZNN) achieves more satisfactory performance than other ZNN solvers. The pFB-ZNN solver suffers from manual tuning of an extra hyper-parameter and may encounter residual error peaks. To tackle the above issues, this paper proposes a new Mangasarian-Solodov function-based ZNN (MS-ZNN) solver. The MS-ZNN solver has no extra hyper-parameter to be tuned and it can eliminate residual error peaks appeared in the pFB-ZNN solver, ensuring a higher solution accuracy. Mathematically, this paper details the design and convergence analysis of the MS-ZNN solver, demonstrating its convergence in the sense of Lyapunov. Numerical studies are comparatively performed, verifying the effectiveness and superiority of the MS-ZNN solver. The MS-ZNN solver is then successfully applied to kinematic control of a parallel robot and a serial robot under joint constraints. Both simulative and experimental results demonstrate that the proposed MS-ZNN solver is applicable to constrained control of parallel and serial robots with joint-limit avoidance achieved.

This article investigates positivity, external positivity, and asymptotic stability for a large class of incommensurate fractional-order nonlinear systems (FONSs) with bounded multiple time-varying delays by virtue of the T-S fuzzy method. The Laplace transformation technique is used to obtain the solutions of T-S fuzzy FONSs. A sufficient and necessary condition is derived for characterizing (internal) positivity, and certain criteria are also provided to guarantee external positivity of FONSs with or without time-varying delays. It is indicated that the positivity of the considered systems is determined purely by system matrices rather than the magnitudes of time-varying delays. Moreover, a sufficient and necessary condition for asymptotic stability of positive FONSs is obtained, and a state-feedback controller is also designed to guarantee that state variables not only converge to the origin asymptotically but also remain nonnegative, where the control gain matrix is obtained by solving an linear programming (LP) problem. Three numerical simulation examples are given to expound validity and feasibility of the theoretical results.

This article presents a control scheme for robot manipulators with the consideration of output error constraints, unknown dynamics, and bounded disturbances. A modified virtual input variable in the second stage design of the dynamic surface control scheme is proposed, which can enhance the robustness of the controller. Bounded disturbances due to the situations that the base is not well fixed if the robot manipulator is mounted at a mobile platform are considered and suppressed. Besides, the detailed implementation process of the composite learning laws adopted for enhancing the radial basis function neural network is presented. Lyapunov stability analysis verifies that the proposed control scheme ensures the trajectory tracking errors stay within predefined boundaries and parameter estimate errors converge without a stringent condition termed persistent excitation. Experimental results show the superiority of the proposed controller regarding parameter estimation and tracking capabilities.

Variable impedance control has been considered as one of the most important compliant control approaches for its abilities in improving compliance, safety, and efficiency in robot-environment interaction. However, existing variable impedance controllers have deficits in stability guarantee. This article proposes a stability-guaranteed variable impedance control approach for robots with modeling uncertainties based on approximate dynamic inversion (ADI). Novel constraints on variable impedance profiles are given to guarantee the exponential stability of the desired variable impedance dynamics. An ADI-based impedance control law is designed to achieve the desired variable impedance dynamics through the convergence of a variable impedance error. Based on the extended Tikhonovs theorem, it is proven that the closed-loop control system has semiglobal practical exponential stability. The proposed impedance controller can be implemented in a PID form and is appealing for its simple structure, easy implementation, and control stability guarantee. The effectiveness of the proposed variable impedance controller is illustrated by an illustrative example taken on a five-bar parallel robot.

Adaptive dynamic surface control (ADSC) is effective for solving the complexity problem in adaptive backstepping control of integer-order nonlinear systems. This article focuses on the ADSC design for parametric uncertain fractional-order nonlinear systems (FONSs). In each backstepping step, the virtual controller is driven to pass through a fractional dynamic surface whose fractional-order derivative can be calculated easily. An ADSC law that ensure tracking error convergence is designed. The proposed ADSC requires a stringent condition called persistent excitation (PE) to achieve parameter convergence. To relax this limitation, a prediction error is defined by using online recorded data and instantaneous data, and a composite learning law is proposed to utilize both the prediction error and the tracking error. Then, a composite learning ADSC (CLADSC) method is developed to guarantee tracking error convergence and accurate parameter estimation under an interval excitation condition that is weaker than the PE one. Finally, an illustrative example is presented to show the performance of our methods.

