Due to their continuous electromechanical deformation, rate-dependent viscoelasticity, and complex mechanical vibration, dynamic modeling and high-speed tracking control of dielectric elastomer actuators (DEAs) remain elusive, significantly limiting their working bandwidth. In this work, we propose a Physics-Informed Token Prediction (PITP) that enables accurate modeling of DEA dynamics and high-speed feedforward tracking control. The PITP framework consists of two key components: a physics-informed encoder and a dynamic decoder. The physics-informed encoder is designed based on a simplified equivalent linear model and trained through the hierarchical optimization training method, which embeds the global dynamic characteristics into tokens, minimizing the need for extensive data and training. Then, the dynamic decoder is developed by using these tokens as state-dependent parameters, capable of describing complex dynamic responses through the autoregressive solution. Finally, by taking advantage of the model's reversibility, a direct inverse compensator is established to linearize the input-output relationship. Experimental results of several DEAs with different configurations and payloads demonstrate that, based on our PITP framework, the complex nonlinear dynamic responses of all DEAs can be precisely described and eliminated within their natural frequency, validating its generality and versatility. By leveraging fast modeling ($< $30 minutes) and high-speed feedforward tracking control, our PITP framework may accelerate DEAs' practical applications.

Trajectory tracking control of flexible continuum robots is challenging due to their inherent compliance and high nonlinearity. Many related works exclude the control of the end's orientation, i.e., only the end's position is considered. In this article, a differential-algebraic equations (DAEs) model-based instantaneous optimal control (IOC) framework for the end's position and orientation cooperative tracking of a cable-driven tensegrity continuum robot (TCR) is developed. Based on the tensegrity concept, a TCR is designed first as the control object, which can achieve multimode deformations such as bending, scoliosis, contraction, and the S- or J-shape. Then, the actuation of cables is introduced as the system kinematic constraints from the view of multibody dynamics so that a control-oriented model of the TCR can be built by DAEs. Subsequently, the original continuous trajectory tracking problem is approximated for a series of IOC problems at each discrete time slot. Finally, considering the constraints of control input saturation, a linear complementarity problem was derived for solving these IOC problems. The method provides an easy-to-implement and unified framework for addressing the trajectory tracking control issues of cable-driven continuum robots, which can improve the control performance of the position-only tracking controllers and exploit the TCR's advantages to handle more application scenarios. The advanced performance and potential applications of the proposed controller have been evaluated via several numerical simulations and experiments on the TCR prototype.

PneuNet, consists of a series of interconnected chambers embedded within a soft elastomer material, can exhibit diverse deformations. 3D printing allows for precise control over both material combinations and geometrical configurations, enabling the fabrication of PneuNets with complicated structures and multifunctionality. However, the increased freedom in material and structures introduced by 3D printing also presents significant challenges for modeling and design, including material nonlinearities, complex cross-sections and varying initial curvatures. In this work, we develop 3D-printed PneuNets with varying initial curvatures and cross-sections demonstrating finite deformation with multiple complete turns. To model the helical shape, we establish a general nonlinear framework based on the minimum potential energy method. The model is validated by PneuNets with various material combinations and geometrical configurations across a range of constitutive models including Mooney-Rivlin, Ogden, Neo-Hookean and Yeoh models. Results show that the nonlinear model, especially the Mooney–Rivlin model, accurately captures the deformation without any fitting parameters, achieving an$R^{2}$value of 0.975, compared to 0.017 for the linear model. Based on the validated model, PneuNets are inverse-designed to achieve desired spatial deformations. Their dynamic responses and payload capacities are also evaluated. We design a 3D-printed octopus with tentacles composed of PneuNets, capable of mimicking the grasping and movement of a real octopus. Additionally, we demonstrate the multifunctional capabilities such as fluid transition and sensing. This study lays a solid foundation for the design and application of 3D-printed PneuNets.

