Simulating the Squish: A New Framework for Realistic Soft Robot Control

by

Author: Denis Avetisyan

Researchers have unveiled SORS, a highly accurate simulation environment designed to bridge the gap between virtual design and real-world performance for soft robotic systems.

This next-generation soft robot challenges established physics, necessitating a simulation framework capable of accommodating novel physical behaviors-a challenge addressed by a validated simulator that extends modeling capabilities across diverse soft robotic systems, from cantilever benchmarks and pneumatic arms to high-resolution, tendon-driven helicoid structures boasting 150,000 degrees of freedom.
This next-generation soft robot challenges established physics, necessitating a simulation framework capable of accommodating novel physical behaviors-a challenge addressed by a validated simulator that extends modeling capabilities across diverse soft robotic systems, from cantilever benchmarks and pneumatic arms to high-resolution, tendon-driven helicoid structures boasting 150,000 degrees of freedom.

SORS is a modular, energy-minimization-based simulator achieving millimeter-scale accuracy and enabling optimization of soft robot design and control.

Despite advances in robotic simulation, accurately modeling the large deformations and complex contact interactions inherent in soft robots remains a significant challenge. This work introduces SORS (Soft Over Rigid Simulator), a high-fidelity framework designed to address these complexities through an energy-based finite element approach. By integrating constrained nonlinear optimization and prioritizing modularity, SORS achieves millimeter-scale accuracy in sim-to-real validation and facilitates control optimization for soft robotic systems. Will this validated tool enable a new era of rapid prototyping and deployment for next-generation soft robots?

Deconstructing Rigidity: The Challenge of Soft Robotics Simulation

Conventional robotics simulations, designed for rigid bodies and predictable movements, face significant hurdles when applied to soft robotics. These systems, constructed from highly deformable materials like elastomers and gels, exhibit nonlinear behavior that traditional algorithms struggle to accurately represent. Unlike the precise calculations possible with rigid links, modeling the continuous deformations of soft robots requires capturing complex interactions between material properties, geometry, and external forces. This presents a computational challenge, as even simple movements necessitate resolving a vast number of degrees of freedom and accounting for intricate stress distributions within the soft structure. The result is often a trade-off between simulation speed and fidelity, hindering the ability to reliably design, test, and control these increasingly sophisticated machines.

Simulating soft robots demands computational methods that move beyond the simplified assumptions of traditional rigid-body dynamics. These systems, often constructed from highly compliant materials, exhibit nonlinear elasticity – meaning their response to force isn’t proportional, and past deformation influences future behavior. Crucially, accurate modeling also requires capturing complex contact interactions; unlike rigid robots with well-defined points of contact, soft robots experience continuous, distributed contact with their environment. This introduces challenges in determining forces and preventing unrealistic interpenetration of surfaces. Consequently, simulations must account for phenomena like self-collision, friction, and the nuanced interplay of stresses within the deformable material itself, often requiring computationally intensive techniques like finite element analysis or material point methods to faithfully represent the robot’s behavior.

Current simulation techniques for soft robots frequently encounter a trade-off between accuracy and efficiency. Many methods capable of realistically depicting the complex, nonlinear behavior of soft materials-such as finite element analysis-demand substantial computational resources, making iterative design cycles prohibitively slow. Conversely, simplified models, while faster, often sacrifice crucial details of material deformation and contact interactions, leading to discrepancies between simulation and physical reality. This lack of fidelity directly impacts the development of robust control algorithms, as controllers trained in inaccurate simulations may fail when deployed on actual robotic systems. The inability to reliably predict behavior, therefore, presents a significant bottleneck in the design, optimization, and practical implementation of soft robotic technologies.

The development of truly versatile soft robots demands a departure from conventional simulation techniques. Current methods, largely designed for rigid bodies, struggle to accurately represent the continuous deformations, intricate contact mechanics, and nonlinear material properties inherent in soft robotic systems. A novel simulation framework must prioritize computational efficiency without sacrificing realism, enabling researchers to rapidly prototype, analyze, and control these complex machines. Such a framework would ideally integrate advanced material models, robust collision detection algorithms, and potentially leverage techniques like machine learning to accelerate simulations and predict robot behavior in diverse environments. This targeted approach promises to unlock the full potential of soft robotics, paving the way for innovations in fields ranging from medical devices to search and rescue operations.

This simulation accurately reproduces contact-induced deformations and maintains shape fidelity in highly nonlinear materials, as demonstrated by comparing the end-effector, contact cylinder, and indentation area with real-world results.
This simulation accurately reproduces contact-induced deformations and maintains shape fidelity in highly nonlinear materials, as demonstrated by comparing the end-effector, contact cylinder, and indentation area with real-world results.

