Unactuated States Research Articles

Enhanced Trajectory Tracking of 3D Overhead Crane Using Adaptive Sliding-Mode Control and Particle Swarm Optimization

Cranes hold a prominent position as one of the most extensively employed systems across global industries. Given their critical role in various sectors, a comprehensive examination was necessary to enhance their operational efficiency, performance, and facilitate the control of transporting loads. Furthermore, due to the complexities involved in disassembling and reinstalling cranes, as well as the challenges associated with precisely determining system parameters, it became essential to implement adaptive control methods capable of efficiently managing the system with minimal resource requirements. This work proposes a trajectory tracking control using adaptive sliding-mode control (SMC) with particle swarm optimization (PSO) to control the position and rope length of a 3D overhead crane system with unknown parameters. The PSO is mainly used to identify the model and estimate the uncertain parameters. Then, sliding-mode control is adapted using the PSO algorithm to minimize the tracking error and ensure robustness against model uncertainties. A model of the systems is derived assuming changing rope length. The model is nonlinear of second order with five states, three actuated states: position x and y, and rope length l, and two unactuated states, which are the rope angles θx and θy. The system has uncertain parameters, which are the system’s masses Mx, My and Mz, and viscous damping coefficients Dx, Dy and Dy. A simulation study is established to illustrate the influence and robustness of the developed controller and it can enhance the tracking trajectory under different scenarios to test the scheme.

Online Trajectory Planning Control for a Class of Underactuated Mechanical Systems

Efficient control of underactuated systems has always been a great challenge, since one has to stabilize both actuated and unactuated states with fewer control inputs. During the past decades, great efforts have been devoted to improving the transient performance and robustness of the system, which are very crucial in plenty of application scenarios. To motivate corresponding research, an online trajectory planning method is proposed for a class of underactuated mechanical systems in this paper. Specifically, reference trajectories are first generated for actuated states. Based on that, appropriate online adjustments are made to these reference trajectories, so as to realize efficient stabilization of the unactuated states. Different from traditional off-line planning methods, the proposed one utilizes real-time feedback to counteract various unfavorable conditions, which endows it stronger robustness and better transient performance. Rigorous Lyapunov-based analysis is performed to show that the closed-loop system is asymptotically stable around the desired equilibrium point. Finally, the proposed method is applied to two underactuated mechanical systems, with simulation/experiment results provided to demonstrate its superior performance.

Concurrent Learning-Based Adaptive Control of Underactuated Robotic Systems With Guaranteed Transient Performance for Both Actuated and Unactuated Motions.

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.

Unactuated and Actuated States Simultaneously Constrained Optimal Trajectory Planning-Based Path-Following Control for Underactuated Robots.

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.

Constrained model predictive control for 3-D offshore boom cranes

Offshore boom cranes are complex nonlinear underactuated systems, whose control problems, when considering the 3-dimensional (3-D) model affected by ship-induced disturbances, are full of various challenges. In fact, it still remains an open problem to efficiently control the 3-D offshore boom cranes. Moreover, most existing works on offshore cranes concentrate upon designing the force/torque controller, whose performance degrades badly in the presence of friction. In this paper, considering the above issues, a novel model predictive control (MPC) method, which successfully considers the constraints of both input and output of the system, is proposed to achieve satisfactory control performance even under the effect of persistent ship roll and heave perturbations. Specifically, a discrete model is first obtained by some careful transformation and discretization on the unactuated dynamics equations, based on which a novel model predictive controller is constructed. To reduce the complexity of the system, the unactuated states and the accelerations of actuated states are considered as system states and control inputs respectively. After that, the requirements for the payload position accuracy and swing suppression as well as other system constraints, are taken into full account by converting them into input constraints to facilitate subsequent handling. At last, hardware experiments are implemented on a self-built testbed, with the obtained results clearly illustrating the effectiveness and robustness of the proposed method.

Underactuated Mechanical Systems With Both Actuator and Actuated/Unactuated State Constraints: A Predictive Control-Based Approach

Underactuated systems are widely used in practice. Due to actuator saturation and transient performance requirements, it is necessary to keep the control inputs and system states within safe limits. However, with fewer control inputs, the state constraints, especially for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> states, are usually difficult to guarantee. Model predictive control (MPC), as a method that can handle constraints naturally, unfortunately, still struggles to deal with unactuated variable constraints directly. To this end, this article proposes a general MPC algorithm <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for a class of underactuated systems</i> . First, an MPC method considering actuator saturation constraints is designed, based on which, different velocity constraint-related matrices are constructed to convert both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actuated</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> velocity constraints into control input constraints. Then, by delicately analyzing the coupling relationship between actuated and unactuated variables, the displacement/angle constraints of unactuated variables are theoretically ensured. To our best knowledge, it is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> MPC approach designed for a class of underactuated systems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> actuated and unactuated state constraints as well as actuator saturation. Finally, the proposed MPC approach is applied to two typical underactuated systems, i.e., tower cranes and boom cranes, and a series of experiments are investigated to verify the effectiveness and superiority of this approach.

