In a rehabilitation exoskeleton, stable and safe operation is of central importance in rehabilitation training. This article develops a soft prescribed performance (SPP)-based reinforcement learning (RL) control method to address the conflict between performance constraints and system degradation, ensuring high accuracy and safe operation. First, a tunnel-type prescribed performance function is used to achieve faster convergence and smaller overshoot. Safety boundaries are used to define the tolerable error range, and an intermediate system links the safety and soft boundaries. The soft boundaries are dynamically adjusted to ensure safe operation by temporarily relaxing constraints during performance degradation. An RL approach based on an actor-critic (AC) structure is employed to handle unknown lumped disturbance. Theoretical analysis confirms the stability of the closed-loop system. Furthermore, a series of experiments is conducted on a self-built upper-limb rehabilitation exoskeleton robot driven by pneumatic artificial muscles to validate the effectiveness and robustness of the proposed method.

This article proposes a trajectory tracking strategy for nonuniform quay cranes to suppress flexible cable vibration and attenuate payload swing and rotation, thereby improving tracking accuracy and transport efficiency. To address the challenges posed by time-varying and spatially distributed partial differential equation models, we propose a Bayesian physics-informed neural network (BPINN) framework that integrates tension constraints into the loss function to suppress flexible cable vibrations. In the Bayesian setting, the BPINN acts as a prior model, and Hamiltonian Monte Carlo (HMC) sampling is employed to infer the posterior distribution of the system states. To handle the underactuated nature of the quay crane, differential flatness is exploited to map BPINN-predicted states into a flat output space, where an adaptive backstepping controller is designed to guarantee global uniform ultimate boundedness. Moreover, a multistrategy improved quantum-behaved particle swarm optimization (MIQPSO) scheme is introduced for online tuning of control parameters, achieving a favorable tradeoff between global exploration and fast convergence. Lyapunov analysis establishes closed-loop stability, and simulations and experiments demonstrate fast and accurate tracking as well as robust vibration suppression under external disturbances.

Antagonistic pneumatic muscle (PM)-actuated wrist robots have great potential in rehabilitation and industrial applications. The antagonistic connection of PMs, which mimics the agonist-antagonist muscle pairs in human joints, provides substantial advantages such as improved joint stability and a better balance of torque disturbances. However, PM-actuated robots exhibit complex nonlinearities, such as hysteresis, creep, input delay, and time-varying parameters, while also confronting challenges such as external disturbances and coupling effects. In this paper, a switching non-singular terminal sliding mode control (NTSMC) method with a double-loop fuzzy neural network (DLFNN) is developed. This method enables the antagonistic PM-actuated wrist robots to achieve fast and precise tracking performance. Specifically, the lumped disturbances are estimated online using the DLFNN, which can adaptively adjust the weight of the inner and outer layers, achieving accurate approximation and robustness. Based on the estimated value of disturbances, a switching NTSMC is implemented to ensure that tracking errors converge to the origin within the fixed time. Switching functions guarantee fast convergence when the sliding surface errors are large. Meanwhile, switching functions ensure non-singularity as the sliding surface errors converge to the origin. Furthermore, joint angles and angular velocities are limited within the specific ranges by designing exponential constraint terms as time-varying proportional-differential gains, rather than traditional barrier functions that may induce excessive control inputs. Both detailed stability analysis and experimental validation demonstrate the effectiveness and adaptability of the proposed method.

By mimicking the movement of biological muscles, pneumatic artificial muscles (PAMs) are developed as a novel type of bionic actuator known for their compliance and high safety; however, the inherent characteristics of PAMs (e.g., hysteresis and creep) increase the difficulty in modeling and control. Moreover, unmodeled dynamics in PAM-actuated parallel robots are unavoidable, which further complicates the efficient tracking task of PAM-actuated parallel robots. Therefore, we propose an output feedback controller with interval type-2 fuzzy neural networks (IT2FNNs) for PAM-actuated parallel robots to obtain satisfactory tracking results. Specifically, compared with most existing methods using the interval type-1 fuzzy neural network (NN), the IT2FNN used is more beneficial for dealing with unmodeled dynamics and system uncertainties on PAM-actuated parallel robots. Meanwhile, considering that most practical systems are often only equipped with displacement/angle sensors and lack velocity sensors, an observer is designed to estimate unmeasurable velocity signals. Next, based on Lyapunov techniques, the convergence of tracking errors is proven through theoretical analysis. To our knowledge, this article is the first to apply IT2FNNs with observation information to PAM-actuated parallel robots with unknown dynamics and unmeasurable velocity signals, and provides rigorous stability analysis. Further, several experiments are implemented, and the corresponding results illustrate the effectiveness and robustness of the proposed controller.

Pneumatic artificial muscle (PAM) actuators have passive compliance and vibration absorption capabilities, adapting to high-intensity human-robot interaction movements. Unfortunately, the asymmetric hysteresis of PAMs is prone to produce motion delays and control inaccuracy, and anti-disturbance control is not friendly when applied in exoskeleton robots. Also, most of existing studies on active compliant control are overly reliant on bulky force-sensing, which is limited by sampling accuracy and communication rate. Therefore, it is still a challenge to realize compliant motions of PAM systems, while ensuring the rapid convergence of output signals. To this end, a new practical finite-time compliant controller is designed in this paper, which realizes satisfactory tracking control of horizontal PAM systems. Specifically, the external contact force is estimated by an improved adaptive law, instead of sensor feedback, thus decreasing noise effects. Meanwhile, the proposed controller ensures that the output tracking error converges quickly within known finite time, while reducing computational complexity. In particular, the desired trajectory is updated in real time by a modified admittance model, so as to achieve motion compliance and interaction safety. Compared with the literature, it is the first attempt to provide a compliant control solution for horizontal PAM systems without force feedback information, and ensures the practical finite-time convergence of the output tracking error. The rigorous stability analysis is presented, and the reliability of the proposed method is verified by hardware experiments. Note to Practitioners—Owing to light weight and flexibility, pneumatic artificial muscle (PAM) actuators can better meet the growing demands of human-machine cooperation tasks. In areas such as power assist and rehabilitation training equipment, it is necessary to ensure that robots can properly adjust the motion trajectory according to the applied force, so as to replace unbearable “hard contact” with more dexterous “compliant interaction”. Inspired by this, a new compliant control method is designed in this paper for horizontal PAM systems, which realizes the online adjustment of desired motion trajectories according to contact forces, and ensures the rapid convergence of the tracking error within known finite time. In particular, the proposed method improves an efficient contact force estimation solution, avoiding bulky and expensive force-sensing, while reducing noise effects. Compared with existing results, this paper for the first time presents a compliant control method without sensor feedback of horizontal PAM systems, and improves the motion rapidity, accuracy, and stability in practical tracking and training cases. Meanwhile, rigorous stability analysis is provided by Lyapunov techniques, and the effectiveness of the proposed method is verified by experiments on a self-built PAM testbench. In the future, we will try to apply the proposed method to limb functional training scenarios, aiming to expand its practical prospects and increase efficiency.

Underactuated robot systems, due to their unique flexibility and economy, are widely used in modern industry and intelligent manufacturing. However, their underactuated nature and complex nonlinearity make the control problem challenging. In addition, most existing control methods for underactuated systems take the measurable actuated and unactuated states as an implicit premise and do not consider the unknown measurement sensitivity of sensors. Unfortunately, due to space/costs or manufacturing technology limitations in practical underactuated robot systems, it is difficult to measure unactuated states and achieve the ideal working mode of sensors. To this end, an adaptive fuzzy control scheme is proposed for a class of uncertain underactuated robot systems without unactuated state sensors, which stabilizes the system even with actuated state measurement errors. Specifically, the dynamics of underactuated systems are reconstructed into a nontriangular normal form, and the backstepping design is completed by using the boundedness of fuzzy basis functions. At the same time, the explosion of complexity is avoided by using dynamic surface control technology. Moreover, the proposed update law availably compensates parameter/structure uncertainties for underactuated robot systems. The asymptotic stability of the closed-loop system is proved by incorporating Lyapunov candidates with sensitivity information. Finally, the proposed control scheme is applied to a tower crane system, whose effectiveness is verified by hardware experiments.Note to Practitioners—This paper is motivated by the common sensor problems in uncertain underactuated robot systems control. Some states in underactuated systems are called unactuated states because they have no direct corresponding control inputs. Such states bring significant challenges to controllers design of underactuated systems. Furthermore, most existing control methods require all states to be measurable and ignore the measurement uncertainty of sensors. However, in many practical situations, it is difficult to install unactuated state sensors, and there are inevitable measurement errors in actuated state sensors. These factors make the feedback controllers developed for underactuated systems difficult to practically apply. To address these issues, this paper presents a control scheme that does not require unactuated state measurements and model information, which can still stabilize underactuated systems to the origin even in the presence of actuated state measurement errors. The stability is rigorously proven theoretically and the experimental results obtained on a self-built tower crane platform demonstrate the feasibility and effectiveness of the proposed control scheme. In future efforts, we intend to apply the proposed control scheme to practical industrial underactuated robot systems.