Hard-magnetic soft robots can form diverse soft-body deformation modes and safely interact with their surrounding environment, offering great promise in performing complex functions. Although there have been significant theoretical developments of small-scale soft robots, the design of centimeter-scale soft robots with larger workspace and output forces remains elusive. In this paper, we develop an analytical model to automatically design centimeter-scale hard-magnetic soft robots that exhibit desired configurations, enabled by programming the magnetization profile. The model considers the varying magnetization profile, gravity effect and large deformation, and directly relates the material, geometric and loading parameters to the final configurations. We develop an inverse design method for configuration matching based on the theoretical model. We demonstrate soft robots designed by the theoretical model with the capability to pass through narrow channels and crawl over obstacles. We further demonstrate optimized soft grippers showing conformal grasping of complex objects. The proposed methodology paves the way to design centimeter-scale soft robots and broaden their applicationsNote to Practitioners—The motivation of this work is to analyze, predict, and control the centimeter-scale hard-magnetic soft robot under external magnetic fields. While smaller magnetic-driven soft robots have been extensively studied, the centimeter-scale soft robots offer larger workspace and output forces, making them more versatile for certain applications. This paper develops an analytical model for centimeter-scale hard-magnetic soft robots that takes into account the varying magnetization profile, gravity effect and large deformation. It allows magnetically driven soft robots to pass through narrow channels and crawl over obstacles. In addition, an optimization method is proposed by virtue of the analytical model, enabling the inverse design of soft robots with prescribed grasping postures. The analytical model and optimization method can be implemented for the dexterous locomotion and manipulation of magnetic soft robots with large workspace and output forces in medical and industrial settings.

Recent studies have reported on the remarkable ability of bioinspired soft robots to exhibit dexterous and contact-friendly motions. However, for these robots with deformable bodies, it is extremely challenging to achieve precise and robust control when undergoing uncertain forces and contact in the environment. In this work, we take a first step to address this issue for slender pneumatic soft robots by proposing a comprehensive modeling and control framework. Our framework employs a fully parametrized model that accurately describes both robot configurations and distributed forces using Hermite interpolation. Leveraging this model, we further establish an estimation algorithm that can infer complete robot configurations and distributed external forces from limited motion data, enabling perception of contact locations and forces. Integrating this model and estimator, our control framework achieves precise robot motion control under diverse forces, with the average trajectory tracking error within 0.3 mm. It also detects and adapts to uncertain contact, demonstrated in tests of automatic obstacle avoidance and precise grasping. This framework holds promise for various applications such as environmental exploration and safe manipulation, where compliant interaction with the environment is required.

Lattice metamaterials exhibit diverse functions and complex spatial deformations by rational structural design. Here, lattice metamaterials are exploited to design pneumatic soft robots with programmable bending, twisting, and elongation deformations. The system comprises an elastomeric tube reinforced by lattice metamaterials. We develop an analytical framework to model the twisting, bending, and elongation finite deformation taking into account the geometric orthotropy and nonlinear elasticity. We experimentally validate our modeling approach and investigate the effects of geometric patterns and input loading on the soft actuators' deformation. Theoretical guided design of lateral-climbing soft robots and exploration soft manipulators are demonstrated. The soft actuator could exhibit a combined twisting–bending–elongation deformation by lattice superimposition. The proposed structural design method paves the way for designing soft robots with complex and dexterous deformations.

The continuous electromechanical deformation of dielectric elastomer actuators (DEAs) suffers from rate-dependent viscoelasticity, mechanical vibration, and configuration dependency, making the generalized dynamic modeling and precise control elusive. In this work, we present a generalized motion control framework for DEAs capable of accommodating different configurations, materials and degrees of freedom (DOFs). First, a generalized, control-enabling dynamic model is developed for DEAs by taking both nonlinear electromechanical coupling, mechanical vibration and rate-dependent viscoelasticity into consideration. Further, a state observer is introduced to predict the unobservable viscoelasticity. Then, an enhanced exponential reaching law-based sliding-mode controller (EERLSMC) is proposed to minimize the viscoelasticity of DEAs. Its stability is also proved mathematically. The experimental results obtained for different DEAs (four configurations, two materials, and multi-DOFs) demonstrate that our dynamic model can precisely describe their complex dynamic responses and the EERLSMC can achieve precise tracking control; verifying the generality and versatility of our motion control framework.

