The structural design of soft robots draws heavily on the morphology and movement mechanisms of biological organisms to achieve efficient, flexible, and environmentally adaptive movement. Typical biomimetic-inspired structures include octopus tentacles, earthworms/inchworms, vines, elephant trunks, and snakes. Table  provides a comparative analysis of the motion characteristics, strengths, weaknesses, applicable scenarios, and control complexity of various soft robots with bio-inspired structures. Additionally, there are soft robots inspired by origami.

Octopus tentacles possess a unique muscle-connective tissue composite structure composed of longitudinal muscle, transverse muscle, and oblique connective tissue, enabling multi-degree-of-freedom motion without skeletal support, including bending, twisting, elongation, and contraction. Based on this principle, constructed a conical silicone continuum soft robot. achieved high-compliant multi-degree-of-freedom movement by simulating longitudinal muscles with linear chambers for bending and extension, spiral chambers for bidirectional twisting, and rigid rings to constrain radial deformation.

Earthworms/inchworms achieve peristaltic movement through the periodic contraction and expansion of their segments. Their locomotion mechanism relies on the antagonistic action of circular muscles and longitudinal muscles, as well as friction regulation by body surface bristles. designed an earthworm-like peristaltic structure composed of continuous silicone gel columns, with a uniform cylindrical cross-section that can undergo nonlinear axial stretching deformation, driven by segmented or continuous strain waves to achieve retrograde peristaltic propulsion. designed an inchworm-like soft structure composed of three segments of fiber-reinforced pneumatic muscles connected in series, with negative pressure suction cups integrated at both ends. Controlled bending and adhesion enable crawling, climbing, and transitional movements.

Vine plants achieve climbing through apical growth and the spiral contraction of tendrils. Their movement relies on the synergistic regulation of tropism and phototropism. and both used thin-walled polyethylene tubes to construct vine-like soft robots, achieving tip extension and turning by releasing pre-stored segments via four sets of electromagnetic steering units.

An elephant's trunk consists of approximately 150 000 muscle bundles, combining flexibility with load-bearing capacity. Its movement relies on hierarchical coordinated muscle contraction and the extensibility of skin folds. designed an elephant-trunk-like hybrid robot comprising a 6-degrees-of-freedom rigid skeleton and a 48-degrees-of-freedom soft hydrostatic segment in series, driven by an adjustable compliance matrix to achieve redundant degree-of-freedom coordination and end-effector interaction adjustment.

Snakes leverage body bending and coordinated muscle contractions to demonstrate powerful locomotion capabilities, including serpentine, sidewinding, and concertina movements. proposed a modular 3D soft robotic snake, whose structure consists of three-segment, actively deformable pneumatic silicone modules connected in series. developed a modular soft robot that achieves a bidirectional crawling motion along the exterior of tubular structures through alternating grip and extension movements.

Origami structures achieve programmable deformation through folding–unfolding mechanisms, with crease designs enabling various deformation modes, including unfolding, bending, and twisting. proposed a cable-free caterpillar-inspired biomimetic robot based on a triangular origami spring skeleton and coupled drive, with internal and external magnets, achieving adjustable structural stiffness and multi-modal motion through programmable crease patterns. were inspired by the Kresling origami structure and proposed an untethered soft robot capable of crawling in pipelines, with a high contraction ratio. proposed a vacuum-driven parallel continuum robot, utilizing soft–hard hybrid 3D-printed self-sensing origami linkages to achieve high load capacity, multi-modal motion, and precise closed-loop control.

These structural designs fully leverage the flexible multi-joint characteristics of the biological world. Compared to rigid robotic arms, soft robots significantly increase degrees of freedom and flexibility in their structure. However, at the same time, this multi-joint design also introduces considerable challenges and uncertainties in motion and mechanical control.

Soft robots primarily utilize elastic materials such as hydrogels, and dielectric elastomers or composite materials (), which exhibit high extensibility, low Young's modulus, and excellent energy absorption properties, making them well suited to soft robotics. Additionally, common materials include shape memory materials and magnetoresponsive materials.

Hydrogels are soft hydrophilic materials composed of a network of hydrophilic polymers and a large amount of water. Their unique properties stem from the interactions between polymer chains and water molecules. Based on their stimulus response characteristics, hydrogels can be classified into various types, including temperature responsive (), light responsive (), and magnetically responsive (). Hydrogels exhibit excellent biocompatibility and mechanical properties similar to those of the environment, but they have low mechanical strength and slow response speeds.