The control problem of underactuated mechatronic systems is one of the key representatives of complex nonlinear dynamical systems. Starting from the dynamical structures of underactuated systems is usually one of the most direct and effective ways to design controllers. However, controllers developed for specific dynamic models are often difficult to be directly generalized to other underactuated systems. Moreover, due to the lack of control inputs, designing robust controllers for unmatched disturbances (acting on unactuated states) remains a challenging problem. Therefore, based on the Euler-Lagrange dynamics of multi-input-multi-output (MIMO) underactuated systems, this paper gives four coordinate transformations according to different configurations of the inertia matrix, whichextendsthe Olfati transformation to some extent and finallyunifiesunderactuated systems into normal forms. A sliding manifold and an adaptive neural network sliding mode controller are developed with the derived normal forms, which improves transient performance andavoidsthe chattering problem in traditional sliding mode controllers by combining an estimation error-driven adaptive law, a high-order sliding-mode differentiator, and the super-twisting algorithm. More importantly, the stability is guaranteed by Lyapunov techniques even in the presence ofbothpersistent matched disturbances and asymptotically vanishing unmatched disturbances. Furthermore, the proposed control strategy is applied to overhead cranes and tower cranes, whose superior control performance is verified by hardware experiments.

As a kind of soft actuator with inherent compliance, pneumatic artificial muscles (PAMs) have great application potential in robots. However, some challenging issues, such as high nonlinearities, sensor noises, and external disturbances, inevitably bring enormous difficulties to the accurate control of PAM-driven robots. To this end, this paper proposes an adaptive output feedback fuzzy switching control method for switched-form PAM-driven parallel robot systems, utilizing admittance models to rebuild compliant trajectories. Specifically, based on the nonrecursive high-order sliding mode (HOSM) differentiators with fixed-time convergence, unmeasurable velocity signals can be reconstructed to eliminate the adverse effects of measurement noises, decreasing the time delay of feedback signals. Moreover, a soft switching strategy is designed to flexibly adjust the switching weights and intervals of fuzzy structures, maintaining smooth control commands. Further, by introducing a nonsingular terminal sliding manifold, tracking errors can rapidly converge to a small neighborhood around the origins within a finite time, and all closed-loop variables are proved to be bounded through the Lyapunov stability theory. Finally, several groups of experiments are carried out on a self-built PAM-driven parallel robot to verify the effectiveness of the suggested method.

Mechanical systems often face unpredictable surrounding situations in applications, which bring lots of intangible uncertainties into system operations. Further, some robot systems, especially, pneumatic artificial muscle (PAM)-driven robot systems, also have accumulative nonlinearities, such as rate-dependent hysteresis, creep, and periodic/regular time-varying parameters, increasing design difficulties of high-accuracy controllers. This paper develops a long short-term memory neural network (LSTM-NN)-enhanced adaptive controller for PAM-driven parallel robot systems with transient and steady-state performance constraints. Specifically, a continuous-time LSTM-NN structure is introduced to recover unknown lumped dynamics, improving the approximation ability of time-dependent terms with accumulative effects. Moreover, a new two-stage error transformation function is designed to flexibly adjust the desired transient and steady-state performance, facilitating better adaptation to task requirements. To our knowledge, this paper proposes the first solution of utilizing the LSTM-NN-based neuroadaptive method for soft actuator-driven robots to enhance tracking accuracy with transient/steady-state performance improvement. The detailed stability analysis and several groups of experimental results on the self-built platform are provided to verify the feasibility and versatility of the proposed method.

Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with nonsmooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this article, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle, respectively, for which numerical simulations are also performed.

In practice, many mechanical systems are underactuated, such as naval vessels, cranes, and helicopters, to reduce energy consumption and enhance flexibility. However, compounded by strong nonlinearity arising from state coupling, the underactuated nature and high-order unavailable states pose great challenges to motion control (particularly for unactuated states lacking independent actuators or kinematic constraints). In this article, an adaptive controller based on fully-actuated system methods is proposed, together with a general and extensible analysis method. First, a group of high-order auxiliary variables, consisting of actuated/unactuated states, their derivatives, and proportional-differential terms, are designed to rearrange the nonlinear underactuated system as a high-order linear fully-actuated system without any linearization operations. The asymptotic convergence of auxiliary variables theoretically eliminates the steady-state errors of actuated/unactuated states together. For high-order unmeasurable variables, they are recovered by the constructed neural network observer to estimate high-order dynamics, which avoids discontinuous robust terms and improves the accuracy of compensation/positioning. Motivated by the inherent features and advantages of fully-actuated systems, this article proposes the first fully-actuated system-based continuous adaptive controller for a class of underactuated robots. Moreover, it is convenient to extend the proposed controller to handle more practical problems, such as state delay, without the need to reconduct Lyapunov-based analysis. In addition to complete theoretical frames, this article also provides several experimental validation.

Underactuated systems are a class of systems in which the number of control inputs is less than the degrees of freedom (DoFs) to be controlled. With the increasing demand for the control performance of underactuated systems, the current research on their optimization of steady-state performance is no longer sufficient. However, owing to limited control inputs, ensuring their transient performance is often difficult. Moreover, some specific composite variables in underactuated systems should be kept within the preset ranges, which poses a significant challenge to collision avoidance safety. In addition, the sensor noises are also an issue that cannot be ignored. To this end, an extended Kalman filtering-based nonlinear model predictive control method for underactuated systems is developed in this article. The key feature of this method is that it simultaneously ensures accurate positioning, multiple constraints, and obstacle avoidance. Specifically, by adding an artificial potential field as an obstacle avoidance penalty term in the cost function and dynamically assigning weight coefficients, efficient collision avoidance control is achieved. Furthermore, it is combined with the extended Kalman filtering and jointly applied to underactuated systems with sensor noises. To the best of our knowledge, it is the first control method that simultaneously considers full-state constraints, specific composite variable constraints, control input and its increment constraints, as well as obstacle avoidance in underactuated systems. The satisfactory control performance of the proposed method is validated by implementing it on two typical underactuated systems, that is, four-DoF overhead cranes and five-DoF tower cranes.

In this paper, an observer-based gain-scheduling tracking control scheme is designed for cyber-physical active suspension systems (ASSs) with uncertainties and external disturbances. Firstly, a fuzzy suspension model is established based on interval type-2 (IT-2) fuzzy rules to capture the nonlinearity and uncertainty of ASSs. Then, considering that it is difficult to obtain the state information of the suspension system in the complex environment, a co-design method based on the high-order free-weighting gain-scheduling (HFG) control law is proposed. At the same time, a class of Lyapunov functions and slack variable techniques, which are homogeneous polynomial parameter-dependent, are designed to simplify the stability analysis of ASSs. Furthermore, under the premise of satisfying the$H_{\infty }$performance index, the exponential stability of the augmented error system under randomly activated network attacks is realized. Finally, the performance of the proposed control scheme is evaluated by numerical and hardware-in-loop (HIL) tests.

This study concentrates on adaptive prescribed-time tracking control forn-link flexible-joint (FJ) manipulators with unmeasurable state variables. First of all, auxiliary signals are constructed utilizing measurable variables. Based on auxiliary signals, the observer is directly designed to estimate the system states, which allows the observer dynamics to incorporate unknown terms. Owing to the uniqueness of the designed observer, the observation errors converge to zero. Furthermore, with the aim of enhancing control efficiency, the prescribed-time scale function is introduced into the controllers, and the unknown terms are processed based on the fuzzy logic system (FLS), so that the tracking error of FJ manipulators converges to the specified range within the prescribed time. Meanwhile, with the help of positive integrable time-varying functions, asymptotic tracking is further achieved. In the whole control design, the tuning functions are adopted to avoid overparameterization. In theory, it is ensured that all signals in the closed-loop system are bounded, and the tracking error converges to the small neighborhood of the zero within a specified time and gradually converges to zero. Finally, the simulation example confirms the feasibility of the control design.

Collaborative double boom cranes (CDBCs) play a crucial role in modern industries, offering superior hoisting capabilities and adaptability. However, the intricate dynamic characteristics of CDBCs, combined with demanding working requirements, pose significant challenges for control safety and efficiency. The existing control methods for CDBCs primarily focus on two-dimensional space and lack theoretical guarantees for rapid error convergence, which limits working efficiency. Furthermore, safety concerns arise when collision-free reference trajectories are unavailable or incomplete during dynamic operations. To this end, this article proposes a novel fixed-time tracking control method with obstacle avoidance and prescribed performance for three-dimensional (3-D) CDBCs. As thefirstcollision-free tracking method for 3-D CDBCs, the proposed method stands as a noteworthy contribution aimed at improving safety, accuracy, and efficiency. By simultaneously considering pitch and rotation motions, the proposed method expands the working space and efficiency of 3-D CDBCs. Elaborately designed sliding surfaces ensure fixed-time convergence, thereby improving response speed. For safe complete trajectory tracking, the proposed method can limit transient tracking errors within a prescribed performance function, preventing collisions from unexpected errors. In scenarios with unavailable or incomplete safe reference trajectories, autonomous obstacle avoidance is achieved through potential function design, thereby enhancing operation safety. Additionally, a thorough closed-loop stability analysis is provided based on Lyapunov methods. Finally, experimental results on a built CDBC prototype offer validation for the tracking and obstacle avoidance performance of the proposed method under various working conditions.