A homogeneous pneumatic soft robot may generate complex output motions using a simple input pressure, resulting from its morphological shape that locally deforms the soft material to different degrees by simultaneously tailoring the structural characteristics and orienting the input pressure. To date, design of the morphological shape (inverse problem) has not been fully addressed. This article outlines a geometry–mechanics–optimization integrated approach to automatically shaping a pneumatic soft actuator or robot that achieves the desired deformation behavior. Instead of constraining the robot's geometry within any predefined regular shape, we employ B-splines to allow generation of freeform boundary surfaces, and use nonlinear mechanical modelling and shape derivative based optimization to navigate the high-dimensional design space. Our design framework can readily regulate the surface quality during the morphological evolution, by imposing the geometric constraints in terms of the principal curvatures and the minimal distance between surfaces as penalty functions. The effect of external forces including the gravity and the interaction force at the end-effector is also taken into account to generalize the method for design problems in which the load capability is also pursued. To improve the computational efficiency, suboptimization problems are constructed within a trust region in which the displacement-dependent objective function is approximated by its first-order Taylor polynomial based on the gradient information to avoid frequently performing time-consuming nonlinear finite element analysis. The suboptimization problems are then solved by the quasi-Newton method combined with the backtracking line search strategy. We showcase various applications to validate our design approach, including actuators for basic extension, bending, and twisting motions, and continuous robot arms that can perform desired in-plane and out-of-plane configurations. We also show that our method can address design of multiple chambers for achieving multiple target deformation behaviors, by co-optimizing the morphological shape and air pressures, which is validated by two examples.

Parallel robots with rigid transmission mechanisms have been widely developed to improve the speed, precision, and load capability. However, it is still challenging in promoting soft parallel robots due to the difficulty in accurate kinematic modeling of soft continuum links. In this article, we present a general framework on the design, kinematic modeling, model-based characterization, and control for a class of soft parallel robots. The designed soft parallel robot consists of three fiber-reinforced soft pneumatic actuators, a base stage, and an output stage. With the introduction of the mathematical toolkit of the absolute nodal coordinate formulation, we develop a continuum-based model to describe and parameterize both the global complex configuration and the local large deformation of the soft parallel robot. In this sense, the mappings among the defined kinematic spaces of the robot can be characterized through force analysis. Based on the developed model, we next analyze the robot’s workspace and stiffness with different design parameters, which are also verified by a set of experiments. Finally, we establish a model-based trajectory tracking controller for the soft parallel robot. The experimental results demonstrate that with the feedforward controller, the end effector of the soft parallel robot can well follow the desired trajectories under different output velocities, where the average positioning error is about 2.6–3.9% of the maximum length of the workspace.

Although many soft robots, capable of crawling or climbing, have been well developed, integrating multimodal locomotion into a soft robot for transitioning between crawling and climbing still remains elusive. In this work, we present a class of inchworm-inspired multimodal soft crawling-climbing robots (SCCRs) that can achieve crawling, climbing, and transitioning between horizontal and vertical planes. Inspired by the inchworm’s multimodal locomotion, which depends on the “$\Omega$” deformation of the body and controllable friction force of feet, we develop the SCCR by 1) three pneumatic artificial muscles based body designed to produce “$\Omega$” deformation; 2) two negative pressure suckers adopted to generate controllable friction forces. Then a simplified kinematic model is developed to characterize the kinematic features of the SCCRs. Lastly, a control strategy is proposed to synchronously control the “$\Omega$” deformation and sucker friction forces for multimodal locomotion. The experimental results demonstrate that the SCCR can move at a maximum speed of 21 mm/s (0.11 body length/s) on horizontal planes and 15 mm/s (0.079 body length/s) on vertical walls. Furthermore, the SCCR can work in confined spaces, carry a payload of 500 g (about 15 times the self-weight) on horizontal planes or 20 g on vertical walls, and move in aquatic environments.

