DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures (2311.18126v3)

Abstract: Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include flexible or soft structures, suffer significantly in one or more of these performance areas. To close this "sim2real" gap, we introduce DisMech, a simulation environment that models highly dynamic motions of rod-like soft continuum robots and structures, quickly and accurately, with arbitrary connections between them. Our methodology combines a fully implicit discrete differential geometry-based physics solver with fast and accurate contact handling, all in an intuitive software interface. Crucially, we propose a gradient descent approach to easily map the motions of hardware robot prototypes to control inputs in DisMech. We validate DisMech through several highly-nuanced soft robot simulations while demonstrating an order of magnitude speed increase over previous state of the art. Our real2sim validation shows high physical accuracy versus hardware, even with complicated soft actuation mechanisms such as shape memory alloy wires. With its low computational cost, physical accuracy, and ease of use, DisMech can accelerate translation of sim-based control for both soft robotics and deformable object manipulation.

• The paper introduces DisMech, a fully implicit DDG-based simulator that bridges the sim2real gap for soft continuum robots.
• It combines the Discrete Elastic Rod framework with advanced friction, contact handling, and natural curvature control to enable larger time steps.
• Validation against benchmarks shows up to three orders of magnitude improvement in simulation speed while maintaining high dynamic accuracy.

DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures

The paper "DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures" introduces a novel simulation environment, DisMech, aimed at addressing the prominent sim2real gap in the modeling of soft continuum robots and structures. The authors present a comprehensive approach combining discrete differential geometry (DDG) with implicit numerical integration schemes to advance the capabilities of soft robot simulations in both accuracy and computational efficiency.

Technical Summary

DisMech utilizes a fully implicit DDG-based physics solver, primarily built upon the Discrete Elastic Rods (DER) framework. This allows for modeling rod-like soft continuum robots with high physical realism. The simulator's architecture supports arbitrary connections between elements, facilitating the simulation of complex soft robotic assemblies and contact-rich environments.

Key technical contributions include:

1. Implicit Time-Stepping: The implicit formulation allows DisMech to handle larger time steps, providing significant computational speed improvements over explicit methods.
2. Friction and Contact Handling: Using the Implicit Contact Model (ICM), DisMech can simulate interactions involving friction and elastic contact, critical for realistic modeling of soft robots in cluttered environments.
3. Natural Curvature Control: By manipulating the natural curvature parameters of rod elements, the simulator can intuitively model the actuation of soft robots, simplifying control tasks in simulations.

Numerical Results and Validation

DisMech's performance was validated through several benchmark cases, comparing its results with analytical solutions and the state-of-the-art simulator Elastica:

• Dynamic Cantilever Beam: Simulations of a cantilever beam’s dynamic response showed excellent agreement with beam theory, achieving time step sizes up to three orders of magnitude larger than Elastica.
• Helical Rod Oscillations: DisMech accurately captured the oscillatory behavior of a suspended helical rod under gravity, maintaining comparable accuracy to Elastica but with substantially reduced computational costs.
• Frictional Interaction: Kinetic energy computations during axial friction tests demonstrated DisMech's ability to model contact and friction accurately, adhering closely to theoretical predictions.

Practical Implications

DisMech's capabilities extend beyond simple validation cases to more complex soft robotic systems. Demonstrations highlighted include:

• Spider-like Robot: A soft robotic spider assembled using DisMech's API showcased the easy integration of multiple rod elements and the simulator’s ability to handle environmental interactions.
• Active Entanglement Gripper: The simulation of an entanglement-based gripping mechanism underscored the robustness of DisMech in modeling highly complex and frictional interactions.
• Real2Sim Open-Loop Control: A proposed gradient descent method for mapping real-world soft robot configurations to DisMech’s control inputs enabled accurate real2sim realization for a shape memory alloy (SMA) actuated soft manipulator, achieving minimal tip position errors.

Implications and Future Directions

The introduction of DisMech signals a substantial advancement in the domain of soft robotics simulation, primarily through improved computational efficiency and accuracy. The simulator's ability to handle highly nuanced interactions and its low computational cost render it a promising tool for accelerating the development and control of soft robots.

Theoretical implications suggest a paradigm shift towards using fully implicit DDG-based formulations for simulating continuum mechanics in robotics. This shift may catalyze further research into more complex soft robotic systems and their interactions within dynamic and contact-rich environments.

Future developments could see the integration of shell structures into DisMech, expanding its versatility. Additionally, incorporating shearing deformations will be critical for a more exhaustive simulation of soft materials, aligning DisMech with other Cosserat rod-based frameworks. Furthermore, the development of robust real2sim2real pipelines leveraging DisMech for reinforcement learning tasks represents a promising trajectory for future research. This could fundamentally enhance control strategies for both soft robots and deformable object manipulation.

In conclusion, DisMech, with its strong numerical results and innovative approach, stands as a pivotal advancement in the simulation and control of soft robotic systems, providing a robust foundation for future research and development.