The safety-critical control of underactuated mechanical systems (UMSs) with both collocated and noncollocated configuration constraints is considered in this article. Based on the popular safety filter (SF) method using high-order control barrier function-based quadratic programs (HOCBF-QPs), this article further overcomes the difficulties caused by the singularity points of time-varying constraints and the underactuation characteristic. Specifically, the time-varying problem is addressed by transforming it into an extended time-invariant one. Then, the existing high-order CBF (HOCBF) theory is applied to construct singularity-free HOCBFs for UMS. Next, a Lipschitz continuous SF is proposed to handle multiple constraints in a hierarchical manner. Finally, experiments are performed on a 3-degrees of freedom boom crane platform to validate the effectiveness.

Tower cranes play a vital role in various industries due to their extensive workspace and high lifting capacity. How-ever, their underactuated characteristics and complex nonlinear dynamics bring significant challenges for control. Previous studies have primarily focused on models and control strategies for point mass payload single pendulum cranes and point mass payload double pendulum cranes, overlooking practical considerations such as variable rope lengths and distributed mass payloads. To address the problems above, this paper uses Euler-Lagrange approaches to establish a dynamic model considering both distributed mass payloads and variable rope lengths. The proposed model avoids approximation and linearization to ensure accuracy and reliability. This research lays a theoretical foundation for advanced control strategies aimed at improving the safety, efficiency, and accuracy of tower crane operations.

In this article, a novel distributed prescribed-time consensus tracking control strategy is presented for heterogeneous nonlinear multi-agent systems (MASs) under deception attacks and actuator faults. Since the original states of the studied system are unavailable under deception attacks, we present a new coordinate transformation technique considering the compromised states and the outputs of command filters to design the corresponding controller. Then, to handle the unknown control gains caused by actuator faults, the rational adaptive laws are cleverly designed for the upper bounds involving the unknown control gains. Besides, by introducing a time-varying constraint function in the backstepping design process, a new adaptive prescribed-time controller is constructed in this paper, such that the prescribed-time tracking control problem of the heterogeneous nonlinear MASs is converted into the constraint problem of the tracking errors. Through the Lyapunov stability analysis, the final results prove that the whole signals in the closed-loop MASs remain bounded and the tracking errors can converge to the pre-set region in the predefined time. Finally, the simulation results demonstrate the availability of the developed control method.Note to Practitioners—This paper investigates the distributed prescribed-time consensus tracking control problem for heterogeneous nonlinear MASs, whose models can be extended to more complex industrial applications, such as flexible manipulators, series elastic actuators and electric systems. In certain practical scenarios, security and fault problems are inevitable. Hence, it is challenging to design a control strategy that achieves distributed consensus tracking control in an insecure network environment. Furthermore, the proposed approach based on the time-varying constraint function ensures the system stability within the predefined time, which provides a viable strategy for engineering applications.

With strong load capacity and high maneuverability of payload attitude regulation, dual rotary cranes (DRCs) are widely applied for transportation and assembly tasks in infrastructure construction. For DRCs, to achieve safe and accurate control of the payload position and attitude, it is necessary to enhance the motion synchronization of two cranes, under the premise of controlling more state variables with fewer control inputs based on nonlinear coupling dynamics; moreover, the finite-time convergence of positioning errors is also expected to be guaranteed for high efficiency. To this end, this paper proposes an assembly-oriented finite-time coordinated controllerwithoutany linearization to the nonlinear crane dynamics, which realizes accurate and stable regulation of the payload position and attitude through coordinated boom motions. To our knowledge, the proposed controller provides thefirstclosed-loop control solution to realize both horizontal and non-horizontal payload hoisting for DRCs based on practical assembly demands. Theoretically, through elaborate design of the synchronization error and coupling errors, the real-time information exchange between the two cranes is realized for thefirsttime, which enhances the boom motion synchronization while suppressing payload swings. Furthermore, by introducing continuous terminal sliding mode surfaces with a multi-layer nested structure, the finite-time convergence of the boom positioning errors and the synchronization error is ensured with chattering reduction. Additionally, rigorous closed-loop stability analysis is provided based on Lyapunov techniques and Barbalat’s Lemma. Finally, the effectiveness and robustness of the proposed controller are verified by hardware experimental results.Note to Practitioners—This paper is motivated by the coordinated motion control problem of dual rotary cranes (DRCs), which aims to achieve safe and accurate control of the payload position and attitude oriented on practical assembly demands. At present, most control methods for DRCs only realize horizontal payload transportation, which not only ignores the requirements of payload attitude regulation in assembly tasks, but also lacks the guarantee for boom motion coordination and the finite-time convergence of state variables. To address these issues, based on the nonlinear crane dynamicswithoutany linearization, this paper proposes an assembly-oriented finite-time coordinated controller for DRCs, which achieves precise and stable regulation of the payload position and attitude through coordinated boom motions, and simultaneously enhances the system rapidity by ensuring the finite-time convergence of boom positioning errors. Furthermore, the detailed controller design and stability analysis process is provided, and the effectiveness of the proposed method is verified by hardware experiments. In the future research, we will try to apply the proposed method to practical operations of DRCs for complex assembly tasks of large heavy objects.

Pneumatic artificial muscle (PAM), featuring good flexibility and safety, has been widely used in rehabilitation and bionic robots. However, the complex hysteretic nonlinearities and uncertainties of the PAM cause great difficulties and challenges to the accurate modeling and controller design, especially when confronted with unknown external disturbances in applications. This paper proposes a robust control strategy with disturbance compensation for the hysteresis compensation and trajectory tracking of PAMs. Considering the high hysteretic nonlinearity of the PAM, a modified Prandtl-Ishlinskii model is used as a feedforward hysteresis compensator. For the linearized system, adaptive set-membership filtering (ASMF) is used to estimate the nonlinear terms and external disturbances of the overall system. A sliding mode controller (SMC) with disturbance compensation is designed and cascaded to the feedforward hysteresis compensator in series. The stability of the closed-loop system is theoretically proved. The proposed method guarantees that the tracking error of the PAM system is bounded. Finally, the effectiveness and robustness of the proposed controller are verified via a series of experiments on an in-house built testbench for PAMs. Note to Practitioners—With the increasing demand on human-robot interaction, the safety and compliance of robots have become one key requirement. PAM is a compliant actuator, exhibiting good flexibility, safety, and clean energy. PAM is widely used in rehabilitation robots, whereas its strong hysteresis nonlinearity and sensitivity to external disturbances affect its motion accuracy. This paper proposes an ASMF-based discrete SMC, which uses an inverse hysteresis model to compensate for the strong hysteresis of the PAM and uses ASMF to estimate the lumped disturbance of the system. Compared with the other filters, ASMF is unique in that its estimation error is bounded, which is very useful in the stability proof of the overall system. The effectiveness of the proposed controller is experimentally verified. Experimental results show that PAM’s hysteresis can be efficiently compensated, and the influence of external disturbances can be attenuated by the proposed controller, resulting in improved motion accuracy and robustness. In future work, efforts will be directed towards the modeling and control of PAMs in multi-DOF robots.

Pneumatic artificial muscles (PAMs), as a kind of soft actuators, can overcome compliance limitations of traditional rigid actuators to improve the adaptability of robots. However, some inherent strong nonlinearities and time-varying properties of PAMs, e.g., complex hysteresis and creep, may lead to a lot of control problems. In addition, PAM-driven systems are also faced with input constraints (e.g., deadzones, saturations, and unidirectional inputs), unknown/unmodeled dynamics and external disturbances, which badly degrade the control performance and even cause accidents. Therefore, this paper proposes anewhysteresis compensation-based immersion and invariance (I&I) adaptive fuzzy control method for PAM-driven humanoid robot manipulators, which can approximate the unknown functions and estimate the unknown parameters. To our knowledge, this is thefirstmethod for PAM-driven systems that compensates for system nonlinearities (not onlycomplex hysteresis,but alsoinput deadzones) by utilizing thepriorinformation in inverse hysteresis models, andsimultaneouslyestimates the unknown functions and parameters by designing a fuzzy update law and a parameter update law based on I&I methodology, respectively, which increases thecontrol frequencyof systems and improves tracking performance during high-speed motions. Finally, we apply the proposed approach on a self-built PAM-driven humanoid robot manipulator to validate its effectiveness and robustness.Note to Practitioners—Faced with the practical requirements of robots that interact closely with humans, improving the adaptability and compliance of robots by utilizing soft actuators, such as PAMs, can satisfy current demands. Moreover, PAMs also have many expective characteristics (e.g., high power density, light material, low costs, clean power, etc.), which makes PAMs occupy an important status in the field of soft robotics. However, unknown parameters/structures, strong nonlinearities, and input constraints, may badly degrade the control performance of PAMs. Based on the above characteristics, this paper proposes anewhysteresis compensation-based adaptive fuzzy controller for PAM-driven humanoid robot manipulators, which realizesaccurate trackingcontrol during high-speed motions by using inverse hysteresis models to compensate for strong nonlinearities in PAMs, and a fuzzy update law and a parameter update law based on I&I methodology are utilized to estimate unknown parameters/structures. In addition, the proposed controller cansimultaneouslycompensate for input deadzones by utilizing the hysteresis information, which improves thecontrol frequencyof the manipulators, and can rapidly suppress tracking errors. Experimental results are provided to validate the effectiveness of the presented method. In the future, more effective compensation methods, such as rate-dependent hysteresis models, will further be carried out to compensate for system nonlinearities.