Hyper-redundant manipulators with slender body and high dexterity are widely applied for operations in confined spaces. Among the motion planning methods for these operations, the follow-the-leader motion controller is generally developed to avoid the obstacles, while the path trajectories are usually given. In this paper, we present an autonomous motion planner with a specialized rapidly exploring random tree (Sp-RRT) approach for follow-the-leader motion of hyper-redundant manipulators. Starting from the target pose in the workspace, the exploring tree can expand to multiple entrances while guaranteeing the final pose of the manipulator’s end-effector. Meanwhile, the dexterity of hyper-redundant manipulators (even with different segments) can be utilized sufficiently with customized expanding parameters. Simulation results compared with existing methods are conducted to demonstrate the aforementioned characteristics and effectiveness. For further validation, we experimentally verify the development with our custom-built hyper-redundant manipulator to realize the generated path with follow-the-leader motion.

Most of the existing soft locomotive robots are capable of moving on horizontal planes and small-angled slopes, but few of them can accomplish the large-angled slope climbing or wall climbing. We introduce an inchworm inspired soft crawling-climbing robot capable of continuous motion from a horizontal plane to a slope of up to 75 degrees and it can perform multiple locomotion including crawling, climbing, and the transition between them. This soft crawling-climbing robot is powered by three pneumatic actuators connected in series that deforms with two degrees of freedom, negative pressure sucker feet that generate periodical adhesion, and a semi-automatic controlling system synchronizing the body shape and anchoring of the feet. The robot mimics the body deformation and feet anchoring pattern exhibited by inchworms and can be applied in inspection, surveillance, and rescuing.

Dielectric elastomer actuators (DEAs) are a promising actuation technology in soft robotics owing to their large voltage-induced deformation and rapid response. However, most existing DEA design paradigms are empirical or intuitive, lacking the mathematical modeling and optimization methodology to exploit their actuation capabilities for prescribed motion tasks. In this paper, we present an automatic design methodology to maximize the concerned displacement(s) of DEAs by topology optimization of the applied spatial electric fields (SEFs). Our method is enabled by integrating the freeform SEF profile captured by implicit level sets, and the constitutive model of DEAs incorporating geometric and material nonlinearities and the electromechanical coupling effect, into a gradient-based optimizer. We implement our method for motions of single and multiple degrees of freedom (DOFs) of planar DEAs, and the optimized SEFs have been found to improve the output displacements by more than 75% compared with their intuitive counterparts. We further demonstrate a proof-of-concept application in which our designed two-DOF DEAs can actively drive various host structures to shape-morph from flat sheets to desired three dimensional configurations. Overall, our paper represents the first step toward automatic design of soft DEAs for diverse potential applications in soft machines and robots.

In this paper, a modified repetitive control (MRC) based approach is developed for high-speed tracking of nanopositioning stages. First, the hysteresis nonlinearity is decomposed as a periodic disturbance over a linear system. Then, the MRC technique is utilized to account for the periodic disturbances/errors caused by the hysteresis and dynamics behaviors. The developed approach provides a simple and effective hysteresis compensation strategy, avoiding the constructions of hysteresis model and its inversion. Besides, with improved loop-shaping properties, the MRC can alleviate the nonperiodic disturbance amplification problem of the conventional repetitive control. Finally, the effectiveness and performance of the developed MRC-based approach are verified by the experimental results on a custom-built piezo-actuated stage in terms of hysteresis compensation, disturbance rejection and tracking accuracy.

Soft dielectric elastomer actuators (DEAs) exhibit interesting muscle-like behavior for the development of soft robots. However, it is challenging to model these soft actuators due to their material nonlinearity, nonlinear electromechanical coupling, and time-dependent viscoelastic behavior. Most recent studies on DEAs focus on issues of mechanics, physics, and material science, while much less importance is given to quantitative characterization of DEAs. In this paper, we present a detailed experimental investigation probing the voltage-induced electromechanical response of a soft DEA that is subjected to cyclic loading and propose a general constitutive modeling approach to characterize the time-dependent response, based on the principles of nonequilibrium thermodynamics. In this paper, some of the key observations are found as follows: 1) Creep exhibits the drift phenomenon, and is dominant during the first three cycles. The creep decreases over time and becomes less dominant after the first few cycles; 2) a significant amount of hysteresis is observed during all cycles and it becomes repeatable after the first few cycles; 3) the peak of the displacement is shifted from the peak of the voltage signal and occurs after it. To account for these viscoelastic phenomena, a constitutive model is developed by employing several dissipative nonequilibrium mechanisms. The quantitative comparisons of the experimental and simulation results demonstrate the effectiveness of the developed model. This modeling approach can be useful for control of a viscoelastic DEA and paves the way to emerging applications of soft robots.

