MAT-DiSMech: A Discrete Differential Geometry-based Computational Tool for Simulation of Rods, Shells, and Soft Robots (2504.17186v1)

Abstract: Accurate and efficient simulation tools are essential in robotics, enabling the visualization of system dynamics and the validation of control laws before committing resources to physical experimentation. Developing physically accurate simulation tools is particularly challenging in soft robotics, largely due to the prevalence of geometrically nonlinear deformation. A variety of robot simulators tackle this challenge by using simplified modeling techniques -- such as lumped mass models -- which lead to physical inaccuracies in real-world applications. On the other hand, high-fidelity simulation methods for soft structures, like finite element analysis, offer increased accuracy but lead to higher computational costs. In light of this, we present a Discrete Differential Geometry-based simulator that provides a balance between physical accuracy and computational speed. Building on an extensive body of research on rod and shell-based representations of soft robots, our tool provides a pathway to accurately model soft robots in a computationally tractable manner. Our open-source MATLAB-based framework is capable of simulating the deformations of rods, shells, and their combinations, primarily utilizing implicit integration techniques. The software design is modular for the user to customize the code, for example, add new external forces and impose custom boundary conditions. The implementations for prevalent forces encountered in robotics, including gravity, contact, kinetic and viscous friction, and aerodynamic drag, have been provided. We provide several illustrative examples that showcase the capabilities and validate the physical accuracy of the simulator. The open-source code is available at https://github.com/StructuresComp/dismech-matlab. We anticipate that the proposed simulator can serve as an effective digital twin tool, enhancing the Sim2Real pathway in soft robotics research.

• The paper introduces MAT-DiSMech, a MATLAB-based computational tool utilizing Discrete Differential Geometry for simulating rods, shells, and soft robots with complex deformations.
• MAT-DiSMech employs methods like Discrete Elastic Rods, hinge-based or mid-edge normal shell models, and an implicit integration scheme to handle nonlinear dynamics and contact efficiently.
• Numerical experiments validate MAT-DiSMech's capability to simulate realistic soft robot behaviors and predict multi-modal locomotion, demonstrating its accuracy and practical utility for research.

Overview of MAT-DiSMech: A Computational Tool for Soft Robotics Simulation

In the paper titled "MAT-DiSMech: A Discrete Differential Geometry-based Computational Tool for Simulation of Rods, Shells, and Soft Robots," the authors present a simulation framework aimed at addressing the modeling challenges in soft robotics. Traditional rigid-body simulators fall short in capturing the complex deformations that characterize soft robots, necessitating the development of specialized tools that can handle these nonlinear dynamics while maintaining computational efficiency.

Key Contributions and Methodology

The paper introduces MAT-DiSMech, a MATLAB-based simulator leveraging Discrete Differential Geometry (DDG) to model the complex behaviors of soft robotic systems composed of rods, shells, and their combinations. The simulator is designed to provide a balance between physical accuracy and computational speed.

• Rod and Shell Modeling: The simulator incorporates the Discrete Elastic Rod (DER) method and offers two alternatives for shell modeling—a hinge-based method and a mid-edge normal-based method. Each method is tailored to handle different types of nonlinear deformations inherent in soft robots.
• Implicit Integration Scheme: MAT-DiSMech employs the implicit Euler method to solve the equations of motion, facilitating the handling of stiff systems often encountered in contact-rich scenarios, thereby allowing for larger time steps compared to explicit methods.
• Self-contact and Friction: The simulator uses the Implicit Contact Model (IMC) to predict self-contact and friction forces, ensuring the non-penetration between interacting edges and modeling frictional behavior with sophistication.
• External Forces: The framework accommodates various external forces, including gravity, buoyancy, viscous friction, Coulomb friction, and aerodynamic drag, thus enhancing its utility for comprehensive soft robotic simulations.

Practical Validation and Applications

The authors present numerical experiments, including the simulation of soft robotic systems such as Pneumatic Network actuators, manta rays, and parachutes. The results demonstrate the simulator's capability to predict realistic deformations and multi-modal locomotion. Notably, the validation against theoretical cantilever beam deflections corroborates its accuracy in modeling elastic deformation, emphasizing its reliability.

Implications and Speculations

MAT-DiSMech exemplifies significant advancements in soft robotics simulation by offering an open-source, modular framework capable of modeling intricate interactions and behaviors of soft robots. The accessibility and versatility of MATLAB ensure that researchers can customize the simulator to meet specific application needs, potentially extending its functionality to incorporate machine learning for adaptive behavior modeling.

Future improvements could revolve around integrating real-time data-driven techniques to enhance modeling capabilities concerning material nonlinearity, nonlinear damping effects, and external environmental influences, thereby contributing to the evolving Sim2Real research pathway. By offering pedagogical value and research utility, MAT-DiSMech stands as a critical tool fostering innovation in soft robotics.