For underactuated robots working in complex environments, an important objective is to drive all variables (particularly for unactuated end-effectors) to move along the specific path and restrict positions/velocities to avoid obstacles, rather than using only point-to-point control. Unfortunately, most path planning methods are only suitable to fully actuated systems or depend on linearized models. The main motivations of our work are to directly fulfill motion constraints and achieve path following for both actuated and unactuated states (e.g., payload swing of cranes) when lacking effective control inputs. To this end, this article presents a new time-optimal trajectory planning-based motion control method for general underactuated robots. By constructing auxiliary signals (in Cartesian space) to express all actuated/unactuated variables (in joint space), their position/velocity constraints are converted into some convex/nonconvex inequalities related to a to-be-optimized path parameter and its derivatives. Then, an optimization algorithm is constructed to solve the available path parameter and derive a group of time-optimal trajectories for actuated states. As we know, this is the first study to ensure path following and necessary full-state constraints for actuated/unactuated states. Then, a tradeoff among path-constrained motions, time optimization, and state constraints is achieved together. This article takes the rotary crane as an example and provides detailed analysis of calculating desired trajectories based on the proposed planning frame, whose effectiveness is also verified through hardware experiments.

With the advantages of natural flexibility, large force-weight ratios, and green cleanliness, pneumatic artificial muscle (PAM) actuators that mimic biological skeletal muscles have attracted much attention. However, the inherent defects of PAMs, such as high nonlinearities, limited contraction lengths and frequencies, and multiple input constraints, pose significant challenges to the motion control of PAM-actuated parallel robots; meanwhile, most existing methods do not take into account motion constraints and working efficiency. To this end, a prescribed-time adaptive fuzzy motion control method is developed in this article, where PAM-actuated parallel robots can accurately achieve prescribed tracking performance within an allowable input pressure range. In particular, regardless of the initial values of target trajectories, the expected tracking accuracy is achieved within the prescribed time by restricting the tracking errors to the improved performance constraints; also, the motion velocities remain within the preset dynamic constraints, thereby improving the working safety and efficiency. To the best of authors' knowledge, this article presents thefirstadaptive fuzzy motion control method for PAM-actuatedparallelrobots, which cansimultaneouslyachieve motion constraints and prescribed tracking performance. Moreover, the stability of all signals is proved through theoretical analysis, and then the effectiveness of the proposed method is fully verified by a series of hardware experiments.

With the increasingly wide applications of underactuated systems, the necessary switching actions in complex multiple-mode tasks may induce overlarge errors, chattering, or even instability. In different working scenarios, there usually exist different plant parameters, dynamic characteristics, and external disturbances, which may further degrade operation performance. To this end, this article designs a learning-based adaptive fuzzy switching controller to compensate for uncertainties online in various modes and realize exponential convergence of actuated states. During multiple-mode operations, bothactuatedandunactuatedconstraints are guaranteed by constructing integral constraint terms as time-variant gains, which introduce control energy in advance, to drive all state variables to converge to their desired values,rather thandirect braking force that may destroy the transient performance ofunactuatedstates (e.g., residual payload swing induced by rapid braking in cranes). Further, when underactuated systems suffer from matched/mismatched disturbances, amodel-independentdisturbance observer is elaborately designed to improve anti-disturbance performance, ensure the boundedness of closed-loop signals, and restrict all variablesin every mode. Based on Lyapunov methods and the concept of average dwell time, the closed-loop stability of entire switched systems is theoretically analyzed and proven; then, the effectiveness of the proposed switching controllers is verified by hardware experiments.

As pneumatic artificial muscles (PAMs) are similar to biological muscles in structure and movement mechanisms, parallel robots actuated by PAMs have development prospects in rehabilitation and industry, with advantages such as compliance, high safety, strong bearing capacity, and satisfactory dynamic performance. However, the parameter uncertainties and model complexity related to inherent characteristics of parallel robots actuated by PAMs (e.g., time-varying, coupling, hysteresis, creep, and high nonlinearity), bring challenges to accurate dynamic modeling and controller design. Therefore, to achieve satisfactory tracking performance, this article presents an adaptive compensation tracking controller with error constraints for parallel robots actuated by PAMs. The proposed controller deals with parameter uncertainties by estimating system parameters to ensure accurate tracking, which is indicated as an effective solution for a combination of PAMs and parallel robots. Furthermore, using desired trajectory signals in the complicated regression matrix, the online computational burden is significantly reduced. Moreover, to improve operation safety further, an auxiliary term with a theoretical demonstration guarantees that the tracking errors are maintained within allowable ranges. Then, the closed-loop stability is demonstrated by Lyapunov techniques. As far as we know, it is the first time that the challenges of parameter uncertainties, computational burdens, and error constraints of parallel robots actuated by PAMs are simultaneously addressed, which has both theoretical significance and practical value. Finally, the hardware experiments are implemented under different scenarios, and the results indicate that the proposed method achieves satisfactory tracking performance.

With the wide applications of underactuated robotic systems, more complex tasks and higher safety demands are put forward. However, it is still an open issue to utilize "fewer" control inputs to satisfy control accuracy and transient performance with theoretical and practical guarantee, especially for unactuated variables. To this end, for underactuated robotic systems, this article designs an adaptive tracking controller to realize exponential convergence results, rather than only asymptotic stability or boundedness; meanwhile, unactuated states exponentially converge to a small enough bound, which is adjustable by control gains. The maximum motion ranges and convergence speed of all variables both exhibit satisfactory performance with higher safety and efficiency. Here, a data-driven concurrent learning (CL) method is proposed to compensate for unknown dynamics/disturbances and improve the estimate accuracy of parameters/weights, without the need for persistency of excitation or linear parametrization (LP) conditions. Then, a disturbance judgment mechanism is utilized to eliminate the detrimental impacts of external disturbances. As far as we know, for general underactuated systems with uncertainties/disturbances, it is the first time to theoretically and practically ensure transient performance and exponential convergence speed for unactuated states, and simultaneously obtain the exponential tracking result of actuated motions. Both theoretical analysis and hardware experiment results illustrate the effectiveness of the designed controller.

Pneumatic artificial muscle (PAM) actuators exhibit practical compliance and great payload-to-weight ratios when driving robotic exoskeletons. However, filling with highly compressed gas makes PAMs susceptible to sensor noises, which may degrade the state response and increase control efforts. In addition, most of the existing optimal controllers require linearized operations or complex network calculations. To this end, a supervised learning control method with preassigned-time performance is studied, which achieves satisfactory motion control of the compliant PAM robots. In particular, the utilized dynamic observer with time-varying gains significantly reduces the effect of observation noises, and enhances the state convergence speed by combining with the preassigned-time constraints. Simultaneously, the improved supervised learning algorithm further optimizes input air consumption, which only involves the iterative adjustment of network weights. In contrast to the literature, this article presents a new solution to minimize energy consumption of the compliant PAM robots, while ensuring that the output states converge within the preassigned time, independent of parameter design. Rigorous stability analysis is provided and several experiments validate the tracking efficacy of the proposed method.

In recent years, with the rapid development of marine engineering, ship-mounted crane control for transporting payloads in the water has attracted more attention. Compared with the case of transporting payloads above water, ship-mounted cranes with underwater payloads are more difficult to control. On the one hand, the underwater payload is directly affected by the hydrodynamic force, and the dynamics of ship-mounted cranes is much more complex, nonlinear, and coupled; on the other hand, the unactuated underwater payload swing is quite sensitive to external disturbances; thus, the harsh marine environment will bring great challenges to the antiswing control of underwater payloads. To address the above issues, this article puts forward a coupling characteristic indicator(CCI)-based nonlinear control method to realize accurate positioning and swing suppression for ship-mounted cranes hoisting payloads in the water, which not only simultaneously suppresses actuated boom overshoots and constrainsunactuatedpayload swing, but also indicates whether the coupling terms are beneficial or harmful to make full use of them to improve transient control performance. Rigorous theoretical derivation proves the closed-loop stability. To the best of our knowledge, this is thefirstsolution to handle state constraints and utilizing the coupling characteristics of ship-mounted cranes for transferring payloads in the water. Finally, the proposed controller is applied to a self-made hardware platform, and the experimental results show that the designed method achieves satisfactory control performance.

