Exploring Modeling Techniques for Soft Arms: A Survey on Numerical, Analytical, and Data-Driven Approaches

Soft arms, characterized by their compliance and adaptability, have gained significant attention in applications ranging from industrial automation to biomedical fields. Modeling these systems presents unique challenges due to their high degrees of freedom, nonlinear behavior, and complex material properties. This review provides a comprehensive overview of three primary modeling approaches: numerical methods, analytical techniques, and data-driven models. Numerical methods, including finite element analysis and multi-body dynamics, offer precise but computationally expensive solutions for simulating soft arm behaviors. Analytical models, rooted in continuum mechanics and simplified assumptions, provide insights into the fundamental principles while balancing computational efficiency. Data-driven approaches, leveraging machine learning and artificial intelligence, open new avenues for adaptive and real-time modeling by bypassing explicit physical formulations. The strengths, limitations, and application scenarios of each approach are systematically analyzed, and future directions for integrating these methodologies are discussed. This review aims to guide researchers in selecting and developing effective modeling strategies for advancing the field of soft robotic arm design and control.

Adaptive Online Learning and Robust 3-D Shape Servoing of Continuum and Soft Robots in Unstructured Environments

In this article, we present a novel and generic data-driven method to servo-control the 3-D shape of continuum and soft robots based on proprioceptive sensing feedback. Developments of 3-D shape perception and control technologies are crucial for continuum and soft robots to perform tasks autonomously in surgical interventions. However, owing to the nonlinear properties of continuum robots, one main difficulty lies in the modeling of them, especially for soft robots with variable stiffness. To address this problem, we propose a versatile learning-based adaptive shape controller by leveraging proprioception of 3-D configuration from fiber Bragg grating (FBG) sensors, which can online estimate the unknown model of continuum robot against unexpected disturbances and exhibit an adaptive behavior to the unmodeled system without priori data exploration. Based on a new composite adaptation algorithm, the asymptotic convergences of the closed-loop system with learning parameters have been proven by Lyapunov theory. To validate the proposed method, we present a comprehensive experimental study using two continuum and soft robots both integrated with multicore FBGs, including a robotic-assisted colonoscope and multisection extensible soft manipulators. The results demonstrate the feasibility, adaptability, and superiority of our controller in various unstructured environments, as well as phantom experiments.

Soft robotics for farm to fork: applications in agriculture & farming

Agricultural tasks and environments range from harsh field conditions with semi-structured produce or animals, through to post-processing tasks in food-processing environments. From farm to fork, the development and application of soft robotics offers a plethora of potential uses. Robust yet compliant interactions between farm produce and machines will enable new capabilities and optimize existing processes. There is also an opportunity to explore how modeling tools used in soft robotics can be applied to improve our representation and understanding of the soft and compliant structures common in agriculture. In this review, we seek to highlight the potential for soft robotics technologies within the food system, and also the unique challenges that must be addressed when developing soft robotics systems for this problem domain. We conclude with an outlook on potential directions for meaningful and sustainable impact, and also how our outlook on both soft robotics and agriculture must evolve in order to achieve the required paradigm shift.

Kinetostatic Modeling of Soft Robots: Energy-Minimization Approach and 99-Line MATLAB Implementation

Soft robots have received a great deal of attention from both academia and industry due to their unprecedented adaptability in unstructured environment and extreme dexterity for complicated operations. Due to the strong coupling between the material nonlinearity due to hyperelasticity and the geometric nonlinearity due to large deflections, modeling of soft robots is highly dependent on commercial finite element software packages. An approach that is accurate and fast, and whose implementation is open to designers, is in great need. Considering that the constitutive relation of the hyperelastic materials is commonly expressed by its energy density function, we present an energy-based kinetostatic modeling approach in which the deflection of a soft robot is formulated as a minimization problem of its total potential energy. A fixed Hessian matrix of strain energy is proposed and adopted in the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which significantly improves its efficiency for solving the minimization problem of soft robots without sacrificing prediction accuracy. The simplicity of the approach leads to an implementation of MATLAB with only 99-line codes, which provides an easy-to-use tool for designers who are designing and optimizing the structures of soft robots. The efficiency of the proposed approach for predicting kinetostatic behaviors of soft robots is demonstrated by seven pneumatic-driven and cable-driven soft robots. The capability of the approach for capturing buckling behaviors in soft robots is also demonstrated. The energy-minimization approach, as well as the MATLAB implementation, could be easily tailored to fulfill various tasks, including design, optimization, and control of soft robots.