An Online Adaptive Policy Iteration-Based Reinforcement Learning for a Class of a Nonlinear 3D Overhead Crane

We consider an online policy iteration-based reinforcement learning for a class of a nonlinear three-dimensional overhead crane with bounded uncertainties. Under the assumption that the rope length is fixed with small swing angles, a linearized model is derived. The system has four states; two actuated states: position x and y, and two un-actuated states, which are the rope angles θx and θy. The adaptive reinforcement learning controller is designed to handle the effects of measurement noises and outliers. We propose a model-free; hence it does not require precise knowledge of the system dynamics. When the state information is not available, a Kalman filter estimator is equipped with a dynamical saturation function to attenuate the effects of measurement noises and to remove outliers. A simulation study is established to illustrate the influence and robustness of the developed controller, and it can enhance the tracking trajectory under different scenarios to test the scheme.

Electro-lattice actuator: a compliant high-contractile active lattice structure

Electro-ribbon actuators are high-performance electrically-driven artificial muscles with high flexibility, low mass, low power consumption, high contraction, and high force-to-weight ratio. They show great promise for driving the deployment of compact folding structures. This article presents the electro-lattice actuator (ELA), a compliant, three-dimensional, free-standing lattice structure that uses this phenomenon to contract to a flat sheet upon the application of a potential difference. The ELA was designed in the form of multiple interconnected buckled structures and fabricated using polyvinyl chloride sheets and tape and copper electrodes. The ELA structure was pre-set into an open-cell configuration by annealing in an oven. Isometric testing at varying compressions showed that the tensile stress of the proposed lattice actuator reaches a maximum of 184 Pa (a 472 Pa change in tensile stress compared with its unactuated state). A cuboid shaped ELA (13.6 cm length × 10.0 cm width × 5.4 cm height) achieved a contraction of 92.6% and a contraction rate of 35.6% s−1. The novel ELA opens up the use of electro-ribbon actuation to more complex and more effective 3D actuating and deploying structures.

Nonlinear vibration suppression control of underactuated shipboard rotary cranes with spherical pendulum and persistent ship roll disturbances

Shipboard rotary cranes are widespread used in industrial fields to carry out large-scale cargoes under marine environment, which are a class of representative nonlinear systems. For crane systems, there exist unactuated state variables (e.g., payload swing angles), which hence make them typically underactuated systems, whose degrees of freedom (DOFs) are more than the number of control inputs. Besides, due to the complexity disturbances of the marine environment, there are always inaccuracies in the three-dimensional (3D) dynamics model of shipboard rotary cranes, such as ocean waves, wind waves, ocean currents and so on, which make the control methods hard to achieve the perfect control effect. Most of the existing methods are built on the basis of simplified linear model, which often require precise model parameters or velocity signals. In order to solve the control problems caused by the above uncertainties, this paper proposes two nonlinear anti-swing control methods. First, considering the uncertain parameters, an adaptive controller is designed, which can achieve the control effect of suppressing swing when the model has unknown parameters. Second, considering the unmeasurable velocity signals, an output feedback controller is designed, which can achieve the control effect to suppress the swing angle with no need of velocity signals. On the basis of the above two control methods, we design corresponding different energy storage functions including kinetic energy and potential energy, respectively. Specifically, this paper has achieved an excellent effect of restraining swing without any linear approximation of the dynamic model. Lyapunov theorem and LaSalle invariance principle are utilized to further prove the asymptotic stability of the closed-loop system. Finally, experiments are implemented to further demonstrate the effectiveness of the proposed control methods.

Optimization of Scattering Parameters Through Numerical Investigation of One-Bit RF MEMS Switch Over Ku, K and Ka Band

Aim: Computation of loss factors for one-bit RF MEMS switch over Ku, K and Ka-band for two different insulating substrates. Objective: Numerical investigation of return loss, insertion loss, isolation loss are computed under both actuated and unactuated states for two different insulating substrates of the 1-bit RF MEMS switch, and corresponding up and down-capacitances are obtained. Methods: The unique characteristics of a 1-bit RF MEMS switch of providing higher return loss under both actuated and unactuated states and also of isolation loss with negligible insertion loss makes it as a prime candidate for phase shifter application. This is presented in this manuscript with a keen focus on improvement capability by changing transmission line width, and also of overlap area; where dielectric constant of the substrate also plays a vital role. Results: The present work exhibits very low down-capacitance over the spectrum whereas considerable amount of up-capacitance. Also when overall performance in terms of all loss parameters are considered, switch provides very low insertion loss, good return loss under actuated state and standard isolation loss. Conclusion: Reduction of transmission line width of about 33% improved the performance of the switch by increasing isolation loss. Isolation loss of -40 dB is obtained at actuated condition in higher microwave spectra for SiO2 at higher overlap area. Down capacitance of ~ 1dB is obtained which is novel as compared with other published literature. Moreover, a better combination of both return loss, isolation loss and insertion loss are reported in this present work compared with all other published data so far.