With the increasing demands of high-precision hoisting, a growing number of to-be-hoisted large-scale heavy payloads not only need accurate positioning transportation, but alsorequire specific attitude adjustments, which mostly relies on dual boom cranes (DBCs) in practice due to their powerful capability. To achieve effective non-horizontal payload hoisting, the two booms of DBCs should reach different positions while guaranteeing safety, high efficiency, and energy conservation, which makes coordinated boom motions particularly difficult. To this end, an optimal collaborative motion planning method for DBCs is proposed in this paper without any linearization, which realizes fast, accurate, and energy-saving payload transportation with swing suppression. To the best of our knowledge, the proposed method provides the first solution for DBCs to transport payloads to the desired non-horizontal attitudes, and simultaneously achieves comprehensive optimization of multiple performance indicators, including transportation time, energy consumption, etc., on the premise of safety. On the theoretical side, novel collaborative auxiliary signal construction and parametric design guarantee the coordination of boom motions, and the solving process of optimal trajectories is simplified through elaborate convex optimization problem reformulation and analysis. At last, the effectiveness and adaptability of the proposed method are verified by hardware experiments under different working requirements.

Due to limited workspace and safety requirements for practical underactuated mechanical systems, it is necessary to restrict all to-be-controlled variables and their velocities within preset ranges, avoid collisions/overshoots, and improve braking performance. However, due to fewer available control inputs, it is quite challenging to ensure error elimination and full-state constraints for both actuated/unactuated variables, including displacements/angles and their derivatives (i.e., velocity signals) together. To handle the above issues, this article designs a new adaptive full-state constraint controller for a class of uncertain multi-input-multi-output (MIMO) underactuated systems. First, different output constraint-related auxiliary functions are constructed in the Lyapunov function candidate to generate nonlinear displacement-/angle-limited terms to control all state variables. Then, this article handles velocity constraints in a new manner, where the elaborately designed velocity constraint-related terms are directly introduced into the presented controller (instead of the Lyapunov function candidate), and strict theoretical analysis is provided by utilizing reduction to absurdity. Hence, both actuated and unactuated velocity constraints are ensured to further improve transient performance. In addition, the impact of model uncertainties is addressed online to realize accurate positioning control for all state variables. Compared with current studies of underactuated systems, this article presents the first adaptive controller to address output and velocity constraints for actuated and unactuated variables together; moreover, their asymptotic convergence is proven by strict stability analysis, which is important both theoretically and practically. In the end, the feasibility and robustness of the proposed controller are verified by hardware experiments.

Featured with high power density, excellent flexibility, shock absorption capacity, etc., pneumatic muscles (PMs) promote the development of exoskeleton robots and rehabilitation equipment. However, the complex nonlinearities of PMs limit efficiency optimization in closed-loop control, while the force-displacement coupling, soft materials, deficient workspace, etc., make it more difficult to simultaneously increase motion speeds and ensure the safety of multiple PM-actuated (PMA) robots. Although force sensors can currently be replaced by applying state estimation techniques, the amplification effects of measurement noises still compromise control accuracy and stability in practice. To this end, this article proposes a reinforcement learning-based robust motion control method with the prescribed performance, which achieves efficient and satisfactory tracking control for PMA robotic arms. In particular, by elaborately incorporating an integral term, a robust generalized proportional integral observer is used to eliminate measurement noises. Meanwhile, by using an actor–critic network to optimize control performance, an error-transformation-based continuous controller is designed to guarantee the uniformly ultimately boundedness of tracking errors. Compared with most existing methods, this article provides the first solution to restrict the entire transient and steady-state performance of PMA robotic arms, improve the noise suppression capability, and optimize the control efficiency simultaneously. Finally, complete stability analysis based on Lyapunov techniques is provided, and several groups of hardware experiments demonstrate the practicability and robustness of the proposed method.

Passive compliance devices driven by cylinders have wide application prospects in industrial grinding areas with advantages of excellent passive adaptability and buffer capacity. However, there exists complex nonlinear hysteresis between the input pressure and the output force of cylinders. Moreover, the changes of the contact grinding force caused by various random external disturbances during the grinding process may severely reduce the grinding precision, and even cause irreversible dam-ages to the workpiece. Hence, how to keep the desired grinding force for compliance devices under the complex environment is an issue worth investigating. Focusing on the high precision grinding stage based on a compliance device driven by a double acting cylinder, the backlash-like hysteresis model is utilized to characterize the complex nonlinearities of the cylinder in this paper, and its inverse hysteresis is used to solve the desired pressure via elaborate iterative treatments. On this basis, an extended-state-observer-based nonlinear sliding mode controller is proposed. In addition, the closed-loop stability analysis is pro-vided via Lyapunov-based methods. Finally, the effectiveness and robustness of the proposed controller are verified by simulation results.

Due to high biological adaptability and flexibility, pneumatic artificial muscle (PAM) systems are widely employed in exoskeleton robots to accomplish rehabilitation training with repetitive motions. However, some intrinsic characteristics of PAMs and inevitable practical factors, e.g., high nonlinearity, hysteresis, uncertain dynamics, and limited working space, may badly degrade tracking performance and safety. Hence, this paper designs a new learning-based motion controller for PAMs, to simultaneously compensate for model uncertainties, eliminate tracking errors, and satisfy preset motion constraints. Particularly, when PAMs suffer from periodically non-parametric uncertainties, the elaborately designed continuous update algorithm can repetitively learn them online to enhance tracking accuracy, without employing upper/lower bounds of unknown parts for controller design and gain selections. Meanwhile, some non-periodic uncertainties are handled by a robust term, whose value is only related to the initial states of PAMs, instead of exact upper bounds of unknown dynamics. From safety concerns, we introduce error-related saturation terms to limit initial amplitudes of control inputs within saturation constraints and avoid overlarge errors inducing overlarge acceleration. Meanwhile, the constraint-related auxiliary term is utilized to keep tracking errors within allowable ranges. To the best of our knowledge, this paper presents the first learning-based error-constrained controller for uncertain PAM-actuated exoskeleton robots, to realize high-precision tracking control and improve safety without additional gain conditions. Moreover, the asymptotic convergence of tracking errors is strictly proven by Lyapunov-based stability analysis. Finally, based on a self-built exoskeleton robot, the effectiveness of the proposed controller is verified by hardware experiments. Note to Practitioners—This work is motivated by the practical requirements of exoskeleton robots in rehabilitation training and exploration fields. Currently, PAM systems, as a kind of new flexible actuator equipment, are playing increasingly important roles in the development of exoskeleton robot control. However, uncertain (or time-varying) parameters/structures and highly nonlinear dynamics, such as creep and hysteresis, may badly increase the control difficulty of PAMs. Moreover, higher and higher tracking accuracy and safety requirements also induce urgently solved problems to practical PAM-actuated exoskeleton robots, e.g., smooth start, motion constraints, and rapid error elimination. To this end, this paper proposes a new learning-based adaptive controller, which realizes accurate tracking control for PAM-actuated exoskeleton robots by utilizing an elaborately designed repetitive learning algorithm and a robust term to handle periodic and non-periodic uncertainties, respectively. More importantly, the proposed controller simultaneously enhances transient performance of PAMs, including gradually improved tracking accuracy, effective constraints for startup acceleration and tracking errors. Additionally, it is not required to consider the upper bounds of unknown dynamics and additional gain selection conditions, which is theoretically and practically important for PAM systems. Some hardware experiments further verify the effectiveness and robustness of the suggested controller. In our future work, we intend to design more effective methods for PAMs with unmeasurable states and time-delay.

In the field of modern industrial engineering, many mechanical systems are underactuated, exhibiting strong nonlinear characteristics and high flexibility. However, the lack of control inputs brings about many difficulties for controller design and stability/convergence analysis., some unavoidable practical issues, e.g., plant uncertainties and actuator deadzones, make the control of underactuated systems even more challenging. Hence, with the aid of elaborately constructed finite-time convergent surfaces, this article provides the first solution to address the control problem for a class of multi-input-multi-output (MIMO) underactuated systems subject to plant uncertainties and actuator deadzones. Specifically, this article overcomes the main obstacle in sliding-mode surface analysis for MIMO underactuated systems, that is, by the presented analysis method, the asymptotic stability of the system equilibrium point is strictly proven based on the composite surfaces. In addition, the unknown parts of the actuated/unactuated dynamic equations and actuator deadzones can be simultaneously handled, which is important for real applications. Furthermore, we apply the proposed method to two kinds of typical underactuated systems, that is: 1) tower cranes and 2) double-pendulum cranes, and implement a series of hardware experiments to verify its effectiveness and robustness.