In recent times, with the incremental demand for fully autonomous systems, research interests are observed in learning machine-based intelligent, self-organizing, and evolving controllers. In this paper, a new evolving and self-organizing controller, namely generic-controller (G-controller), is proposed. The G-controller works in a fully online mode with minor expert domain knowledge. It is developed by incorporating the sliding mode control (SMC) theory with an advanced incremental learning machine, namely generic evolving neuro-fuzzy inference system. The controller starts operating from scratch with an empty set of fuzzy rule, and therefore, no offline training is required. To cope with the changing dynamic characteristics of the plant, the controller can add or prune the rules on demand. Control law and adaptation laws for the consequent parameters are derived from the SMC algorithm to establish a stable closed-loop system, where the stability of the G-controller is guaranteed by using the Lyapunov function. The uniform asymptotic convergence of tracking error to zero is witnessed through the implication of an auxiliary robustifying control term. In addition, the implementation of the multivariate Gaussian function helps the controller to handle the nonaxis parallel data from the plant and consequently, enhances the robustness against uncertainties and environmental perturbations. Finally, the controller's performance has been evaluated by observing the tracking performance in controlling simulated plants of unmanned aerial vehicle, namely bio-inspired flapping wing micro air vehicle and hexacopter for a variety of trajectories.

Backstepping control for fractional-order nonlinear systems (FONSs) requires the analytic calculation of fractional derivatives of certain complicated stabilizing functions, which becomes prohibitive as the order of the system increases. This article aims to facilitate the adaptive neural network (NN) backstepping control design for FONSs with actuator faults whose parameters and patterns are fully unknown. A fractional filtering approach, which obviates the requirement of analytic fractional differentiation, is used to generate command signals together with their fractional derivatives. Compensated tracking errors that can eliminate approximation errors of command signals are generated by fractional filters. The proposed adaptive NN command filtered backstepping control (ANNCFBC) approach, together with fractional adaptive laws, guarantees not only the boundedness of all involved variables but also the convergence of both the tracking error and the compensated tracking error to a sufficiently small region. Finally, simulation studies are given to indicate the effectiveness of the proposed control method.

The desired impedance dynamics can be achieved for a robot if and only if an impedance error converges to zero or a small neighborhood of zero. Although the convergence of impedance errors is important, it is seldom obtained in the existing impedance controllers due to robots modeling uncertainties and external disturbances. This brief proposes two composite learning impedance controllers (CLICs) for robots with parameter uncertainties based on whether a factorization assumption is satisfied or not. In the proposed control designs, the convergence of impedance errors, reflected by the convergence of parameter estimation errors and some auxiliary errors, is achieved by using composite learning laws under a relaxed excitation condition. The theoretical results are proven based on the Lyapunov theory. The effectiveness and advantages of the proposed CLICs are validated by simulations on a parallel robot in three cases.

In this paper, identification and control for a class of nonlinear systems with unknown constant or variable control gains are investigated. By reformulating the original system dynamic equation into a new form with a unit control gain and introducing a set of filtered variables, a novel neural network (NN) estimator is constructed and a new estimation error is used to update the augmented weights. Based on the identification results, two singularity-free NN indirect adaptive controllers are developed for nonlinear systems with unknown constant control gains or variable control gains, respectively. Because the singularity problem is eradicated, the proposed methods remove limitations on parameter estimates that are used to guarantee the positiveness of the estimated control gain. Consequently, a more accurate estimation result can be achieved and the system state can track the given reference signal more precisely. The effectiveness of the proposed identification and control algorithms are tested and the superiority of the proposed singularity-free approach is demonstrated by simulation results.

Emerging applications of robots with direct physical interactions with humans have led to the development of a variety of series elastic actuators (SEAs) which are compliant, force controllable, and back drivable. The performance of current SEAs is mainly dependent on the specific stiffness of the spring. In our previous work, a compliant actuator with two-stage stiffness has been designed to overcome the performance limitations in current SEAs. The key novelty is that a low-stiffness spring and a high-stiffness spring are employed instead of a single spring in current SEAs, which has the advantages of high fidelity, low output impedance, and also large force range and bandwidth. In this paper, a tracking control scheme is proposed for the compliant actuator with two-stage stiffness. Although the overall stiffness is discontinuous, the proposed controller is continuous by integrating different control modes for two springs into a single one. The transition between control modes is smooth and embedded inside the controller, and it is also automatically realized by monitoring the output force of the actuator. The stability and convergence of the closed-loop system are analyzed, and experimental results are presented to demonstrate the effectiveness of the proposed control scheme.Note to Practitioners—An SEA is developed by placing an elastic element into the actuator; this elasticity gives SEAs several unique properties including low mechanical output impedance, tolerance to impact loads, and passive mechanical energy storage, which makes it suitable for human–robot interaction. The performance of existing SEAs is highly dependent on the stiffness of a single spring. To overcome the limitations, a novel SEA with two-stage stiffness was proposed in our previous work. This paper suggests a continuous tracking control method for the proposed compliant actuator. Although the overall stiffness is discontinuous, the transition between different control modes for two springs is smooth and automatically realized. Experimental results show that the output force of the actuator is bounded. In future research, uncertainties in actuator dynamics will be considered, such that system identification or calibration is not required.

