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Data-driven Methods Applied to Soft Robot Modeling and Control: A Review

Zixi Chen, Federico Renda, Alexia Le Gall, Lorenzo Mocellin, Matteo Bernabei, Théo Dangel, Gastone Ciuti, Matteo Cianchetti, Cesare Stefanini

arXiv:2305.12137v3cs.RO

TL;DR

Soft-robot modeling and control are challenging because their materials and motion are nonlinear, delayed, and highly deformable. This review compares data-driven approaches for both tasks and concludes that method trade-offs leave no single solution optimal for every task.

  • Problem

    Soft robots’ nonlinear and delayed responses, infinite degrees of freedom, and changing material properties complicate modeling and make control more challenging than for rigid robots.

    Source: §I · p. 1

  • Method

    The review introduces physical models and the Jacobian matrix, then compares statistical methods, neural networks, and reinforcement learning for soft-robot modeling and control.

    Source: §I · p. 2

  • Results

    Statistical methods require moderate data and offer intermediate control frequency, neural networks suit nonlinear modeling and control but train slowly, and reinforcement learning supports high-level tasks at high resource cost.

    Source: B. Advantages and Limitations · pp. 11–12

  • Takeaways & Limitations

    Each approach has advantages and disadvantages, so no single method is optimal for all tasks.

    Source: A. Summary · p. 11

    Reinforcement learning requires substantial time and computation, while real-world exploration may damage robots or be infeasible in settings such as the human body.

    Source: B. Advantages and Limitations · p. 12

Abstract

from arXiv · show

Soft robots show compliance and have infinite degrees of freedom. Thanks to these properties, such robots can be leveraged for surgery, rehabilitation, biomimetics, unstructured environment exploring, and industrial grippers. In this case, they attract scholars from a variety of areas. However, nonlinearity and hysteresis effects also bring a burden to robot modeling. Moreover, following their flexibility and adaptation, soft robot control is more challenging than rigid robot control. In order to model and control soft robots, a large number of data-driven methods are utilized in pairs or separately. This review first briefly introduces two foundations for data-driven approaches, which are physical models and the Jacobian matrix, then summarizes three kinds of data-driven approaches, which are statistical method, neural network, and reinforcement learning. This review compares the modeling and controller features, e.g., model dynamics, data requirement, and target task, within and among these categories. Finally, we summarize the features of each method. A discussion about the advantages and limitations of the existing modeling and control approaches is presented, and we forecast the future of data-driven approaches in soft robots. A website (https://sites.google.com/view/23zcb) is built for this review and will be updated frequently.

I. INTRODUCTION

Soft robots’ nonlinear, delayed responses, infinite degrees of freedom, and material aging complicate modeling and control. This review organizes data-driven approaches alongside their foundations and physical models, comparing modeling and control methods in parallel.

I. INTRODUCTION

  • Nonlinearity, delayed responses, infinite degrees of freedom, and material aging make soft-robot modeling and control challenging.These characteristics make modeling more complex than for rigid robots and contribute to difficult control tasks.Source: §I · p. 1
  • Modeling maps actuation to robot state, while control maps a desired state and sensing input to actuation.The state can include end position, orientation, and shape; control inputs may vary by strategy.Source: §I · p. 2, Figure 1 · p. 2
  • Data-driven methods use motion data without requiring robot-design knowledge and support kinematic or dynamic modeling, open- or closed-loop control, and observer applications.The review notes that data from real robots can capture their features, unlike physical approaches based on simplifications and hypotheses.Source: §I · p. 2
  • The review compares statistical methods, neural networks, and reinforcement learning for modeling and control, after introducing physical models and the Jacobian matrix as foundations.It compares methods within and across categories and discusses challenges and emerging directions.Source: §I · p. 2

II. FOUNDATIONS FOR DATA-DRIVEN APPROACHES

  • Physical models and the Jacobian matrix support data-driven methods by providing simulators or inferring data relationships.Physical models also offer insight into soft-robot motion and deformation.Source: §II · p. 2, A. Physical Models · p. 3

A. Physical Models

  • Physical-model options include FEM simulation, Cosserat-rod and GVS formulations, PCC simplifications, and robot-specific concentric-tube or pseudo-rigid models.FEM can provide high-accuracy simulation but requires material parameters; it is often used offline to produce data or an RL exploration environment. Cosserat-rod models include bending, twisting, stretching, and shearing, while PCC includes bending.Source: A. Physical Models · pp. 3–4

B. Jacobian matrix

The Jacobian matrix provides a concise way to relate actuation and position velocities through model linearization. Soft-robot approaches initialize and update it online, then use it to determine actuation for control, while adapting the method to address its limitations.