Recently, the pneumatic artificial muscle (PAM) that can reproduce natural muscle functionalities has become one of the core actuator mechanisms of intelligent interactive soft robots. Unfortunately, some inherent defects (e.g., unignorable nonlinearities, hysteresis, low shrinkage frequencies, etc.) have limited the application progress of humanoid PAM arm robots. Additionally, the input constraints (e.g., saturations, dead zones, unidirectional inputs, etc.), unexpected external disturbances, unidentifiable system parameters, and inevitable unmodeled dynamics are usually complicated, which cannot be easily eliminated through existing adaptive control methods. This article proposes an adaptive fuzzy-sliding mode control method for humanoid PAM arm robotswithoutany information of precise model structures and system parameters, which can suppress the unexpected effects of complicated unknown functions and achieve high performance tracking control,simultaneously. To the best of our knowledge, the proposed controller is thefirstmethod for the humanoid PAM arm robots that considers the nonlinear input constraints including unidirectional conditions, saturations, and dead zones,simultaneously. Next, all the input constraints, system parameter uncertainties, unmodeled dynamics, and external disturbances can be estimated adaptively by utilizing the proposed fuzzy update law. Particularly, a sliding mode control law is designed to compensate possible fuzzy approximation errors, and rigorous Lyapunov-based stability analysis is provided to ensure that the state errors can converge to zero withinfinitetime. Hardware experiments are carried out later tovalidate the effectiveness and robustness of the proposed method.

With large load capacity and flexible payload attitude adjustment capability, dual rotary cranes (DRCs) play crucial roles in infrastructure construction with heavy hoisting demands. However, as a kind of collaborative control systems, DRCs have complex collaborative constraints, and large-scale payloads cannot be simply regarded as mass points; moreover, due to the lack of control inputs, some state variables can only be indirectly controlled through complicated nonlinear coupling relationships, which make the controller design and corresponding analysis particularly difficult. Additionally, in practical applications of DRCs, many factors (such as boom motion overshoots, inaccurate gravity (torque) compensation, etc.) are prone to result in unexpected steady errors, large payload swing, and boom collisions, which may result in inaccurate assembly, and even lead to safety accidents. To this end, this article proposes an adaptive nonlinear proportional-integral-derivative-like collaborative control method for DRCs, which can realize accurate and efficient antiswing hoisting. To our knowledge, this is thefirstcontroller embedded with integral termswithoutany linearization during the controller design or stability analysis, which can effectively reduce steady errors, and keep boom motions within safety ranges by adaptive gravity (torque) compensation and elaborately designed constraint terms. Theoretically, the closed-loop stability and convergence are proven through strict mathematical analysis by using Lyapunov techniques and LaSalle’s invariance theorem. Finally, several groups of hardware experimental results are presented for effectiveness and robustness verification.

In the field of practical engineering, the performance of mechatronic systems is influenced by model uncertainties, velocity unavailability, input nonlinearities (e.g., actuator deadzones/faults), etc.Moreover, some complex nonlinear dynamics do not satisfy the linear parameterization condition. Hence, due to intractable approximation errors, some existing controllers may obtainonlyuniformly ultimately bounded results and require velocity feedback to accomplish online estimation. To overcome the aforementioned obstacles, this article designs a new output feedback controller to fulfill accurate trajectory tracking and obtain state estimates for a class of Euler–Lagrange (EL) mechatronic systems. Specifically, we first construct a group of auxiliary variables to accurately recover velocitieswithoutnumerical differential operations. Then, by employingonlythe available output information, unknown model knowledge and actuator deadzones/faults are simultaneously approximated online; more importantly, the asymptotic stability of the system equilibrium point is guaranteed by strict theoretical analysis. Another merit of the proposed controller is that the approximation errors are addressed in anew way, wherenodiscontinuous robust terms are required; hence, the chattering problem is effectively alleviated. To the best of our knowledge, for uncertain EL mechatronic systems with actuator deadzones/faults, this article proposes thefirstsolution to eliminate tracking errors and accurately recover unmeasurable states bycontinuouscontrol signals. The asymptotic convergence of closed-loop signals is proven based on Lyapunov methods, and the performance of the proposed controller is validated by hardware experiments.

Underactuated dual boom crane (DBC) systems exhibit complicated nonlinearity and strong coupling due to the lack of independent actuators. Moreover, plant parameters may change in different transportation tasks and are difficult to be measured accurately, which leads to inaccurate gravity (torque) compensation and further brings positioning errors. Hence, most existing controllers based on exact model knowledge cannot ensure satisfactory control performanceany longer. In order to handle the above issues, this article designs an adaptive sliding mode tracking controller for DBC systems based on the original complicated nonlinear dynamicswithoutany linearization/simplification operations, which is thefirstone to effectively achieve both anti-swing and trajectory tracking control in the presence of parametric uncertainties. Not only can the state variables converge to the proposed sliding surface within finite time but also payload swing angles can be completely eliminated; consequently, the working efficiency and operation safety are further guaranteed. The corresponding stability and convergence for the equilibrium point of the closed-loop system are proven by rigorous mathematical analysis based on the Lyapunov techniques and Barbalat’s lemma. Hardware experimental results demonstrate the effectiveness and robustness of the presented controller.

Underactuated systems are widely applied in industry, construction, manufacturing, etc., and the complex working environment puts forward higher demands for safety and transient performance. Hence, it is necessary to consider how to simultaneously ensure actuated and unactuated motion constraints by fewer control inputs, especially when systems suffer from model uncertainties, unavailable velocities, etc. Unfortunately, it is still a significant challenge to overcome in real applications and theoretical analysis. Additionally, most existing studies merely consider the specific control objects and few general methods are applicable to a class of underactuated systems. To this end, we design a new adaptive output-feedback controller for a class of uncertain underactuated systems. Compared with existing methods only handling actuated constraints, an important merit of this article is that by introducing the elaborately designed coupling term composed of actuated and unactuated constraints together, all state variables are kept within the preset time-variant ranges and converge to their desired values. Furthermore, a new Lyapunov function candidate is utilized to provide a theoretical guarantee. As far as we know, without the need of exact model knowledge and velocity feedback, this article provides the first solution to achieve accurate motion control and state constraints for both actuated and unactuated variables, which is meaningful both theoretically and practically. Meanwhile, the asymptotic stability of the equilibrium point for the closed-loop system is proven by utilizing Lyapunov techniques and Barbalat’s lemma. For verification, the presented controller is applied to underactuated overhead and rotary cranes, respectively, together with detailed theoretical analysis and experimental validations.

With the exploitation of marine resources, the underwater crane system has become an indispensable transportation tool on the sea; however, its control problems are still open. For this type of crane system, due to the flexible characteristics of its payload, the system dynamic model is very complex; meanwhile, the payload transverse deviation is amplified due to the hydrodynamic force, resulting in residual vibration of the payload. Moreover, the bad operating environment leads to many uncertain disturbances, bringing more challenges to its control issues. To solve the problems mentioned above, an effective neuro-adaptive controller is designed in this paper. Specifically, without linearizing the obtained nonlinear model, the controller is designed through a two-layer neural network, and the approximation error of the neural network is also eliminated. Then, we use Lyapunov stability theory to prove that the controller can make all state variables converge to their desired values. As far as we know, this paper yields the first complete control solution for the control problem of the underwater flexible crane system, which can well deal with the complex nonlinear characteristics caused by the flexible payload, achieve excellent control performance, and improve the robustness of the system with respect to parameter uncertainties and external disturbances. Finally, through a series of simulation results, it is verified that the proposed method can make the trolley arrive at the desired position accurately and suppress the flexible payload’s residual vibration effectively.

The aerial transportation system is a kind of nonlinear underactuated mechatronic system, which suspends the cargo beneath the rotorcraft’s fuselage and undertakes two basic missions of rotorcraft positioning and cargo swing suppression. Currently, most available methods need simplifications such as the near hovering hypothesis and dimension reduction operations, which may badly degrade the control performance when state variables get far away from the equilibrium point. In addition, integral terms, which can eliminate the steady errors, are not reflected in controller design and stability analysis processes. To tackle the aforementioned issues, this article provides a novel nonlinear control approach with an elaborately constructed integral term for aerial transportation systems, which not only achieves satisfactory antiswing and positioning performance but also reduces steady errors in practical flight. Meanwhile, the actuating constraint is taken into consideration so as to avoid saturation problems. Without linearization operations, we prove the closed-loop asymptotic stability of the equilibrium by the explicit Lyapunov-based analysis. As far as we know, this article is the first solution for controller design with the consideration of both steady errors elimination and actuating constraints. Finally, several groups of hardware experimental results are provided to validate the effectiveness of the presented control scheme.Note to Practitioners—This article is motivated by the requirement of effective control schemes for aerial transportation systems. The unexpected cargo swing motion may lead to safety accidents; thus, the dual objective of swing suppression and rotorcraft positioning is the focus of research. Nevertheless, with underactuated property, the cargo swing motion cannot be directly controlled. Up until now, at the cost of model accuracy, most existing methods utilize the simplified models in near hovering state or 2-D transverse plane to reduce the control difficulty. Accounting for the foregoing problems, this article presents a novel control scheme with improved antiswing and positioning performance. With an elaborately constructed integral term, the designed controller could improve the positioning accuracy of the rotorcraft with the guaranteed theoretical analysis. Moreover, to avoid the problem of actuator saturation, the control inputs are restricted in allowable ranges during the transportation process. All these aspects are verified by rigorous theoretical analysis and groups of hardware experiments in different conditions. In future studies, we will apply the suggested control scheme in practical applications.

