Physical Model

Physical models are significant in soft robotics because they can illustrate the nature of soft robot motion and deformation. Also, they are fundamental to data-driven methods by providing simulation environments and data. Discretization methods like FEM have been applied for robot simulation. The Cosserat model and its discretization method, like geometric variable-strain (GVS), provide simulators specifically for soft robots. Piecewise constant curvature (PCC) can be seen as a special case of GVS and is widely applied to the soft robot simulation based on the assumption of deformation shape. Some specific models, like the pseudo-rigid model and the concentric tube model, are proposed for specific soft robots. Some typical physical models are shown in Fig. 4.

Fig. 4. Diagrams of (a) FEM, (b) PCC, (c) Cosserat rod model, and (d) concentric tube model. Small elements in (a) represent the soft robot deformation. The grey soft robot in (b) is represented by a series of constant curves, and the augmented rigid robots model the soft robot dynamically. The Cosserat rod model in (c) includes forces and moments inherently. The concentric tube model in (d) represents the robot with the configurations l_1,l_2,\theta_1, and \theta_2.

Table 2. Physical model paper comparison

Paper List:

FEM:

17GR: Runge G, Wiese M, Raatz A. FEM-based training of artificial neural networks for modular soft robots[C]//2017 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, 2017: 385-392.

FEM is applied in this paper for kinematic modeling and data generation for neural network training.

18CS: Schlagenhauf C, Bauer D, Chang K H, et al. Control of tendon-driven soft foam robot hands[C]//2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids). IEEE, 2018: 1-7.

FEM is applied in this paper as the exploring environment for RL.

12FF: Faure F, Duriez C, Delingette H, et al. Sofa: A multi-model framework for interactive physical simulation[J]. Soft tissue biomechanical modeling for computer assisted surgery, 2012: 283-321.

This paper introduces SOFA, a popular soft robot simulator based on FEM.

13CD: Duriez C. Control of elastic soft robots based on real-time finite element method[C]//2013 IEEE international conference on robotics and automation. IEEE, 2013: 3982-3987.

This work applies FEM in real-time robot control. To achieve online control, a compliance matrix is built to infer the relationship between forces and positions.

Cosserat rod model:

18MGb: Gazzola M, Dudte L H, McCormick A G, et al. Forward and inverse problems in the mechanics of soft filaments[J]. Royal Society open science, 2018, 5(6): 171628.

This paper solves forward and inverse problems in the mechanics of soft filaments with the Cosserat rod model and proposes the simulator PyElastica.

20FR: Renda F, Armanini C, Lebastard V, et al. A geometric variable-strain approach for static modeling of soft manipulators with tendon and fluidic actuation[J]. IEEE Robotics and Automation Letters, 2020, 5(3): 4006-4013.

This paper introduces the most general strain-based discretization method of the Cosserat rod model, GVS, which discretizes the continuous Cosserat rod model into a finite set of strain basis functions.

22AM: Mathew A T, Hmida I B, Armanini C, et al. A MATLAB toolbox for hybrid rigid soft robots based on the geometric variable strain approach[J]. IEEE Robotics & Automation Magazine, 2023, 30(3): 106-122.

Based on 20FR, this paper proposes a simulator SoRoSim in Matlab, which integrates GVS for soft, rigid, and hybrid robotic system simulation.

PCC

16IG: Godage I S, Medrano-Cerda G A, Branson D T, et al. Dynamics for variable length multisection continuum arms[J]. The International Journal of Robotics Research, 2016, 35(6): 695-722.

Compared with the original PCC, only a geometrical model, this paper introduces novel spatial dynamics and applies these to variable length multisection continuum arms with any number of sections.

21EM: Milana E, Stella F, Gorissen B, et al. Model-based control can improve the performance of artificial cilia[C]//2021 IEEE 4th International Conference on Soft Robotics (RoboSoft). IEEE, 2021: 527-530.

This paper employs PCC as the cilia model and implements a close-loop controller under variant drag forces due to the external fluid.

Specific

10PD: Dupont P E, Lock J, Itkowitz B, et al. Design and control of concentric-tube robots[J]. IEEE Transactions on Robotics, 2009, 26(2): 209-225.

Considering concentric tube robots, the authors leverage rotations and translations of tubes as actuation variables for the concentric tube robot model, as shown in Fig. 4-(d).

18CSb: Della Santina C, Katzschmann R K, Biechi A, et al. Dynamic control of soft robots interacting with the environment[C]//2018 IEEE International Conference on Soft Robotics (RoboSoft). IEEE, 2018: 46-53.

Based on PCC, rigid robots are leveraged to approximate the motion of soft robots.

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