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The dielectric electro-active polymer (DEAP) actuator, which features large deformation and fast response, has been widely utilized in soft robots. However, the complex hysteresis, creep and quadratic input nonlinearity of the DEAP actuator pose great difficulties and challenges for its controller design. In this article, an inverse compensation-based global fast terminal integral sliding mode control scheme with lumped uncertainty fuzzy estimation is presented for the high-precision tracking control of the DEAP actuator. On the basis of the analytical inverse of a modified Prandtl–Ishlinskii model and a square root module, an inverse compensator is developed to compensate for the hysteresis and the quadratic input nonlinearity of the DEAP actuator. For the system after inverse compensating, a K-observer is adopted to estimate the immeasurable state, and a fuzzy system is used to estimate the lumped uncertainty. Then, a global fast terminal integral sliding mode controller is devised and cascaded in series with the inverse compensator to form a closed-loop control system. The stability and the finite time convergence of the closed-loop control system are proven in theory. Finally, the practical application feasibility and the excellent performance of the developed control scheme are demonstrated via experiments on a testbench for the DEAP actuator.

In this paper, we present an adaptive control method for a conically shaped dielectric elastomer actuator (CSDEA) with different loads to achieve its tracking control objective. Firstly, a dynamic model of the CSDEA is constructed to describe its asymmetrical, rate-dependent hysteresis behavior and creep behavior simultaneously. Then, an offline parameter identification method based on the nonlinear-least-squares algorithm is presented to obtain the nominal values of the model parameters of the CSDEA corresponding to the load of 200 (g). The obtained values are regarded as the initial values of the adaptive online parameter identification. Next, an adaptive online parameter identification method (AOPIM) based on the least-mean-square algorithm is proposed, which can dynamically calculate and update the model parameter values to cope with the load changing of the CSDEA. Lastly, based on two kinds of analytical inverses of the dynamic model and the proposed AOPIM, two adaptive inverse compensators are respectively designed to realize the tracking control of the CSDEA. The control experiments with different desired trajectories and different loads are implemented to demonstrate the effectiveness of the presented adaptive control method. Since the root-mean-square errors of the results of all control experiments are lower than 2.7%, the presented method is remarkable from the perspective of the practical application. Note to Practitioners—The dielectric elastomer material has beneficial properties of high energy density, low mass density, large deformation, fast response and good biological compatibility. Thus, the soft actuator based on the dielectric elastomer material (SADE) has shown great potentials for being used in soft robots. Nevertheless, the SADE has the complex nonlinear behaviors, which brings a big challenge for its precision control. To deal with this issue, some approaches have been presented in previous literatures. However, the load of the SADE is usually fixed in these studies. This paper focuses on the tracking control of the SADE with different loads. To this end, a dynamic model of the CSDEA is constructed, whose parameter values are dynamically calculated and updated to cope with the load changing of the CSDEA. Through calculating the analytical inverse of the dynamic model, two adaptive inverse compensators are developed. The control experimental results demonstrate that the presented adaptive control method is effective. Considering that the load of the SADE is usually diverse in practical applications, this study pays the way for the application of the SADE.

The dielectric elastomer actuator (DEA) is an intelligent device with an actuation-sensing integration capacity, which exhibits prospective applications in the field of soft robotics. Previous studies mainly focus on the actuation capacity of the DEA, while the studies on its sensing capacity and the practical realization of its actuation-sensing integration still confront great challenges. This article presents a self-sensing motion control scheme to realize the tracking control objective of the DEA, thus leaving out the use of the external displacement sensor. First, a self-sensing model of the DEA is established based on the nonlinear autoregressive with exogenous inputs (NARX) neural network to predict its own displacement. Then, by adopting the dynamic model of the DEA as the control object, a simulation environment based on the iterative learning control architecture is built to obtain the feedforward control sequence for tracking a target trajectory. Next, to enhance the control quality, the proportional–integral feedback controller is designed to combine with the feedforward control sequence to handle the uncertainties in practical experiments, in which the feedback signal is the output of the self-sensing model. Finally, several trajectory tracking control experiments are performed. The maximum value of the relative root-mean-square errors for all experimental results is less than 3.60%, which illustrates the effectiveness of the presented self-sensing motion control scheme.