A Geometric Approach towards Inverse Kinematics of Soft Extensible Pneumatic Actuators Intended for Trajectory Tracking

Soft robots are interesting examples of hyper-redundancy in robotics. However, the nonlinear continuous dynamics of these robots and the use of hyper-elastic and visco-elastic materials make modeling these robots more complicated. This study presents a geometric inverse kinematics (IK) model for trajectory tracking of multi-segment extensible soft robots, where each segment of the soft actuator is geometrically approximated with a rigid links model to reduce the complexity. In this model, the links are connected with rotary and prismatic joints, which enable both the extension and rotation of the robot. Using optimization methods, the desired configuration variables of the soft actuator for the desired end-effector positions were obtained. Furthermore, the redundancy of the robot is applied for second task applications, such as tip angle control. The model's performance was investigated through kinematics and dynamics simulations and numerical benchmarks on multi-segment soft robots. The results showed lower computational costs and higher accuracy compared to most existing models. The method is easy to apply to multi-segment soft robots in both 2D and 3D, and it was experimentally validated on 3D-printed soft robotic manipulators. The results demonstrated the high accuracy in path following using this technique.

Modeling, Analysis, and Computational Design of Muscle-driven Soft Robots

Muscle driving is a critical actuation mode of soft or flexible robots and plays a key role in the motion of most animals. Although the system development of soft robots has been extensively investigated, the general kinematic modeling of soft bodies and the design methods used for muscle-driven soft robots (MDSRs) are inadequate. With a focus on homogeneous MDSRs, this article presents a framework for kinematic modeling and computational design. Based on continuum mechanics theory, the mechanical characteristics of soft bodies were first described using a deformation gradient tensor and energy density function. The discretized deformation was then depicted using a triangular meshing tool according to the piecewise linear hypothesis. Deformation models of MDSRs caused by external driving points or internal muscle units were established by the constitutive modeling of hyperelastic materials. The computational design of the MDSR was then addressed based on kinematic models and deformation analysis. Algorithms were proposed to infer the design parameters from the target deformation and to determine the optimal muscles. Several MDSRs were developed, and experiments were conducted to verify the effectiveness of the presented models and design algorithms. The computational and experimental results were compared and evaluated using a quantitative index. The presented framework of deformation modeling and computational design of MDSRs can facilitate the design of soft robots with complex deformations, such as humanoid faces.

Evaluation of Objective Functions for the Optimal Design of an Assistive Robot

The number of individuals with upper or lower extremities dysfunction (ULED) has considerably increased in the past few decades, resulting in a high economic burden for their families and society. Individuals with ULEDs require assistive robots to fulfill all their activities of daily living (ADLs). However, a theory for the optimal design of assistive robots that reduces energy consumption while increasing the workspace is unavailable. Thus, this research presents an algorithm for the optimal link length selection of an assistive robot mounted on a wheelchair to minimize the torque demands of each joint while increasing the workspace coverage. For this purpose, this research developed a workspace to satisfy a list of 18 ADLs. Then, three torque indices from the literature were considered as performance measures to minimize; the three torque measures are the quadratic average torque (QAT), the weighted root square mean (WRMS), and the absolute sum of torques (AST). The proposed algorithm evaluates any of the three torque measures within the workspace, given the robot dimensions. This proposed algorithm acts as an objective function, which is optimized using a genetic algorithm for each torque measure. The results show that all tree torque measures are suitable criteria for assistance robot optimization. However, each torque measures yield different optimal results; in the case of the QAT optimization, it produces the least workspace with the minimum overall torques of all the joints. Contrarily, the WRMS and AST optimization yield similar results generating the maximum workspace coverage but with a greater overall torque of all joints. Thus, the selection between the three methods depends on the designer's criteria. Based on the results, the presented methodology is a reliable tool for the optimal dimensioning of assistive robots.