Dielectric elastomers are a class of polymer materials with high dielectric constants and excellent elastic deformation capabilities, whose operational mechanism is based on the Maxwell stress effect. When an external electric field is applied to both sides of an electrically polarized dielectric elastomer film, the material compresses in the thickness direction and expands in the planar direction, resulting in significant electromechanical deformation. Dielectric elastomers have fast response speeds and high energy density, and can directly convert electrical energy into mechanical energy, making them widely used in soft robots (). However, they also face challenges such as high driving voltages and insufficient long-term cycling stability.

Shape memory alloys are a class of metallic materials with unique shape memory effects and superelasticity, capable of restoring their preset shapes under external stimuli. The most commonly used shape memory alloy is nickel-titanium-based alloy, which exhibits excellent shape recovery rates, biocompatibility, and long cycle lifetimes. However, it suffers from slow response speeds and low driving efficiency ().

Magnetoresponsive materials are a class of functional materials that generate controllable mechanical responses under external magnetic fields. Common types include magnetorheological materials (including magnetorheological fluids and magnetorheological elastomers), magnetic composite materials (where magnetic particles are dispersed in polymers/hydrogels; ), and liquid magnetic materials (such as ferromagnetic fluids; ). Magnetoresponsive materials possess wireless remote control and precise positioning control capabilities, demonstrating significant application potential in fields such as micro-robots and medical robots.

The actuators of soft robots are closely related to their motion performance and modeling control. Common actuators include pneumatic drive, cable drive, and tendon drive.

Pneumatic drive induces deformation of the elastomer by regulating the air pressure within a sealed cavity. When the internal air pressure increases, the elastic cavity expands and deforms; when the air pressure decreases, the material's elastic recovery force causes it to contract (). Typical pneumatic actuators employ a multi-layer elastic material structure with a complex network of air channels embedded internally (). Enhanced designs incorporate fiber reinforcement layers within the elastic matrix to control deformation direction and improve mechanical performance (). Recent research has also developed vacuum-driven variants, which offer advantages such as energy efficiency, safety, and rapid response ().

The cable drive system consists of a high-strength fiber cable core and a low-friction outer sheath. A servo motor winds the flexible cable, converting rotational motion into axial tensile force on the flexible skeleton, thereby generating bending/contraction (). Multiple cables working together can achieve complex movements (). It features high force transmission efficiency and precise motion control () but can only transmit tensile force, not compressive force, and suffers from friction losses and hysteresis effects ().

Tendon-driven systems are based on biomimetic design, mimicking biological muscle-tendon systems. They achieve bidirectional motion through the synergistic action of opposing tendon pairs, with changes in tendon tension regulating joint stiffness (). Common tendon materials include high-strength fibers, steel wires (), and nylon threads (). By controlling the contraction length or tension of single or multiple tendons, the structure generates motions such as bending and deformation (). While tendon-driven systems exhibit highly biomimetic motion patterns and enable variable stiffness adjustment (), they suffer from slow dynamic response and complex control requirements.

Kinematic models are used to describe geometric relationships and the motion characteristics of robots, serving as the foundation for trajectory planning and position control. The continuous deformation characteristics of soft robots render traditional Denavit–Hartenberg (DH) parameter methods inapplicable, necessitating alternative methods such as the segment curvature assumption or Cosserat rod theory.

Dynamic models study the relationship between force and motion, i.e., what kind of force needs to be applied to a physical object to achieve a certain motion. They reveal the dynamic relationship between driving inputs and motion responses, providing a theoretical framework for force/position hybrid control, impedance control, and other control methods.

Trajectory planning determines the efficiency, safety, and stability of task execution. In addition to meeting movement constraints and obstacle avoidance requirements, its planning objectives typically include time optimization, shortest path, and minimum energy consumption.

To ensure precise motion along predefined trajectories, vision systems are frequently utilized for trajectory tracking in soft robots. The visual module primarily executes three functions: environmental perception, including target object recognition (), obstacle detection, and map reconstruction; pose estimation, which uses visual information to reconstruct the soft robot's shape and pose in real time (); and motion correction, which adjusts control signals with visual feedback to prevent path deviation and improve accuracy (). Notably, developed a novel vision-based force sensor to achieve closed-loop grasping force control for soft grippers.