Smart soft dielectric elastomer actuators (SSDEAs) possess wide applications in soft robotics due to their properties similar to natural muscles, including large deformation ratio, high energy density, and fast response speed. However, the complicated asymmetric and rate-dependent hysteresis property, creep property and quadratic input property of the SSDEA pose enormous challenges to its dynamic modeling and motion control. In this paper, first, we construct the dynamic model of the SSDEA by connecting a square module, a one-sided Prandtl–Ishlinskii (OSPI) model and a linear system in series to describe the above properties. The key and innovative aspect of the dynamic modeling lies in cascading the square module in series with the OSPI model to construct the asymmetric hysteresis model. Subsequently, a PI-funnel and inverse hysteresis compensation (PIFIHC) cascade control method of the SSDEA is proposed to actualize its tracking control objective. By performing the inversion operation on the asymmetric hysteresis model, the inverse hysteresis compensation controller (IHCC) is designed to compensate the asymmetric hysteresis property and quadratic input property of the SSDEA. In addition, a PI-funnel controller is designed to cascade with the IHCC to construct the PIFIHC cascade controller to obtain a good tracking performance. Then, the stability analysis of the PIFIHC cascade control system of the SSDEA is performed to theoretically prove that the tracking error can be controlled within the performance funnel and the steady-state error converges to zero. Finally, several practical tracking control experiments of the SSDEA are conducted, and RRMSEs are less than 2.30% for all experiments. These experimental results indicate the effectiveness and feasibility of the proposed PIFIHC cascade control method of the SSDEA.

A dielectric elastomer smart actuator (DESA) has shown great potentials in soft robot applications. The control of the DESA is one of key issues for soft robots. However, the precise control of the DESA is a challenge work, especially when tracking high-frequency trajectories and guaranteeing a certain robustness. To this end, this article presents a robust tracking control method for a DESA to track various high-frequency trajectories. First, to characterize the complex nonlinear properties (including the quadratic input, asymmetric and rate-dependent hysteresis, as well as creep) of the DESA, its dynamic model is built by combining a square function module, a modified Prandtl–Ishlinskii (P–I) hysteresis model, and a linear system. Subsequently, by combining the inverse of the modified P–I hysteresis model with a square root function module, the quadratic input and asymmetric hysteresis properties of the DESA are compensated to reduce the tracking control error. Since model uncertainties and external disturbances are unavoidable in practical applications, a robust controller is designed to achieve the tracking control of the DESA, the controller also guarantees the robustness of the control system. Finally, the effectiveness of the proposed control method is demonstrated through a series of tracking control experiments with different high-frequency trajectories, whose maximal frequency is 8 Hz. The root-mean-square errors of all the experimental results are lower than 1.5%, which proves that the presented method is remarkable from the perspective of the practical application.

This article presents a model reference adaptive control method (MRACM) for the high-precision tracking control of a dielectric elastomer material-based intelligent actuator (DEMIA). First, a dynamics model of the DEMIA is established to delineate its complex nonlinear behaviors. Second, a feed-forward inverse compensation control method (FICCM) is proposed to compensate for the nonlinear behaviors of the DEMIA, so as to preliminarily achieve its tracking control. Third, due to the fact that model uncertainties and external disturbances are inescapable in practical applications, a MRACM based on the established nominal model of the DEMIA is further presented to improve the tracking control performance. The stability of the entire control system is proved via the Lyapunov method. In the end, a series of tracking control experiments with different multifrequency expected trajectories are executed to illustrate the validity of the proposed control methods. The root-mean-square errors of all control experiment results are less than 2.8%, which reflects that the proposed MRACM is distinguished from a practical application perspective.