Sliding mode control (SMC) is attractive for nonlinear systems due to its invariance for both parametric and nonparametric uncertainties. However, the invariance of SMC is not guaranteed in a reaching phase. Integral SMC (ISMC) eliminates the reaching phase such that the invariance is achieved in an entire system response. To reduce chattering in ISMC, it was suggested that the switching element is smoothed by using a low-pass filter and an integral sliding variable is modified. This study discusses several crucial problems regarding the performance, modification, and improvement of ISMC. First, the modification of the integral sliding variable is revealed to be unnecessary as it degrades the performance of a sliding phase; second, ISMC is shown to be a kind of global SMC; third, it is manifested that a high-order ISMC design with super twisting involves a stability condition that may be infeasible in theory; finally, an efficient solution is suggested to attenuate chattering in ISMC without the degradation of tracking accuracy and the solution is extended to the case with uncertain control gain functions. Comprehensive simulation results have verified the arguments of this study.

This paper investigates the online recorded data-based composite neural control of uncertain strict-feedback systems using the backstepping framework. In each step of the virtual control design, neural network (NN) is employed for uncertainty approximation. In previous works, most designs are directly toward system stability ignoring the fact how the NN is working as an approximator. In this paper, to enhance the learning ability, a novel prediction error signal is constructed to provide additional correction information for NN weight update using online recorded data. In this way, the neural approximation precision is highly improved, and the convergence speed can be faster. Furthermore, the sliding mode differentiator is employed to approximate the derivative of the virtual control signal, and thus, the complex analysis of the backstepping design can be avoided. The closed-loop stability is rigorously established, and the boundedness of the tracking error can be guaranteed. Through simulation of hypersonic flight dynamics, the proposed approach exhibits better tracking performance.

Teleoperated robot systems are able to support humans to accomplish their tasks in many applications. However, the performance of teleoperation largely depends on motor functionality and human operator's skill, especially when a human operator is short of skill training. In order to adapt to various unstructured environments for the robot system and the human operator, in this paper, a teleoperation scheme using integrated tremor attenuation with a variable gain control algorithm involving surface electromyogram is proposed to achieve personalized control performance and to reduce reliance on operator's skill. For attenuating tremor, a filter based on support vector machine is developed to guarantee normal operation. This filter depends on the machine learning scheme and does not rely on a priori filter parameters. Semiphysical experiments have been performed to demonstrate the effectiveness of the proposed methods.

This brief presents a biomimetic hybrid feedback feedforward neural-network learning control (NNLC) strategy inspired by the human motor learning control mechanism for a class of uncertain nonlinear systems. The control structure includes a proportional-derivative controller acting as a feedback servo machine and a radial-basis-function (RBF) NN acting as a feedforward predictive machine. Under the sufficient constraints on control parameters, the closed-loop system achieves semiglobal practical exponential stability, such that an accurate NN approximation is guaranteed in a local region along recurrent reference trajectories. Compared with the existing NNLC methods, the novelties of the proposed method include: 1) the implementation of an adaptive NN control to guarantee plant states being recurrent is not needed, since recurrent reference signals rather than plant states are utilized as NN inputs, which greatly simplifies the analysis and synthesis of the NNLC and 2) the domain of NN approximation can be determined a priori by the given reference signals, which leads to an easy construction of the RBF-NNs. Simulation results have verified the effectiveness of this approach.

Series elastic actuators (SEAs) are known to offer a range of advantages over stiff actuators for human–robot interaction, such as high force/torque fidelity, low impedance, and tolerance to shocks. While a variety of SEAs have been developed and implemented in initiatives that involve physical interactions with humans, relatively few control schemes were proposed to deal with the dynamic stability and uncertainties of robotic systems driven by SEAs, and the open issue of safety that resolves the conflicts of motion between the human and the robot has not been systematically addressed. In this paper, a novel continuous adaptive control method is proposed for SEA-driven robots used in human–robot interaction. The proposed method provides a unified formulation for both therobot-in-chargemode, where the robot plays a dominant role to follow a desired trajectory, and thehuman-in-chargemode, in which the human plays a dominant role to guide the movement of robot. Instead of designing multiple controllers and switching between them, both typical modes are integrated into a single controller, and the transition between two modes is smooth and stable. Therefore, the proposed controller is able to detect the human motion intention and guarantee the safe human–robot interaction. The dynamic stability of the closed-loop system is theoretically proven by using the Lyapunov method, with the consideration of uncertainties in both the robot dynamics and the actuator dynamics. Both simulation and experimental results are presented to illustrate the performance of the proposed controller.

Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.

This paper investigates the disturbance observer-based composite fuzzy control of a class of uncertain nonlinear systems with unknown dead zone. With fuzzy logic system approximating the unknown nonlinearities, composite learning is constructed on the basis of a serial–parallel identifier. By introducing the intermediate signal, the disturbance observer is developed to provide efficient learning of the compounded disturbance which includes the effect of time-varying disturbance, fuzzy approximation error, and unknown dead zone. Based on the disturbance estimation and fuzzy approximation, the adaptive fuzzy controller is synthesized with novel updating law. The stability analysis of the closed-loop system is rigorously established via Lyapunov approach. The performance of the proposed controller is verified via simulation that faster convergence and higher precision are obtained.

Series elastic actuators (SEAs) are known to offer a number of advantages such as high force/torque fidelity, low impedance, and tolerance to shocks, which make it suitable for the applications involving human-robot interaction. In existing SEA-driven robot systems, the control objective is usually specified as a predefined trajectory or an impedance model that describes the relationship between the desired motion of robot and the external force, and controllers are always activated to regulate the desired motion or the desired impedance model. In this paper, a region control scheme is proposed for robots driven by SEAs, where the control objective is specified as a region, instead of trajectory or desired impedance. The region control has the advantage of flexibility, in the sense that the robot is able to move freely inside the desired region and thus compliant with the environment or physical interactions with humans. Though the overall dynamics that includes both actuator and robot dynamics is a fourth-order system, the proposed control method does not require the high-order derivatives or the construction of any observer. Experimental results are presented to demonstrate the effectiveness of the proposed control method.

It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine nonlinear systems. Variable-gain PD control is designed to globally stabilize the plant. An optimal FAE is shown to be bounded by the norm of the plant state vector multiplied by a globally invertible and nondecreasing function, which provides a pivotal property for stability analysis. Without discontinuous control compensation, the closed-loop system achieves global and partially asymptotic stability in the sense that all plant states converge to zero. Compared with previous adaptive approximation-based global/asymptotic stabilization approaches, the major advantage of our approach is that global stability and asymptotic stabilization are achieved concurrently by a much simpler control law. Illustrative examples have further verified the theoretical results.

High-gain observers have been extensively applied to construct output-feedback adaptive neural control (ANC) for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle. Yet due to static-gain and linear properties, high-gain observers are usually subject to peaking responses and noise sensitivity. Existing adaptive neural network (NN) observers cannot effectively relax the limitations of high-gain observers. This paper presents an output-feedback indirect ANC strategy under a nonseparation principle, where a hybrid estimation scheme that integrates an adaptive NN observer with state variable filters is proposed to estimate plant states. By applying a single Lyapunov function candidate to the entire system, it is proved that the closed-loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters. Our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability. Simulation results have shown effectiveness and superiority of this approach.

This paper studies both indirect and direct global neural control of strict-feedback systems in the presence of unknown dynamics, using the dynamic surface control (DSC) technique in a novel manner. A new switching mechanism is designed to combine an adaptive neural controller in the neural approximation domain, together with the robust controller that pulls the transient states back into the neural approximation domain from the outside. In comparison with the conventional control techniques, which could only achieve semiglobally uniformly ultimately bounded stability, the proposed control scheme guarantees all the signals in the closed-loop system are globally uniformly ultimately bounded, such that the conventional constraints on initial conditions of the neural control system can be relaxed. The simulation studies of hypersonic flight vehicle (HFV) are performed to demonstrate the effectiveness of the proposed global neural DSC design.

Rehabilitation robots, by necessity, have direct physical interaction with humans. Physical interaction affects the controlled variables and may even cause system instability. Thus, human-robot interaction control design is critical in rehabilitation robotics research. This paper presents an interaction control strategy for a gait rehabilitation robot. The robot is driven by a novel compact series elastic actuator, which provides intrinsic compliance and backdrivablility for safe human-robot interaction. The control design is based on the actuator model with consideration of interaction dynamics. It consists mainly of human interaction compensation, friction compensation, and is enhanced with a disturbance observer. Such a control scheme enables the robot to achieve low output impedance when operating in human-in-charge mode and achieve accurate force tracking when operating in force control mode. Due to the direct physical interaction with humans, the controller design must also meet the stability requirement. A theoretical proof is provided to show the guaranteed stability of the closed-loop system under the proposed controller. The proposed design is verified with an ankle robot in walking experiments. The results can be readily extended to other rehabilitation and assistive robots driven with compliant actuators without much difficulty.