Gain-adapting coupling control for a class of underactuated mechanical systems

While presenting many advantages in application, the loss of actuators also brings about great challenge to the control of underactuated systems. Specifically, the unactuated DOFs (degrees of freedom) cannot be directly controlled, instead, they have to be stabilized indirectly through appropriate regulation of actuated ones. As an unfortunate fact, the natural couplings between actuated and unactuated states are often relatively weak. Hence, in many practical cases, even the actuated states are well regulated, the performance of the unactuated states still fails to meet expectations. Such phenomenon is particularly obvious when the system faces various disturbances, since the unactuated states are more vulnerable to them and more difficult to be re-stabilized. To deal with the aforementioned issues, a nonlinear gain-adapting controller is proposed for a class of underactuated mechanical systems, which incorporates extra unactuated states-related information into the controller to enhance the state couplings. In this way, the closed-loop system reacts more appropriately and efficiently to the unactuated dynamics, which is expected to obtain improved transient performance and robustness. With a relatively concise structure, the proposed strategy imposes few requirements on the system configuration, which makes it more convenient for practical application. Theoretical analysis and experiment results are presented to demonstrate the performance of the proposed method.

Adaptive fractional-order terminal sliding mode control of rubber-tired gantry cranes with uncertainties and unknown disturbances

Using three actuators for tracking five outputs, rubber-tired gantry (RTG) crane is found to be a highly under-actuated system subject to random wind due to working outdoors. Applying fractional calculus to sliding mode control (SMC), we construct an adaptive robust control system for RTG cranes under parametric variations and unknown wind. The adaptive feature is achieved by using an estimation mechanism for approximating five crane parameters and wind disturbances. The core of the sliding mode displays robust behavior against uncertainties. For comparison, another robust controller is proposed based on finite-time sliding mode. Simulation and experiment results show the superiority of adaptive fractional-order sliding mode control, in which the controller well tracks actuated states and stabilizes unactuated states despite parametric uncertainties and unknown disturbances.

Lyapunov-Based Nonlinear Control Applied to a Control Moment Gyroscope

One of the main applications of a mechanical control moment gyroscope (CMG) as actuator is the attitude control of spacecraft and satellites, which requires a wide operating range. Motivated by this, this paper investigates the feasibility of a Lyapunov-based nonlinear control applied to the tracking task of a CMG unit from Educational Control Products, model 750, in its SISO configuration. This problem involves an underactuated system, in which the output signal is the unactuated state, posing additional challenges to control design. To deal with it, an additional internal control signal is employed and the stability analysis of the closed-loop system is given by invoking both Lyapunov stability and Matrosov’s theorem. To validate the proposed controller, numerical simulations and practical experiments were performed and contrasted with the authors’ previous designed nonlinear controllers.

Adaptive non‐linear integral sliding mode fault‐tolerant control allocation scheme for octorotor UAV system

This study proposes a new active fault-tolerant control (FTC) and fault estimation scheme for a non-linear octorotor system. The proposed method utilises the idea of an online control allocation (CA) scheme to fully engage the rotors redundancy based on the information from the fault estimation unit. The nominal performance is first achieved using non-linear dynamic inversion (NDI) technique and then to incorporate the robustness, an adaptive non-linear sliding mode control is united with a baseline NDI controller. The proposed method is used to attain the desired altitude and attitude tracking control of an octorotor system. Furthermore, to control the un-actuated states (called internal dynamics) of octorotor system, a separate integral sliding mode-based NDI controller is designed that provides the translational axes control by generating the desired roll and pitch commands. Simulations on the non-linear model of octorotor system validate the dominant performance of the proposed scheme compared to the existing methods in the literature.

Passivity-Based Nonlinear Control Approach for Tracking Task of an Underactuated CMG

This article proposes a passivity-based nonlinear control approach to deal with the tracking task of a control moment gyroscope (CMG), which is an underactuated nonlinear MIMO system with coupled dynamics, where the main goal is the tracking of the unactuated states in a wide range of operation. To overcome this underactuation, the proposed nonlinear controller employs the CMG intrinsic reaction torques. The closed-loop system stability is analyzed by invoking the Lyapunov stability and Matrosov's theorem. Numerical simulations and real-time practical experiments with the real plant are performed to validate the proposed nonlinear controller, as well as its performance is analyzed by contrasting the experiment results with the ones obtained by authors’ previous established nonlinear controllers.