Bayesian Optimization for Design of Multi-Actuator Soft Catheter Robots

Catheter-based diagnosis and therapy have grown increasingly in recent years due to their improved clinical outcomes including decreased morbidity, shorter recovery time and minimally invasiveness compared to open surgeries. Although the scalability, customizability, and diversity of soft catheter robots are widely recognized, designers and roboticists still lack comprehensive techniques for modeling and designing them. This difficulty arises due to their continuum nature, which makes characterizing the properties and predicting a soft catheter's behavior challenging, complicating robot design tasks. In this paper, we propose modeling multi-actuator soft catheters to enable alignment with desired vessel shapes near the target area. We develop mathematical models to simulate the catheter's positioning due to the moments exerted by multiple pneumatic actuators along the catheter and use those models to compare optimization approaches that can achieve catheter alignment along a desired vessel shape. Specifically, our approach proposes finding the optimal geometric and material properties for a multi-actuator soft catheter robot using a bi-level optimization framework. The upper-level optimization process uses a modified Bayesian technique to seek the optimal geometric and material properties of the soft catheter, which minimize the deviance of the actuated catheter from a desired vessel shape, while the lower-level optimization process uses a gradient-based technique to obtain the actuator moments required to achieve that vessel shape. The results demonstrate the capability of our proposed multi-actuator soft catheter to align with the desired vessel shapes, and show that the proposed framework which is in the context of Bayesian optimization has the potential to expedite the design process.

Fusing Dexterity and Perception for Soft Robot-Assisted Minimally Invasive Surgery: What We Learnt from STIFF-FLOP

In recent years we have seen tremendous progress in the development of robotic solutions for minimally invasive surgery (MIS). Indeed, a number of robot-assisted MIS systems have been developed to product level and are now well-established clinical tools; Intuitive Surgical’s very successful da Vinci Surgical System a prime example. The majority of these surgical systems are based on the traditional rigid-component robot design that was instrumental in the third industrial revolution—especially within the manufacturing sector. However, the use of this approach for surgical procedures on or around soft tissue has come under increasing criticism. The dangers of operating with a robot made from rigid components both near and within a patient are considerable. The EU project STIFF-FLOP, arguably the first large-scale research programme on soft robots for MIS, signalled the start of a concerted effort among researchers to investigate this area more comprehensively. While soft robots have many advantages over their rigid-component counterparts, among them high compliance and increased dexterity, they also bring their own specific challenges when interacting with the environment, such as the need to integrate sensors (which also need to be soft) that can determine the robot’s position and orientation (pose). In this study, the challenges of sensor integration are explored, while keeping the surgeon’s perspective at the forefront of ourdiscussion. The paper critically explores a range of methods, predominantly those developed during the EU project STIFF-FLOP, that facilitate the embedding of soft sensors into articulate soft robot structures using flexible, optics-based lightguides. We examine different optics-based approaches to pose perception in a minimally invasive surgery settings, and methods of integration are also discussed.

Learning Optimal Fin-Ray Finger Design for Soft Grasping

The development of soft hands is an important progress to empower robotic grasping with passive compliance while greatly decreasing the complexity of control. Despite the advances during the past decades, it is still not clear how to design optimal hands or fingers given the task requirements. In this paper, we propose a framework to learn the optimal design parameter for a fin-ray finger in order to achieve stable grasping. First, the pseudo-kinematics of the soft finger is learned in simulation. Second, the task constraints are encoded as a combination of desired grasping force and the empirical grasping quality function in terms of winding number. Finally, the effectiveness of the proposed approach is validated with experiments in simulation and using real-world examples as well.