B. Jacobian matrix

  • The Jacobian relates actuation and position velocities through linearization, and soft-robot implementations may estimate it without an explicit physical model.In, the general model p = fθ(a) is used for illustration rather than calculation.Source: B. Jacobian matrix · p. 4
  • Initialization actuates each actuator incrementally to estimate J0, and subsequent updates use the latest actuation and end-position changes.The update is applied to the unit Jacobian matrix at successive steps.Source: B. Jacobian matrix · p. 4
  • Control selects actuation through an optimization constrained by the Jacobian and target end position, with actuation bounded by the robot’s minimum and maximum values.The inverse Jacobian is another control option.Source: B. Jacobian matrix · pp. 4–5
  • Because the prior-step Jacobian may be inaccurate under nonlinearity and hysteresis, adaptations include smoothing, force-displacement modeling, multi-step changes, rotation, and fused sensing.These adaptations target force control, motion differences, and more stable and precise Jacobian estimation, –.Source: B. Jacobian matrix · p. 5
  • The method is simple and often updated online at high frequency, but its oversimplified linearization makes frequent updating necessary; it also motivates data-driven alternatives such as reinforcement learning.The comparison includes the first Jacobian-control paper, force control, and a later RL implementation on the same robot.Source: B. Jacobian matrix · p. 5

III. STATISTICAL METHOD

Statistical methods use collected data to map between variable spaces without requiring physical relationships among them. The review covers regression approaches as well as distribution-based modeling and state estimation.

III. STATISTICAL METHOD

  • Statistical methods learn mappings between variable spaces from data without requiring physical relationships between those spaces.Examples include mapping actuation to image feedback and planning actuation from temporal values [70],.Source: §III · p. 5
  • Soft robots use several regression approaches, including linear regression, local weight regression (LWR), support vector regression (SVR), Gaussian process regression (GPR), and local weight projection regression (LWPR).Source: §III · p. 5
  • Beyond regression, GMM summarizes collected data with a joint distribution, while EKF estimates robot states as an observer,.Source: §III · p. 5

A. Regression Method

Regression methods fit data with a selected model and use the trained mapping to predict outputs from observations. The review discusses linear and local regression, GPR, LWPR, and SVR, including their use in soft-robot modeling and control.

A. Regression Method

  • Regression fits training data by optimizing a model’s parameters and loss, then predicts outputs from observations; linear regression maps FBG signals to end position.LWR also fits a linear function, weighting data by distance from the observation; human demonstrations can provide temporal inputs for action selection.Source: A. Regression Method · p. 5
  • SVR is used for forward kinematic modeling and closed-loop position control; on a simple function it approximates more accurately than NN, but takes longer to converge on 15625 samples,.The passage attributes the convergence difference possibly to optimization strategies or mature NN optimization software.Source: A. Regression Method · p. 5
  • SVR maps actuation to robot state for kinematics modeling and desired displacement to actuation for control, with C trading estimation error against regularization.Its formulation uses a nonlinear feature transformation and an extended Vapnik ϵ-insensitive loss based on L2-norm.Source: A. Regression Method · p. 5
  • GPR predicts robot states, such as position or shape parameters, from training data and current actuation, producing a predictive mean and variance; it supports control strategies,,.Examples include predicting desired actuation variables from robot-state feedback in close-loop kinematics control and predicting differences between robot states for optimal control.Source: A. Regression Method · p. 6
  • LWPR combines local linear models weighted by Gaussian kernels and uses a user-defined null-space behavior to guide parameter optimization,,.The cited examples minimize robot elongation or overall inflated-chamber pressures during control,.Source: A. Regression Method · p. 6

B. Gaussian mixture model

The Gaussian mixture model (GMM) encodes collected data as a joint distribution, then uses conditional means to predict robot states or actuation. Its encoding also supports planning and demonstration transfer.

B. Gaussian mixture model

  • GMM represents collected data with multiple Gaussian components and predicts outputs from the posterior conditioned on input data.Each data dimension can serve as a prior for deriving expectations on the remaining dimensions.Source: B. Gaussian mixture model · p. 6
  • For forward modeling, the conditional mean estimates the next robot state from the current state and actuation.The joint model is P[p[k + 1], p[k], a].Source: B. Gaussian mixture model · p. 6
  • For control, the conditional mean estimates actuation from the desired next state and current robot state.This uses the same joint model as forward modeling, with desired state and current state as conditions.Source: B. Gaussian mixture model · p. 6
  • GMM data encoding also supports navigation, planning with coordinate-system parameters, and transferring rigid-robot demonstrations to the STIFF-FLOP continuum robot.Examples include navigating narrow holes from human demonstrations and transferring demonstrations to STIFF-FLOP.Source: B. Gaussian mixture model · p. 6

C. Extended Kalman filter

The extended Kalman filter (EKF) combines a nonlinear forward model with sensor measurements to estimate soft-robot states. It predicts a state from the previous state and actuation, then corrects that prediction using sensing.

