Continuum robots (CRs) show great potential in complex environments due to their excellent deformability. For practical applications, the position control of the CRs is an important research field. The common drives of the CRs are rigid motors with mature control schemes. However, the driving force of the rigid motors is often impactive, which may cause safety concerns during interaction. Soft drives based on pneumatic soft actuators (PSAs) can provide compliant driving force for the CRs robot bodies to solve this problem, but it is necessary to comprehensively consider the control of the soft drives and the robot bodies. This article takes a CR with soft drives as the research objective, and proposes a double closed-loop adaptive position control method to achieve the endpoint position control of the CR. This CR includes a length-variable robot body with millimeter-scale diameter and pneumatic soft drives. The kinematic model of the robot body is built based on the piecewise constant curvature (PCC) method, and the static models of the soft drives are derived from the three-element model. Based on these models, we propose a double closed-loop adaptive position control method. The inner loop is used to control the displacements of the soft drives, and the outer loop combines the endpoint position control with the nonsingular fast terminal sliding mode function to adaptively control the endpoint position based on the inner loop. By Lyapunov method, we prove the convergence of the endpoint position error. The effectiveness of the proposed control method is verified through experiments.

This paper proposes efficient modeling and control methods for a continuum robot (CR) composed of a three-segment robot body (two proximal segments and a distal segment with an endpoint) and soft drives. Each segment incorporates multiple mutually exclusive magnetic spacer disks for a flexible structure, and the soft drives are designed based on pneumatic soft actuators (PSAs) to ensure operational safety. For both computational efficiency and tracking performance, an open-loop control method based on the kinematic model of the robot body is adopted to operate the two proximal segments, and a feedforward-feedback control method based on the dynamic model of the distal segment derived from the Euler-Lagrange method is proposed to control the endpoint trajectory. During the dynamic modeling process of the distal segment, the magnetic potential energy is considered additionally by simplifying the magnetic spacer disks to multiple magnetic dipoles. Moreover, the relationship between the input pressures of the soft drives and the generalized force of the dynamic model is derived from the three-element model and the principle of virtual power. Experiments demonstrate the effectiveness of the proposed modeling and control method.

Due to the complex nonlinear behavior and external sensitivity of pneumatic soft actuators (PSAs), it is difficult to design control methods to achieve their control objectives by establishing their precise specific models. This article takes a PSA with bellow-type folds, called pneumatic bellow actuator (PBA), as the object, and proposes an adaptive nonsingular fast terminal sliding mode (NFTSM) control method with time-delay estimation (TDE) to achieve the trajectory tracking control of the PBA without relying on its specific model. The model framework of the PBA is first discussed, but the specific model is unknown, and all the unknown model information is defined as the lumped unknown dynamics. The TDE is applied to obtain the estimation of the lumped unknown dynamics using only the measured system states. Based on the estimation information, an adaptive NFTSM control method is proposed. This control method is nonsingular, continuous, adaptive, and accurate. Since the step of establishing the specific model of the PBA is omitted, and the model framework used in this article is universal for many PSAs, this control method exhibits universal applicability for controlling other PSAs that have difficulty obtaining specific models. The effectiveness is validated through stability analysis and PBA tracking experiments under different loads.

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.

Soft manipulators have been widely developed due to their manipulation safety, design versatility, and motion dexterity. However, accurate kinematic modeling and control of soft manipulators are still challenging due to the complex nonlinear hysteresis in their motion characteristics. This article presents the fabrication of an elephant-trunk-inspired soft manipulator (ESM) using pneumatic bellows actuators (PBAs) and proposes a kinematic modeling and control method considering hysteresis. The ESM contains three soft arms and a pneumatic claw, while each soft arm consists of four PBAs connected in parallel. The forward kinematics of the ESM are modeled using the piecewise constant curvature (PCC) method. The kinematic model of the ESM consists of three parts: actuator space, configuration space, and task space. To address the inability of the PCC method to characterize the nonlinearity of soft materials, the hysteresis of the PBA in the actuator space is modeled using the Prandtl–Ishlinskii model. The inverse kinematic model of the ESM is derived from its forward kinematic model, and on this basis, a feedforward controller is developed to achieve position control of the ESM. The positional workspace of the ESM is analyzed using the Monte Carlo method. The validity of the kinematic model is verified experimentally. Position control and application experiments are conducted to demonstrate the practical application of the ESM.

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.

For a three-link vertical underactuated manipulator (TVUM) with only one active joint, the control target is to swing up its endpoint from the straight-down equilibrium point (SDEP) and to stabilize the endpoint at the straight-up equilibrium point (SUEP) eventually. Up to now, there are few effective control strategies to achieve the above control target. In this article, we propose an effective control method based on the trajectory optimization to realize the system control target, and the main steps of this article are: 1) a continuous trajectory that consists of two segments with design parameters is planned for the actuated link, along which the actuated link can be swung up from the initial states to the final states; 2) the design parameters are optimized by using the intelligent optimization algorithm to guarantee that the states of the underactuated links are continuous at the junction. In this way, the underactuated links are also moved to their final states with the actuated link simultaneously; 3) a tracking controller is designed by using the sliding-mode method to track the trajectory with optimized design parameters, so the endpoint is swung up from the SDEP to the SUEP directly; and 4) a stabilizing controller is further devised through the LQR method to keep the endpoint being stable at the SUEP. Finally, simulation results show that the proposed control method achieves the swing-up and stable control target of the system, and the control performance of the proposed method is superior than that of the existing control methods through the comparisons.

When a flexible link manipulator lacks a joint motor, how to use the remaining motors to achieve the control objective is a challenge, and the research in this direction is limited. This article presents a tip position control and vibration suppression approach for a planar two-link rigid-flexible (TLRF) underactuated manipulator with a passive first joint. First, we establish a dynamic model of the system by using the assumed mode method (AMM) and the Lagrangian modeling method. Then, we obtain the dynamic coupling relationship of the two links based on the dynamic model. According to this dynamic coupling relationship, we find that the passive rigid link can be controlled indirectly by controlling the active flexible link. Thus, we calculate the target angles of the two links by using the inverse kinematic method and design a controller for the active flexible link to stabilize it at its target angle and to suppress its vibration. Next, we optimize the parameters of this controller by using the genetic algorithm (GA). GA helps us simultaneously stabilize the passive rigid link at its target angle while realizing the control objective of the active flexible link. The simulation results demonstrate the effectiveness of the proposed control approach.

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

Single-link flexible-joint manipulator (FJM) is a kind of time-varying nonlinear system with underactuated characteristics. This paper takes the uncertain single-link FJM (USLFJM) as the object, and presents a novel robust control approach based on equivalent input disturbance (EID) method for motion control (i.e., position control and trajectory tracking control) of the USLFJM. Based on the uncertain dynamic model and desired target of this system, an error system is constructed. The error system is considered as a linear system with a nonlinear virtual disturbance. The motion control objective of the USLFJM can be realized by globally asymptotically stabilizing this linear system and compensating the influence of the nonlinear virtual disturbance. Then, an EID-based control system is designed to realize this control objective. Only position measurements are utilized in this paper, and the stability of the control system is proved. The simulation results are presented to illustrate the validity and the robustness of the proposed control method.