Tower crane systems exhibit high nonlinearity and underactuation, making the control issue challenging. Most reported methods for tower crane systems utilize linearized models, and accurate plant parameters (e.g., cargo mass, jib moment inertia) and full state feedback are usually required; moreover, most existing works only consider a part of the crane motions, and the control issue of five degree-of-freedom (5-DOF) tower cranes (i.e., 2-DOF cargo swing, slew, hoisting, and translation) is still open. However, tower cranes are practically influenced by uncertainties and disturbances, which may make linearized models ineffective; additionally, exact values of plant parameters may be difficult to obtain, and velocity signals are usually not directly measurable in practice. To address the aforementioned problems, this article proposes an adaptive output feedback control method for 5-DOF varying-cable-length tower cranes. As far as we know, this article provides the first adaptive output feedback controller, designed and analyzed without linearizing the dynamic equations, which can simultaneously achieve cargo hoisting/lowering, jib slew, trolley translation, and swing suppression, by avoiding using velocity-related feedback signals. Resorting to an elaborately constructed virtual spring-mass system, the control objectives are satisfactorily achieved even without involving any velocity signals with theoretical/experimental guarantee. Moreover, by elaborately designing a new adaptive law, the exact values of unknown cargo masses can be estimated through online identification. We provide rigorous stability/convergence analysis for the closed-loop system. Hardware experiment results are included for effectiveness/robustness verification.

Rotorcrafts, with satisfactory maneuver performance and ability under complex terrains unreachable for ground robots, are playing important roles for goods transportation. In this article, we focus on the control of the cable-suspended transportation way due to its lower costs and more agility of the rotorcraft's rotational motion. Compared with traditional crane systems and single rotorcrafts without loads, the aerial transportation system presents “double” underactuated property, stronger system nonlinearity, and more complex dynamic coupling, which are huge challenges for control schemes design. Meanwhile, aerial transportation usually suffers from external disturbances and uncertainties presented with aerodynamic damping coefficients and rope length. Additionally, overshoots of the rotorcraft's position are potential threats for flight safety, especially in confined and complex environments. To address these problems, a novel adaptive control scheme is designed, which ensures effective rotorcraft positioning and payload swing suppression with restricted overshoot amplitudes. Asymptotic results are obtained with rigorous theoretical derivations provided by the Lyapunov-based stability analysis and LaSalle's invariance theorem. Real-time experiments are performed to validate the effectiveness of the proposed control scheme even in the presence of external disturbances. To the best of our knowledge, this is the first method designed for aerial transportation systems which achieves simultaneous rotorcraft positioning and swing suppression, together with insurance for overshoot restriction even in the presence of parametric uncertainties.

To meet real-world production demands, two or more cranes are used to cooperatively complete transportation tasks. Dual boom cranes (DBCs) are widely used in large construction sites owing to their strong load capacity. However, for typical nonlinear underactuated multi-crane systems, most of the existing control methods focus on the overhead crane systems with simpler dynamic characteristics and not enough attentions are paid to DBCs with stronger coupling and more complex dynamics. Based on the existing model, geometric constraints are analyzed to obtain the relationship between the higher-order derivatives of state variables, which can simplify the dynamic model of DBCs reasonably. The dynamic relationship between the boom pitch angles and the payload attitude is analyzed accurately. Moreover, the oscillation period of DBCs is obtained, and an extra insensitive input shaper is designed by rigorous mathematical derivation. Finally, simulation results verify that the input shaping control method has a satisfactory anti-swing ability and can realize accurate positioning.

As a class of underactuated systems, cooperative dual rotary crane systems (DRCSs) are widely used to complete the task of large payload transportation in complex environments, since the working capacity of single cranes is quite limited. However, the control issues of DRCS fail to receive enough attention at present. Compared with single cranes, DRCSs contain more state variables, geometric constraints, and coupling relationships. Therefore, the complex kinematic and dynamic characteristics make controller design/stability analysis very challenging for DRCS. In order to solve these problems, based on the dynamic model of DRCS established by Lagrange's method, an output feedback control method with consideration for actuator constraints is designed to realize accurate dual boom positioning and rapid elimination of payload swings. The stability of the equilibrium point for the closed-loop system is analyzed by using Lyapunov techniques and LaSalle's invariance principle. To the best of our knowledge, this article yields the first solution for effective control of DRCS, which needs no velocity feedback, respects the actuator constraints, and is designed and analyzed without linearizing the complicated nonlinear dynamic equations. Finally, a series of hardware experiments on a self-built experimental platform is carried out to illustrate the effectiveness of the proposed controller.

Pneumatic artificial muscle (PAM) systems are a kind of tube-like actuators, which can act roughly like human muscles by performing contractile or extensional motions actuated by pressurized air. At present, it is still an open and challenging issue to tackle positioning and tracking control problems of PAM systems, due to inherent characteristics, e.g., unidirectional inputs, high nonlinearities, hysteresis, time-varying characteristics, etc. In this paper, a new adaptive control method is proposed for PAM systems, which achieves satisfactory tracking performance. To this end, an update law is designed to estimate unknown system parameters online. Also, some control input transforming operations are applied to address unidirectional constraints (i.e., control inputs of PAM systems should always be positive). As far as we know, compared with most of the existing control methods, this paper gives the first continuous control solution for PAM systems that can simultaneously compensate parametric uncertainties, reject external disturbances, and meet unidirectional constraints. Without linearizing the nonlinear dynamics, the closed-loop system is theoretically proven to be asymptotically stable at the equilibrium point with the stability analysis. In addition, a series of hardware experiments are implemented on a self-built hardware platform, indicating that the proposed method achieves satisfactory tracking control and exhibits robustness against parametric uncertainties and disturbances.

As a type of indispensable oceanic transportation tools, ship-mounted crane systems are widely employed to transport cargoes and containers on vessels due to their extraordinary flexibility. However, various working requirements and the oceanic environment may cause some uncertain and unfavorable factors for ship-mounted crane control. In particular, to accomplish different control tasks, some plant parameters (e.g., boom lengths, payload masses, and so on) frequently change; hence, most existing model-based controllers cannot ensure satisfactory control performance any longer. For example, inaccurate gravity compensation may result in positioning errors. Additionally, due to ship roll motions caused by sea waves, residual payload swing generally exists, which may result in safety risks in practice. To solve the above-mentioned issues, this paper designs a neural network-based adaptive control method that can provide effective control for both actuated and unactuated state variables based on the original nonlinear ship-mounted crane dynamics without any linearizing operations. In particular, the proposed update law availably compensates parameter/structure uncertainties for ship-mounted crane systems. Based on a 2-D sliding surface, the boom and rope can arrive at their preset positions in finite time, and the payload swing can be completely suppressed. Furthermore, the problem of nonlinear input dead zones is also taken into account. The stability of the equilibrium point of all state variables in ship-mounted crane systems is theoretically proven by a rigorous Lyapunov-based analysis. The hardware experimental results verify the practicability and robustness of the presented control approach.

A tower crane is a nonlinear mechatronic system with complicated underactuated characteristics, which is widely used in modern construction sites. At present, most existing methods for tower cranes are proposed by linearizing the original nonlinear dynamics near equilibrium points, which are, thus, prone to suffering from unexpected steady errors due to such factors as unmodeled dynamics, imperfect friction compensation, etc., since they have not included integral terms in either controller design or stability analysis. Therefore, in this paper, an improved feedback controller with an elaborately constructed integral term is proposed for 3-D tower cranes without linearization, which can achieve both antiswing and positioning control while being able to effectively reduce steady errors in the presence of, e.g., inaccurate friction compensation. Furthermore, asymptotic stability results are proven through rigorous theoretical analysis. Owing to no linearization, the proposed controller is applicable when state variables (e.g., cargo swing angles) are not close enough to the equilibrium points, which makes it suitable for complicated working conditions. Hardware experimental results are included to verify the effectiveness of the proposed controller.