Liquid crystal elastomer (LCE) is a promising candidate for actuation in light-driven soft robot applications. Due to the fact that LCE has complex hysteretic nonlinearities, which are highly dependent on the environment, modeling of actuators made of LCE is a very challenging issue. In this article, a model is proposed to describe the deformation of the LCE actuator accurately and analytically by considering the dynamic phase transition process of LCE molecules. First, an overview of the physical process of LCE’s deformation is presented, and the schematic of the LCE actuator, as well as the modeling scheme are then introduced. Next, a thermodynamic analysis of the system’s free energy is performed to establish the model for the LCE actuator, which gives the relationship between the system’s deformation and the temperature. Here, to describe the complex hysteretic nonlinearity in the model, the dynamic process of the phase transition of LCE molecules is exploited. To effectively identify the model parameters, a two-step parameter identification strategy based on the differential evolution algorithm and nonlinear least-squares method is utilized. Finally, experimental results verify the validity of the proposed model. This modeling provides an approach to describe LCE’s deformation with high accuracy and can fully reflect the physical nature of LCE’s deformation, especially hysteresis. It can be utilized as a basis for accurate control over LCE actuators in photoresponsive soft robot applications.

In recent years, the dielectric elastomer actuators (DEAs) have been increasingly used to drive the soft robots. This paper proposes a tracking control method for the DEA based on the inverse dynamic compensation method. Firstly, a dynamical model of the DEA is established to depict its asymmetric hysteresis, rate dependent hysteresis and creep nonlinear behaviors simultaneously. Next, according to the inverse of the dynamical model, an inverse dynamic feedforward compensator (IDFC) is devised to compensate the hysteresis nonlinearity and creep nonlinearity of the DEA. Then, a PI feedback controller is designed to collaborate with the IDFC, which can enhance the robust performance of the whole control system. Finally, the tracking control experiments with different target trajectories are carried out. The root-mean-square errors of all control results are less than 1 % and the maximum value of the relative tracking errors is less than 8 % , which illustrates that the proposed tracking control method is effective and excellent. [ABSTRACT FROM AUTHOR]

This paper presents a new control strategy based on Fourier transformation and intelligent optimization for a planar Pendubot with a passive second link, which can be treated as a second-order nonholonomic system whose control has been an open and challenging issue. A controller acting within a time corresponding to the frequency of its fundamental harmonic term is designed to realize the system control objective, which is to move the system from its initial position to the target position. By employing Fourier transformation, a general expression of the controller composed of a constant term and harmonic terms is obtained. Next, the constant term is obtained by the angular momentum theorem, and the particle swarm optimization algorithm is employed to obtain the harmonic terms of the controller. A feedback control strategy based on a nonlinear disturbance observer is then applied to overcome the uncertainties/disturbances in the system. Finally, simulation results prove the validity of this control method. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n -link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n -link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy. [ABSTRACT FROM AUTHOR]

This paper presents a quick two-stage position control strategy based on a hybrid intelligent optimization algorithm for a planar n -link underactuated manipulator with a passive first joint. In stage 1, the system is directly reduced to a planar virtual Acrobot by controlling n -2 active links to their target angles. A hybrid intelligent optimization algorithm, which includes genetic algorithm (GA) and particle swarm optimization algorithm (PSO), is used to solve all link target angles according to the target position of the system. By coordinating GA and PSO, the hybrid intelligent optimization algorithm ensures that all link target angles, the angle of the passive link at the end of stage 1, and the initial angle of the active link of the planar virtual Acrobot meet the angle constraint of the planar virtual Acrobot. So, the position control objective of the planar n -link underactuated manipulator is realized by controlling the active link of the planar virtual Acrobot to its target angle in stage 2. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers (LCEs) offer promising prospect in applications such as soft robot actuators due to the fact that they can be chemically doped to have photo-responsive deformation characteristics. With the purpose of accurate control of LCE actuators in soft robot applications, the establishment of a model which quantitatively describes the deformation characteristics of LCE becomes essential. However, current models for LCE are very preliminary, which restricts the implementation of LCE actuators. This paper develops a model to describe the deformation of LCE actuators. First, the deformation process is discussed, which is in nature the macroscopic shape change corresponding to the phase change of LCE. Then, the relationship between the deformation and the temperature of LCE is established according to thermodynamic analysis on the free energy, and the phase transition process. Unknown parameters are determined through parameter identification with experimental data based on the non-linear least-squares method. This model has the advantage that it quantitatively describes the deformation characteristics of LCE without the aid of numerical simulation, and it reflects the physical nature of the deformation of LCE. This model lays a basis for the accurate control of the LCE actuators, which leads to future photo-responsive soft robot applications. [ABSTRACT FROM AUTHOR]

