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.

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.

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.

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.

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.

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 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 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.

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.

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.

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.

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.

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 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.