This paper presents a biomimetic hybrid feedback feedforword (HFF) adaptive neural control for a class of robotic arms. The control structure includes a proportional-derivative feedback term and an adaptive neural network (NN) feedforword term, which mimics the human motor learning and control mechanism. Semiglobal asymptotic stability of the closed-loop system is established by the Lyapunov synthesis. The major difference of the proposed design from the traditional feedback adaptive approximation-based control (AAC) design is that only desired outputs, rather than both tracking errors and desired outputs, are applied as NN inputs. Such a slight difference leads to several attractive properties, including the convenient NN design, the decrease of the number of NN inputs, and semiglobal asymptotic stability dominated by control gains. Compared with previous HFF-AAC approaches, the proposed approach has two unique features: 1) all above attractive properties are achieved by a much simpler control scheme; 2) the bounds of plant uncertainties are not required to be known. Simulation results have verified the effectiveness and superiority of this approach.

This paper proves that adaptive neural plus proportional-derivative (PD) control can lead to semiglobal asymptotic stabilization rather than uniform ultimate boundedness for a class of uncertain affine nonlinear systems. An integral Lyapunov function-based ideal control law is introduced to avoid the control singularity problem. A variable-gain PD control term without the knowledge of plant bounds is presented to semiglobally stabilize the closed-loop system. Based on a linearly parameterized raised-cosine radial basis function neural network, a key property of optimal approximation is exploited to facilitate stability analysis. It is proved that the closed-loop system achieves semiglobal asymptotic stability by the appropriate choice of control parameters. Compared with previous adaptive approximation-based semiglobal or asymptotic stabilization approaches, our approach not only significantly simplifies control design, but also relaxes constraint conditions on the plant. Two illustrative examples have been provided to verify the theoretical results.

This paper certifies that standard adaptive fuzzy control (AFC) can guarantee asymptotic stabilization performance rather than uniformly ultimately boundedness (UUB) even in the presence of fuzzy approximation errors (FAEs). Under a direct AFC scheme, the resulting optimal FAE is shown to be bounded by the norm of the plant state vector multiplying a globally invertible and nondecreasing function, which provides a pivotal property for asymptotic stability analysis. Without any additional control compensation, the closed-loop system is proved to be partially and asymptotically stable in the sense that all involved signals are UUB and the plant state variables converge to zero. The resulting control law is certainly continuous since it only contains an adaptive fuzzy system. Compared with previous adaptive approximation-based asymptotic stabilization approaches, the proposed approach not only simplifies control design, but also relaxes constraint conditions on the controlled plant. A simulation example of inverted pendulum control is provided to verify the discovery of this study.

In this paper, an enhanced adaptive fuzzy control (AFC) strategy with guaranteed convergence of an optimal fuzzy approximation error (FAE) is presented for a class of uncertain nonlinear systems in the general Brunovsky form. Based on the fuzzy logic system (FLS) with variable universes of discourse, relaxed sufficient conditions that guarantee the optimal FAE being convergent are given, and the upper bound of the optimal FAE is obtained. The control singularity problem resulting from the unknown affine term is resolved by a novel fuzzy approximation equation, and the parameter adaptive law of the FLS is derived by the Lyapunov synthesis. By means of the optimal FAE bound result, it is proved that the closed-loop system achieves partially asymptotic stability under a certain selection of control parameters. The proposed approach retains all advantages of a previous similar approach under relaxed constraint conditions. Thus, it provides a more flexible solution to the AFC with optimal FAE convergence. Simulation studies have demonstrated high-precision tracking performance with smooth control input of the proposed approach.

With no a priori knowledge of plant boundary functions, a novel direct adaptive fuzzy controller (AFC) for a class of single-input single-output (SISO) uncertain affine nonlinear systems is developed in this paper. Based on the theory of fuzzy logic systems (FLSs) with variable universes of discourse (UDs), sufficient conditions that guarantee that the optimal fuzzy approximation error (FAE) is locally convergent are given. By the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters, a variable UD FLS with an optimal FAE local convergence is constructed, and its parameter adaptive law is derived by virtue of the Lyapunov stability theorem. Under the assumption that the optimal FAE is bounded, it is proved that the closed-loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero. The proposed approach eliminates the influence of the FAE on the tracking errors by means of the inherent mechanism of the variable UD FLS. Thus, it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules. Simulation studies demonstrate the superiority of the proposed AFC in terms of the settling time, tracking accuracy, smoothness of the control input, and robustness against external disturbances and parameter variations.