In this paper, we develop a quick and effective position control strategy based on the differential evolution (DE) algorithm for a planar three-link passive-active-active (PAA) underactuated system with first-order nonholonomic constraint. Due to the existence of the constraint, when the angular velocities of the two active links are proportional, the planar PAA system is transformed from a first-order nonholonomic system to a holonomic system like an Acrobot. Making full use of the angular constraint of the like-Acrobot, we employ the DE algorithm to calculate the target angles of all links and the target ratio between the angular velocities of the two active links. After that, one continuous controller for one active link is designed to ensure the target ratio in the whole control process; meantime, the other continuous controller for the other active link is designed to make its angle asymptotically converge to the corresponding target value. In this way, the angles of all links can asymptotically converge to the corresponding target values according to the angular constraint, and thus the position control of the system is realized using the continuous control method. Finally, the simulation results demonstrate the quickness and effectiveness of our proposed control method. [ABSTRACT FROM AUTHOR]

Multiple magnetically controlled soft robots are more efficient in terms of task execution. However, how to realize such multiple robots moving along the respective different paths is still a challenge since they are in one driving magnetic field. In order to deal with this problem, this paper proposes a cooperative control method by fusing their parallel cooperative motion (multiple robots moving simultaneously) and their independent cooperative motion (single robot moving). Yet, there are two strong couplings in the fusion of such two cooperative motions, which makes the control more difficult. Thus, an enumeration-based decoupling algorithm is developed for the first combined mode coupling, and the speed of each robot is planned for the second motion speed coupling. Then, a neural network-based controller is developed to achieve the respective speed control simultaneously of multiple robots, and the deviation limiting controller is constructed to compensate the deviation angle. Finally, through the actual experiments, it is verified that the proposed method realizes effectively the motion of two robots along different paths and the mean absolute error of speed is about 0.1091 mm/s and 0.2118 mm/s, while the mean absolute error of tracking is about 0.3369 mm and 0.4454 mm, respectively. [ABSTRACT FROM AUTHOR]

Currently, there are some new challenges for pneumatic soft robots brought by complex application environments and variable task objectives. To address these challenges, inspired by the building blocks, we develop a novel pneumatic soft actuator named pneumatic bellows actuator (PBA) that can generate bidirectional deformation, and propose a building block design concept for the soft robots based on the developed PBA. The PBA consists of three parts: a soft rubber layer (SRL), a fiber-reinforced layer (FRL) and some rigid joints. We design the SRL as a bellows-like shape so the PBA can generate bidirectional deformation, and weave an FRL as the coating of the SRL to prevent the significant radial expansion of the SRL that may affect the application of the PBA. The rigid joints include sealing glands and connectors. The sealing glands are used to seal the SRL, while the connectors having interfaces on their five surfaces are used to connect the PBAs through the customized plugs corresponding to these interfaces. Moreover, the experimental results indicate that the PBA can generate large deformation and driving force, while it has the advantages of good repeatability and approximate rate-independent under low frequency. Based on the building block design concept for the soft robots, we construct three PBA-based soft robots: a soft crawling robot, a soft gripper, and a soft manipulator, to demonstrate that we can easily use the PBAs to construct various soft robots. [ABSTRACT FROM AUTHOR]

Zero residual vibration (RV) in the position control of a flexible system is difficult to achieve because this system has low stiffness and underactuated feature. In this paper, we present a position control strategy to achieve zero RV in the position control of two degrees-of-freedom (DOF) flexible systems. First, a general dynamic model for two-DOF flexible systems is established. Next, we transform the position control with zero RV to motion planning and tracking control. Based on the position control objective with zero RV, three constraints for the desired system trajectory are given. To make the desired system trajectory satisfy these three constraints, we propose a motion trajectory optimization method. Specifically, we plan a forward system trajectory and a reverse system trajectory based on bidirectional trajectory planning method. Then, the rewinding strategy and the trajectory optimization based on genetic algorithm are used to connect these two system trajectories and to obtain a complete desired system trajectory. Finally, a sliding mode tracking controller is designed to make the system track this desired system trajectory. In this way, the system can reach its target-rest-position with zero RV. The effectiveness and superiority of the proposed control strategy are demonstrated in simulations. [ABSTRACT FROM AUTHOR]