C. Extended Kalman filter

  • The EKF serves as an observer that uses measurements to correct predictions from an existing model.P, Q, and R denote estimation, process-noise, and measurement-noise covariance, respectively.Source: C. Extended Kalman filter · pp. 6–7
  • The EKF predicts the next state from the prior state and actuation, then corrects it using the sensor measurement.It is widely used instead of the original linear Kalman filter because soft robots have nonlinear responses.Source: C. Extended Kalman filter · pp. 6–7
  • Its correction uses a locally linearized measurement process, while the Kalman gain evaluates the reliability of measurement and prediction.The forward model is nonlinear and locally linearized for prediction.Source: C. Extended Kalman filter · p. 7
  • EKF applications include estimating robot poses and physical parameters, external forces, and snake-robot shape during advancing or retracting motion.In one approach, position-sensor signals correct pose estimates based on actuator variables and segment parameters.Source: C. Extended Kalman filter · p. 7

D. Summary Statistical Method

Statistical methods fit assumed data distributions and can support both modeling and control, while neural-network approaches range from constrained ELM and RBF designs to more flexible architectures. Across the reviewed methods, inputs and model structures have evolved to incorporate richer sensing and task-specific information.

D. Summary Statistical Method

  • Statistical approaches have expanded from actuation inputs to position feedback, temporal values, vision, and signals from resistance and force sensors.Different inputs can support modeling, control, or modeling adjustment in the cited examples.Source: D. Summary Statistical Method · p. 7
  • The reviewed statistical methods also evolve in model structure, including adaptive and unscented Kalman filters and GPR approaches for local, online, or new workspaces.Examples include a meta-learning GPR for multiple new unknown workspaces.Source: D. Summary Statistical Method · p. 7
  • Statistical methods can perform acceptably with small datasets, improve with more data, and often support both modeling and control.The review compares SVR, GPR, LWPR, and EKF examples in Table IV.Source: D. Summary Statistical Method · p. 7, Table IV · p. 8

IV. NEURAL NETWORK

  • Neural-network choices include ELM and RBF, MLP and RNN, and task-specific AE or CNN architectures for image processing.The review associates MLP with generalization and RNN with sequence-related structure,.Source: §IV · p. 7

A. ELM and RBF

  • ELM fixes randomly assigned input weights and biases while training output weights; its constrained controller enforces positive actuation and real-actuation range.The constraints preserve actuation direction and impose an actuation-range limit; ELM has also been used for online pose estimation.Source: A. ELM and RBF · pp. 7–8
  • RBF replaces ELM's sigmoid activation with Gaussian functions, whose centers can be selected by clustering, but both methods use fixed parameters that limit their potential.RBF was used for forward kinematic modeling.Source: A. ELM and RBF · p. 8

B. MLP

MLP is a widely used neural network for soft-robot modeling and control, with actuation-to-state and state-to-actuation mappings. Its many adjustable components offer flexibility, but no single hyperparameter and structure combination is optimal for every task.

B. MLP

  • MLP maps actuation to robot state for modeling and maps desired and real robot states to estimated actuation for control.Its layered computation applies weights, biases, and activation functions.Source: B. MLP · p. 8
  • MLP designs vary in neuron counts, activation functions, optimizers, layer counts, and batch sizes, with no combination optimal across all tasks.Most tested choices can achieve acceptable performance on most tasks,,,.Source: B. MLP · p. 8
  • The influence of individual MLP hyperparameters on performance remains incompletely explored and explained.Source: B. MLP · p. 9
  • Other MLP variants directly condition hidden neurons, connect layers in a U-Net-like structure, or combine networks for simulation and sim-to-real transfer.The combined MLPs can collect simulated actions and estimate their corresponding robot states.Source: B. MLP · p. 9
  • Soft-robot MLP inputs can incorporate physical-model parameters or past end positions to address robot structure and time-delayed motion.Examples include concentric-tube variables, PCC curvature and length, and current and past end positions for control.Source: B. MLP · p. 9

C. RNN

RNNs process soft-robot data sequentially, using recurrent states to represent temporal relationships and delayed responses. The review describes several RNN variants and their uses in prediction and dynamic control.