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Magnetostrictive actuators featuring high energy densities, large strokes, and fast responses are playing an increasingly important role in micro/nano-positioning applications. However, such actuators with different input frequencies and mechanical loads exhibit complex dynamics and hysteretic behaviors, posing a great challenge on applications of the actuators. Therefore, it is important to develop a dynamic model that can characterize dynamic behaviors of the actuators, including current-magnetic flux nonlinear hysteresis, frequency responses, and loading effects, simultaneously. To this end, a comprehensive model, which thoroughly considers the electric, magnetic, and mechanical domain, as well as the interactions among them, is developed in this paper. To validate the developed model, the parameters of the model are identified where the hysteresis of the magnetostrictive actuator is described, as an illustration, by the asymmetric shifted Prandtl-Ishlinskii model. The experimental results demonstrate that the comprehensive model presents an excellent agreement with dynamic behaviors of the magnetostrictive actuator.

This paper presents a trajectory tracking control strategy based on the subspace stabilization approach to accurately manipulate an under-actuated flying robot from a known initial state to the desired terminal state. To facilitate the development of this tracking strategy, the dynamical model of the quadrotor is firstly proposed. Subsequently, an optimal trajectory generation algorithm is adopted to generate dynamically consistent trajectories regarding the initial and terminal state constraints in specific missions. Then, a trajectory tracking control strategy based on the subspace stabilization approach is developed considering the lumped disturbances and time delays. The developed control strategy is applied for ball juggling of a highly under-actuated quadrotor, which is a popular flying robot in recent years. Real-time experimental results show that the quadrotor can be accurately manipulated from a known initial state to the desired terminal state within a given time horizon. In the consecutive juggling tasks, the quadrotor with a racket of radius 0.065 m can consecutively juggle the ball for averagely 4 hits in each rally, and a longest rally achieved by the developed control strategy is 14 hits. The feasibility of the developed control strategy is also preliminarily verified through the cooperative juggling between two quadrotors. All of these results demonstrate the effectiveness of the developed control strategy.

This paper presents a novel high-bandwidth control approach for piezo-actuated nanopositioning stages. A delayed position feedback (DPF) controller is first developed in the inner loop to damp the resonant mode of piezo-actuated stages. A generalized Runge-Kutta method (GRKM) is proposed to determine the parameters of the DPF controller with pole placement. The benefit of the DPF for active damping is its simple structure and ease of implementation. Then, a high-gain proportional-integral (PI) controller is designed in the outer loop to deal with the hysteresis nonlinearity, disturbance and modeling errors. The stability of the control system is analyzed via a graphical method. Finally, experiments are conducted to demonstrate the effectiveness and superiority of the proposed approach in terms of tracking accuracy at high speed as compared to the PI controller.

In this paper, a new type of decoupled 2-DOF translational parallel micro-positioning stage is designed to realize the 2-DOF ultra-precision linear motion. The stage consists of two piezoelectric actuators (PZTs) and a monolithic compliant mechanism. The monolithic compliant mechanism adopts two types of compound double parallel four-leaf flexures and a mirror symmetric structure to reduce the input and output cross coupling and parasitic motion. Based on the stiffness matrix method and screw theory, a mathematical model is constructed to analyze the compliant mechanism. The optimal design is performed in view of performance constraints. The design results show good static and dynamic performances of the stage, which are well validated by the simulation of finite-element-analysis (FEA) and experimental results. The experimental results show that the proposed stage has a full range of 40µm × 40µm when the full voltage(100V) is applied on the two PZTs. Besides, the stage only has the maximum cross coupling of -50dB between the two axes, low enough to utilize single-input-single-out(SISO) control strategies for positioning and tracking.