Data-driven methods are widely used in visual perception for soft robots. proposed a bending-sensing algorithm based on image preprocessing and deep learning, training a convolutional neural network with multi-task learning to obtain the bending state of a soft robotic finger. trained a convolutional neural network to map visual feedback to the tip pose of the actuator. combined a traditional neural network with B-spline curves, capturing external visual images and mapping them to the robot's shape. Additionally, used a recurrent neural network to estimate the pose of a proprioceptive bending sensor. also implemented multi-modal tactile sensing for a soft robotic finger based on a neural network model. employed machine learning to convert signals captured by low-cost sensors into shape parameters of a soft robot.

Model-based control utilizes internal models to predict robot behavior, thereby computing the control commands needed to achieve desired objectives. This approach offers high control efficiency and eliminates the need for a large number of sample data. Although soft robots present significant modeling challenges and exhibit unmodeled dynamics, researchers have made dedicated efforts and improvements within the model-based control framework. Through technical approaches such as robust control that accounts for uncertainties, adaptive control with online parameter adjustment, and control strategies that integrate data-driven methods, controllers capable of resisting, adapting to, and learning from unmodeled dynamics have been designed, thereby optimizing control performance.

established the dynamic model of the soft robot based on the absolute nodal coordinate formulation and solved the driving force through inverse dynamics. combined the reduced-order finite element model with the equivalent input disturbance method to achieve coordinated feedforward-feedback-disturbance compensation control, suppressing modeling uncertainties and disturbances. proposed a control strategy based on finite element dynamics models, combining feedforward with PID feedback to enhance the system's disturbance rejection capability and tracking accuracy. established the dynamic model of the underactuated soft robot and used the P-satI-D shape regulation control law with saturated integral term, which did not require precise stiffness parameters and could suppress constant disturbances. The block diagram of the control structure is shown in Fig. b. They () also proposed a PD+ feedback control method with gravity compensation to improve control performance. combined the pseudo-rigid-body model of the soft robot with elastic statics to achieve compensation for the connecting rod deformation. By implementing feedforward compensation based on the model and combining it with methods such as PID to suppress disturbances, relatively high control accuracy can be achieved in slow-tracking tasks. However, such methods require an accurate model. Otherwise, control precision may be difficult to guarantee. Additionally, their robustness to unmodeled dynamics and sudden external disturbances is limited.

established an articulated joint dynamic model for the soft robot and proposed an impedance control scheme, effectively reducing actuator torque requirements during impact. compared the torque estimation performance of musculoskeletal models and inverse dynamic models, and computed control commands through an admittance controller. utilized a pseudo-rigid-body model and employed an admittance force control strategy to achieve safe, compliant, and low-energy-consumption control performance. combined the developed nonlinear finite element model with admittance control to execute robot sensing and control at high rates. The control block diagram is shown in Fig. a. Impedance/admittance control adjusts the dynamic interaction between the robot and the environment to achieve compliant operation, enhancing system compatibility and safety. It is well suited to tasks involving human-robot interaction or contact with uncertain environments. However, its performance relies on the tuning of impedance/admittance parameters, and its control accuracy is relatively low.

proposed a robust control method based on a linear time-invariant system model, integrating singular value decomposition decoupling, PI control, and anti-windup compensation. addressed robots with system uncertainties and input saturation, achieving constrained shape control through a dynamic model and a sliding-mode controller. utilized the dynamic model of the soft robot, employing super-twisting sliding-mode control and an input estimator to achieve position control of the end effector. proposed a sliding-mode controller based on a super-twisting extended state observer to robustly control the robot's attitude within a finite time, building upon the dynamic model. Robust control is capable of addressing model uncertainties, parameter variations, and external disturbances, ensuring convergence within a finite time frame while maintaining the stability and precision of the control system. It is suitable for tasks with strong environmental disturbances and high demands on control accuracy and stability. However, its controller design typically requires prior knowledge of the uncertainty bounds, and to guarantee robustness, the controller gains are often set relatively high, which may lead to potential control input chattering.

established a pseudo-rigid-body dynamic model for the modular soft robot and employed an adaptive backstepping sliding-mode controller to mitigate the effects of model uncertainties and external disturbances. developed a dynamic model based on the constant curvature assumption and proposed an adaptive sliding-mode controller to achieve robust curvature tracking control against external disturbances and parametric uncertainties. combined a decoupled reduced-order dynamic model with a robust fractional-order controller to realize adaptive motion control of the soft robot under model uncertainties. proposed a virtual reference adaptive control strategy based on visuo-tactile sensing to achieve closed-loop adaptive force control. Adaptive control enables the online estimation and compensation of unknown or slowly time-varying system parameters, thereby reducing reliance on the accuracy of the initial model. It performs particularly well in scenarios where system parameters are uncertain or difficult to identify precisely offline. However, the proofs of stability and convergence for adaptive control are complex. Furthermore, its convergence speed may be slow, making it difficult to track abrupt parameter changes, and its effectiveness in handling unmodeled dynamics remains limited.