As a class of typical representatives for conveyance, shipboard crane systems are usually fixed on ship decks to transport cargoes on the sea, which is greatly different from land-fixed cranes. Due to some disturbances induced by sea waves, payload positions are always difficult to control precisely. In addition, unless equipped with velocity sensors, it would be difficult to obtain velocity signals for feedback control, by noting that the traditional way of numerical differentiation operations (to recover velocities from positions/angles) may induce extra noises in practice. In this paper, we propose an observer-based dynamic feedback control method to deal with the foregoing issues. Specifically, both boom/rope positioning and payload swing elimination can be achieved simultaneously by utilizing only measurable displacement/angle feedback signals. Moreover, as far as we know, this paper gives the first input-saturated control method including nonlinear coupling terms to realize the objective of effective positioning and swing suppression without the requirement of velocity feedback, which is developed on the basis of the complicated nonlinear shipboard crane dynamics with no linearization operations during controller design or stability analysis. Meanwhile, the corresponding velocity signals are accurately recovered online by means of the suggested observer. In addition, the amplitudes of the control inputs can be guaranteed within the allowable ranges to avoid falling into saturation. The asymptotic stability for the equilibrium point of the crane system in closed loop with the controller and the observer is proven by rigorous analysis with Lyapunov techniques and LaSalle's invariance theorem. After a series of hardware experiments, we validate the effectiveness and robustness of the presented controller.

Among various large-scale mechanical equipments, a rotary crane is one of the most practical hoisting machineries utilized in factories and docks. However, the inaccurate measurement of friction coefficients and the requirement of accurate gravity-related compensation may inevitably increase the difficulty for controlling such systems. For most existing control methods, the exact model knowledge is required; otherwise, positioning errors would unavoidably appear, which brings many limitations for their practical applications. To deal with these problems, in this paper, a novel adaptive control approach is suggested, in which a novel update law is designed to achieve accurate identifications of unknown parameters as well as exact compensation of the gravity-related lumped term. Moreover, the payload can be transported to its specified location precisely via the boom's rotation with effective payload swing suppression. Specifically, without linearizing the nonlinear dynamic model of the rotary crane system, the state variables are ensured to be asymptotically convergent to the equilibrium point, which is proven strictly in theory by utilizing Lyapunov techniques and LaSalle's invariance principle. Finally, experimental results indicate the effectiveness and practicability of the proposed approach.

In real-world applications, industrial cranes commonly suffer from effects caused by the so-called double-pendulum phenomenon in many situations. However, at present, the double-pendulum phenomenon is usually directly roughly neglected when designing control methods. For double-pendulum cranes, most currently available approaches are open loop control; the existing feedback methods are mostly developed based on linearized dynamic models (around the equilibrium point) or designed without adding integral terms in the control laws, which may cause positioning errors in the presence of unmodeled dynamics. To address these problems, this paper proposes a new quasi-proportional integral derivative control method to effectively control underactuated double-pendulum crane systems. Then, we provide rigorous theoretical analysis for the equilibrium point of the closed-loop system based on the original nonlinear dynamic equations. To our knowledge, this paper gives the first plant-parameter-free controller that incorporates both integral action and actuating constraints without any linearizing operations during controller design or closed-loop analysis, which theoretically ensures that the controller can work well in the presence of unmodeled dynamics (e.g., insufficient friction compensation), actuating constraints, and large swing angles (i.e., not satisfying linearization conditions). Finally, hardware experimental results are provided to examine the effectiveness of the suggested control method.

In mechanical engineering, multi-translational oscillator with rotational actuator (multi-TORA) systems have been introduced to study the self-synchronized phenomenon as well as to investigate the vibration damping problem associated with many vibrational mechatronic systems, e.g., hand-held drills. Due to the lack of available actuators, multi-TORA systems are typically underactuated. Multi-TORA systems consist of a series of single TORA subsystems connected to and coupled with each other by elastic springs. For practical multi-TORA systems, the plant parameters are usually unknown or difficult to measure. Moreover, they exhibit strong nonlinear coupling behaviors. These factors bring much difficulty for both controller design and analysis. The control problem for underactuated multi-TORA systems with parametric uncertainties is challenging and still open. To address the above issues, this paper proposes a nonlinear increased motion control scheme for multi-TORA systems with parametric uncertainties. Specifically, a novel energy function is constructed and some extra coupling terms are introduced into the proposed controller for improving the transient performance. Then, based on Lyapunov techniques, we rigorously prove the asymptotic stability for the equilibrium point of the closed-loop system. As far as we know, this paper gives the first smooth control law to yield global asymptotic control results for underactuated multi-TORA systems suffering from unknown/uncertain plant parameters. To verify the effectiveness of the proposed controller, a series of hardware experiments are carried out on a self-built double-TORA hardware testbed, which indicate that the controller achieves effective control results in various conditions.

In practical applications, industrial cranes may exhibit double-pendulum swing effects, due to many factors, such as large payload scales and non-negligible hook masses. Currently, for double-pendulum cranes, most available methods are open-loop controllers designed based on linearized crane dynamics; even for existing closed-loop approaches, they are also mostly developed using linearized dynamics and require the exact knowledge of system parameters, which makes them sensitive to parametric uncertainties. To handle these issues, we present an adaptive antiswing control strategy for crane systems with double-pendulum swing effects and uncertain/unknown parameters, which can make the trolley accurately reach the target position with reduced overshoots and effectively eliminate the double-pendulum swing angles at the same time. A complete stability analysis, based upon the full nonlinear dynamics (i.e., without linearizing the dynamics), is included to support the theoretical derivations. We present hardware experimental results to demonstrate that the proposed controller achieves better performance than existing ones and exhibits good robustness.

In practical applications, boom cranes are widely used as useful transportation tools in various fields, owing to such advantages as high flexibility, good mobility, strong operability, and so on. As a typical nonlinear underactuated system, a boom crane presents complicated dynamical characteristics mainly due to its complex multidimensional movements like rotational motions, pitching motions, as well as payload swings, which brings much difficulty for controller design. In this paper, a new nonlinear controller is proposed for underactuated boom cranes. Specifically, the presented control scheme can achieve 2-D rotary positioning and 2-D swing suppression simultaneously, with an additional coupling term as well as an overshoot-limiting term being incorporated to increase the transient performance. Consequently, the asymptotic stability of the closed-loop system's equilibrium point is proven by utilizing Lyapunov techniques and LaSalle's invariance theorem. To the best of our knowledge, the proposed approach is the first closed-loop control method to solve the positioning and anti-oscillation problem for 3-D boom cranes without needing to linearize the original nonlinear dynamics for controller design or analysis, which is of great significance. Finally, hardware experimental results are presented to demonstrate the efficiency of the proposed control method.

Presently, ship-mounted cranes are playing more and more important roles in modern ocean transportation and logistics. Different from traditional land-fixed crane systems, ship-mounted cranes present much more complicated nonlinear dynamical characteristics and they are persistently influenced by different mismatched disturbances due to harsh sea environments, e.g., sea waves, ocean currents, sea winds, and so forth; these unfavorable factors bring about many challenges for the development of effective control schemes. This paper presents a novel nonlinear stabilizing control strategy for underactuated ship-mounted crane systems. Specifically, some novel coordinate change procedures are first introduced to tackle the disturbing terms by transforming the original dynamics into a new form, which facilitates both controller design and stability analysis. After that, a nonlinear control law is constructed to regulate the cargo position to the desired location asymptotically, in the presence of ship roll and heave movements. The boundedness and convergence of the closed-loop signals are proven with Lyapunov-based analysis. To the best of our knowledge, this is the first closed-loop scheme that can achieve asymptotic control results, without linearizing/approximating the original nonlinear dynamics when performing controller design and stability analysis, for underactuated ship-mounted cranes with ship roll and heave movements. Hardware experimental results are included to show that the proposed control method can achieve satisfactory control performance and it admits strong robustness against external perturbations.

The present paper exploits a partially saturated nonlinear control law for underactuated crane systems, which is achieved by converting the crane model into an objective (or equivalently, desired closed-loop) system. The proposed method guarantees “soft” trolley start by incorporating a smooth saturated function into the control law. More specifically, we first establish an objective system with guaranteed signal convergence and stability performance; then based on the structure of the objective dynamics, a partially saturated control law is derived straightforwardly by solving one partial differential equation, without performing any partial feedback linearization operations on the original crane model. The convergence and stability performance of the objective (i.e., closed-loop) system is guaranteed with Lyapunov techniques and LaSalle's invariance theorem. To validate the practical performance of the proposed method, we implement hardware experiments to illustrate that the new method achieves superior performance with reduced control efforts.

Inspired by the desire to achieve fast payload transportation as well as sufficient swing suppression, a novel phase plane based motion planning method is proposed for underactuated overhead cranes. Specifically, the variation law of the underactuated system states in the phase plane is firstly derived via mathematical analysis for the phase portraits. Based on this, an analytical three-segment acceleration trajectory (namely, a trapezoid velocity trajectory) with the coupling behavior being taken into consideration is obtained under actual crane control constraints. To deal with the jerk (discontinuity) problem, we then present two modified acceleration trajectories by introducing some transition stages and performing some rigorous analysis. Moreover, the trajectories generated by the proposed method can evaluate the maximum payload swing and the arrival time for a given transportation task in advance, which provides essential control indexes for crane operation. Simulation results are provided to illustrate the superior performance of the proposed trajectory planning method.