C. RNN

  • RNNs use prior hidden states to infer sequential relationships, making them more suitable than MLPs and CNNs for soft robots’ delayed responses.Unlike MLPs, which take temporal data simultaneously, RNNs require data from multiple time steps.Source: C. RNN · p. 9
  • Modified Elman networks use context nodes to retain information from earlier steps, while NARX networks feed prior outputs into the current input.The review cites these variants in work on dynamic control.Source: C. RNN · p. 9
  • LSTMs address long-term dependence and have been used for force and position prediction, shape reconstruction, object recognition, and dynamic control.The cited control applications include reducing contact force and handling nonlinear behavior.Source: C. RNN · p. 9

D. Special NN

The review covers neural networks for visual and temporal data, then summarizes their breadth and resource demands. It also introduces reinforcement learning implementations using statistical or neural-network agents for control and manipulation tasks.

D. Special NN

  • Neural networks support image-based shape, joint-value, and orientation estimation; CNNs can also model dynamics from rearranged pressure inputs.The review also describes autoencoders for image-feature extraction and a GAN for synthetic data.Source: D. Special NN · p. 9

E. Summary Neural Network

  • NN applications have progressed from ELM and RBF to MLP, with RNNs for time-related data and autoencoders and CNNs for images.The review describes NNs as broadly applicable, but notes their large data requirements and difficulty of online updating.Source: E. Summary Neural Network · p. 9

V. REINFORCEMENT LEARNING

  • RL trains an agent for complicated tasks through exploration and rewards, but requires long learning times and massive amounts of data and cannot be used for modeling.The explored environment may be provided by modeling methods.Source: §V · p. 10

A. RL implementation

  • RL agents include statistical models and Q-learning, while neural-network agents have been used for reaching, trajectory following, gait design, obstacle avoidance, and endoscopy navigation.Q-learning selects actions from states using a policy; the review also describes statistical agents for shape estimation and robot control.Source: A. RL implementation · p. 10

B. RL in soft robots

Soft-robot RL uses discretization and simulation to manage broad state and action spaces and costly real-world exploration. The review characterizes RL as resource-intensive but capable of complex tasks.

B. RL in soft robots

  • Researchers discretize broad action and state spaces to simplify exploration and decrease training time, though this limits RL’s potential.Examples include six available actions and a workspace grid with 0.01 m resolution.Source: B. RL in soft robots · p. 10
  • Because real-world exploration is time-consuming and may damage robots, researchers train RL in simulators or modeled environments before testing or continuing learning in reality.The review describes physical models and trained neural networks as sources of simulation environments.Source: B. RL in soft robots · p. 10

C. Summary Reinforcement Learning

  • The review reports that RL strategies have enabled complicated soft-robot tasks and have also stimulated simulator development.Earlier statistical-model agents were later joined by neural-network agents; discretization is also widely used.Source: C. Summary Reinforcement Learning · p. 10
  • RL’s high data and interaction costs accompany its capacity for complex, high-level tasks; discretization and simulation transfer can reduce time and resource costs to some extent.RL requires a predefined agent and interaction with the environment.Source: C. Summary Reinforcement Learning · p. 10

VI. CONCLUSIONS AND DISCUSSIONS

The review surveys foundations and data-driven methods for soft-robot modeling and control, then compares their trade-offs and discusses future directions. It highlights unresolved constraints for medical applications, including safety, interpretability, and data requirements.

A. Summary

  • Physical models provide simulators, Jacobian matrices support robot description and control, statistical models and NNs support modeling or control, and RL addresses control and planning tasks.The review describes RL as exploiting an existing environment rather than generally providing a robot model.Source: A. Summary · p. 11

B. Advantages and Limitations

  • No approach is optimal for every task: sophisticated methods such as RL require more data and computation, while Jacobian methods suit limited simple tasks but offer high control frequency.Statistical methods occupy an intermediate position in data needs and control frequency, but some are local and lack generalization.Source: A. Summary · p. 11, B. Advantages and Limitations · p. 11
  • NN data collection takes time and may accelerate soft-robot aging, while slow training limits online use; RL demands time and computation and may require highly realistic simulators.Real-world exploration may damage robots, and some settings, such as the human body, cannot be explored.Source: B. Advantages and Limitations · p. 12

C. Emerging Directions

  • Future work may use larger, more complex NNs for challenging tasks, while balancing model complexity against control frequency and computation cost.The review also describes combining methods to address difficult problems such as model mismatch.Source: C. Emerging Directions · p. 12
  • Medical soft-robot control remains nascent in safety and data requirements; whole-shape control and contact avoidance remain challenging, and NN and RL lack interpretability for surgery.RL cannot explore in vivo and must be trained in simulation or physical simulators; the review calls for cooperation among researchers, doctors, and related departments.Source: C. Emerging Directions · p. 12
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