constructed data-driven linear and nonlinear dynamic models based on Koopman operator theory and accomplished trajectory tracking control for the soft robot through a model predictive controller. established an RNN-based forward dynamic model and proposed a continual learning control method incorporating elastic weight consolidation to accurately control the soft manipulator under varying load conditions. established a soft-arm kinematic model based on the segmented constant curvature assumption. By employing the Q-learning reinforcement learning method, they achieved motion control with attitude constraints, satisfying task requirements without the need for motion planning. established a closed-loop control framework based on reinforcement learning and proprioceptive self-sensing, training the control policy through a physical simulation model to achieve coordinated movement of a multi-segment soft robot. proposed a data-driven model predictive control method with input mapping based on a system state-space model, reducing the impact of model inaccuracies. established a piecewise discrete dynamic model, designed an adaptive controller based on a radial basis function neural network, and combined it with a Lyapunov function to achieve precise trajectory tracking under motion constraints. The system block diagram is shown in Fig. c. also designed an adaptive learning control method based on a radial basis function neural network on the basis of a reduced-order dynamic model of a soft trunk robot, achieving accurate trajectory tracking of the end effector. proposed a control algorithm combining a fractional-order sliding surface and deep reinforcement learning based on a nonlinear dynamic model to achieve trajectory tracking and suppress oscillations. compared analytical models and Koopman data-driven models, and realized trajectory tracking using a linear quadratic regulator combined with an unscented Kalman filter. Experiments showed that the system incorporating the Koopman model exhibited superior tracking accuracy and robustness. adopted an improved particle swarm optimization algorithm to optimize PID parameters for high-precision control, based on a data-driven control model for a pneumatic soft robot. improved the disturbance rejection capability and control accuracy of the soft robot based on a dynamic model and a particle swarm optimization algorithm. used iterative learning control to compensate for model uncertainties and correct errors online based on a flexible rod dynamic model, achieving high-precision control. Combining kinematic or dynamic models with data-driven methods for control can effectively balance tracking accuracy and generalization capabilities, offering flexible performance suitable for tasks requiring high precision, robustness, and adaptive capability. However, this approach involves higher design complexity and still requires a certain number of data for training and learning.

Model-based control features clear theoretical foundations and strong interpretability. Under ideal conditions – accurate models, known environments, and sufficient computational resources – it can achieve high-performance control of soft robots. However, due to its heavy reliance on models and the difficulty in obtaining accurate ones, this approach exhibits limited robustness against model uncertainties and unmodeled dynamics. Additionally, since most models are developed for specific soft robots and are influenced by factors such as structure and materials, and the controllers are designed based on these models, the generality and transferability of such controllers are often poor.

Model-free control does not rely on prior models. Its core principle involves directly learning the mapping relationship between states and actions from data, enabling it to handle complex tasks. Such controllers inherently avoid the series of issues caused by modeling difficulties, meaning they are insensitive to model uncertainties and exhibit strong adaptability and robustness.

proposed a data-driven control method based on Bayesian optimization and Gaussian processes, which online learned gait controller parameters and combined transfer learning to achieve adaptive control across different task spaces, improving data efficiency. and generalization. proposed a model-free closed-loop control system combining PID and iterative learning to achieve end-effector position tracking and improve the response speed for repetitive tasks. The control system block diagram is shown in Fig. d. proposed a model-agnostic deep reinforcement learning control method, achieving rapid adaptation and generalization through Sim2Real transfer learning, significantly outperforming traditional PID control. combined feedforward control based on probabilistic model predictive control and feedback control based on a non-parametric learning method, realizing hybrid force/position tracking for the robot. It adapted to unknown environments without requiring precise modeling. proposed a self-tuning PID control method based on online identification using a discrete wavelet neural network, achieving gain adaptive adjustment and trajectory tracking relying only on position measurements.

Model-free control circumvents the challenges of modeling but introduces its own set of issues, including low sample efficiency, lengthy training times, difficulties in debugging, and poor interpretability. Therefore, in practical applications, the choice between model-based and model-free control often involves trade-offs among factors such as stability, accuracy, and safety.