Adaptive Sliding-Mode Control of an Offshore Container Crane With Unknown Disturbances

In this paper, an adaptive sliding-mode control (ASMC) for offshore container cranes that load/unload containers from a mega container ship to a smaller vessel is investigated. To withstand the harsh working conditions in the open sea, such as ship motions and winds, a 4-degrees-of-freedom control model consisting of plant uncertainties and known/unknown disturbances is newly developed. After decoupling the actuated (i.e., trolley displacements) and unactuated (i.e., swing angles) joint variables, a sliding surface that incorporates the decoupled dynamics is designed. Then, a new sliding-mode control (SMC) algorithm with two adaptation laws for switching- and equivalent-control inputs is developed. The asymptotic stability to the “real” sliding surface introduced in the decoupled (actuated, unactuated) state space is proven without a priori knowledge on the bounds of unknown disturbances. For the experiment, a three-dimensional crane mounted on a Steward platform to generate the ship motions is utilized. To verify the effectiveness of the proposed ASMC method, experimental results of the proposed method are compared with two representative works: the SMC presented by Ngo and Hong and the ASMC presented by Zhu and Khayati. The vibration suppression capability of the proposed method in the presence of ship motions, large initial swings, parameter uncertainties, and sudden disturbances is superior to the two compared methods. The developed algorithm can be used for a mobile harbor system as a new tool in the modern maritime industry.

Nonlinear Control of Underactuated Systems Subject to Both Actuated and Unactuated State Constraints With Experimental Verification

In practice, underactuated systems are widely used, and their control problems have attracted much attention in recent years. For safety concerns or transient performance requirements, some state constraints should be guaranteed both theoretically and practically, particularly those exerted on unactuated states. To the best of our knowledge, there are few closed-loop control methods that can treat unactuated state constraints with theoretical guarantees (i.e., that can theoretically guarantee unactuated state variables to be always within the preset ranges). For this purpose, in this article, we propose a new control strategy for a class of underactuated systems that can treat the various constraints including actuated and unactuated state constraints and the constraints on some specific composite variables. Specifically, we elaborately design some new auxiliary terms that are composed of constrained variable signals and actuated velocity signals. These terms can enhance the couplings between unactuated and actuated states that are further utilized to tackle the unactuated state and composite variable constraints. Then, the performance of the designed method is proven by rigorous analysis. Finally, the proposed method is applied to a double pendulum crane system and a tower crane system to verify its superior performance by experiments.

Neural Network-Based Adaptive Antiswing Control of an Underactuated Ship-Mounted Crane With Roll Motions and Input Dead Zones.

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.

Continuous Sliding Mode Control Strategy for a Class of Nonlinear Underactuated Systems

Sliding mode control (SMC), which is known to present strong robustness against various disturbances, has been extensively employed on underactuated systems, whose control problem has been a research focus in recent years. However, though received great attention, the study on SMC for underactuated systems still remains quite open since it is very challenging to construct a proper manifold which can simultaneously stabilize both actuated and unactuated system states. Motivated to promote the corresponding research, we propose an improved second-order SMC (IS-SMC) method for a class of nonlinear underactuated systems in this paper, which guarantees that the closed-loop system's equilibrium point is asymptotically stable even in the presence of unknown nondiminishing disturbances. Different from traditional SMC methods presenting with chattering problem, the control inputs of the proposed method are essentially continuous, which brings much convenience for practical applications. Moreover, for the disturbances which are second-order differentiable, an enhanced IS-SMC (EIS-SMC) method is derived to guarantee the smoothness for both the control inputs and their derivatives. Finally, the proposed approach is applied to a practical underactuated system: The overhead crane system, with sufficient simulation results provided to validate the efficiency of the proposed method.

Bioinspired Design of Vascular Artificial Muscle

AbstractRecently, liquid crystal elastomers (LCEs) have drawn much attention for its wide applications as artificial muscle in soft robotics, wearable devices, and biomedical engineering. One commonly adopted way to trigger deformation of LCEs is using embedded heating elements such as resistance heating wires and photothermal particles. To enable the material to recover to its unactuated state, passive and external cooling is often employed to lower the temperature, which is typically slow and environmentally sensitive. The slow and uncontrollable recovery speed of thermally driven artificial muscle often limits its applications when even moderate cyclic actuation rate is required. In this article, inspired by biology, a vascular LCE‐based artificial muscle (VLAM) is designed and fabricated with internal fluidic channel in which the hot or cool water is injected to heat up or cool down the material to achieve fast actuation as well as recovery. It is demonstrated that the actuation stress, strain, and cyclic response rate of the VLAM are comparable to mammalian skeletal muscle. Because of the internal heating and cooling mechanism, VLAM shows a very robust actuating performance within a wide range of environmental temperatures. The VLAM designed in this article may also provide a convenient way to harvest waste heat to conduct mechanical work.