SORS: Modular Design for Emergent Behavior

The Soft Robot Simulation (SORS) framework is designed to model the behavior of soft robots through constrained energy minimization. This approach formulates the robot’s simulation as an optimization problem where the system seeks a configuration minimizing potential energy while satisfying defined constraints, such as fixed points or volume preservation. Modularity is achieved through a component-based architecture allowing users to define custom energy potentials representing material properties, external forces acting on the robot, and geometric constraints limiting its deformation. Extensibility is supported by a plugin system that facilitates the integration of new components without modifying the core framework, enabling researchers to easily experiment with diverse robot designs and control strategies. The resulting optimization problem is then solved numerically to determine the robot’s equilibrium configuration or dynamic response.

The SORS framework utilizes modular interfaces to define the physical characteristics and interactions of soft robotic systems. These interfaces allow users to specify energy potentials, representing internal forces like stiffness and stretching resistance, and external forces such as gravity or applied loads. Critically, system constraints – defining limits on movement or fixed points – are also implemented through these interfaces. This modularity enables the construction of complex models by combining individual energy terms, force vectors, and constraints without requiring code modification, promoting adaptability and simplifying the process of simulating diverse soft robot designs and behaviors. The system supports various constraint types, including fixed displacements, prescribed velocities, and contact interactions.

The SORS framework utilizes the Finite Element Method (FEM) to approximate the continuous physical properties of soft robots, transforming them into a discrete system amenable to numerical computation. This discretization process involves dividing the robot’s geometry into a mesh of smaller, interconnected elements – typically tetrahedra or hexahedra – each with defined material properties and nodal degrees of freedom. By representing the robot in this discrete form, SORS allows for the application of standard numerical techniques to solve for deformation, stress, and dynamic behavior. The size and complexity of the mesh directly influence computational cost and accuracy; however, FEM provides a scalable approach to modeling the complex, continuous deformations characteristic of soft robotics, enabling efficient simulation of large and intricate designs. The resulting system of equations, derived from energy minimization principles, is then solved using sparse linear algebra techniques optimized for performance.

Mass-Proportional Damping (MPD) is integrated into the SORS framework to enhance the fidelity of dynamic simulations of soft robots. MPD introduces damping forces proportional to the mass matrix and velocity, represented by the equation $F = -cM\dot{x}$, where $c$ is the damping coefficient, $M$ is the mass matrix, and $\dot{x}$ is the velocity vector. This approach provides stable and realistic energy dissipation, particularly crucial for accurately modeling the behavior of viscoelastic materials commonly used in soft robotics. Unlike simpler damping models, MPD accounts for the distribution of mass within the robot, leading to more accurate predictions of settling times, oscillations, and overall dynamic response.

Our simulator computes energy terms at the element level and evaluates external forces system-wide, allowing users to define custom geometry, physical laws, and parameters to model dynamic interactions.
Our simulator computes energy terms at the element level and evaluates external forces system-wide, allowing users to define custom geometry, physical laws, and parameters to model dynamic interactions.

Validating the Virtual: Empirical Correspondence in Simulation

SORS employs numerical integration schemes to solve the equations of motion over discrete time steps, enabling efficient simulation of dynamic systems. Both Backward Euler and Crank-Nicolson methods are implemented, offering differing trade-offs between computational cost and stability. Backward Euler, a first-order implicit method, is computationally inexpensive but may require smaller time steps for stability. Crank-Nicolson, a second-order implicit method, generally provides improved accuracy and stability for a given time step size, though it necessitates solving a system of equations at each time step. The selection of an appropriate scheme and time step size is crucial for balancing simulation speed with the desired level of accuracy in representing the system’s temporal behavior.

SORS prioritizes accurate contact modeling, and validation against the PokeFlex Dataset demonstrates millimeter-scale accuracy. Specifically, a Chamfer Distance of 6.9 mm was achieved when comparing simulated contact behavior to real-world data. This metric quantifies the average distance between points on the simulated and real contact surfaces; a value of 6.9 mm represents a strong geometric correspondence given the 160 mm cube edge length used in the dataset, indicating a less than 4.3% discrepancy relative to the characteristic dimension of the tested objects.

The Chamfer Distance metric quantifies the average distance between points on two point clouds, representing the simulated and real-world contact surfaces. It is calculated by finding the nearest point in the second point cloud for each point in the first, and averaging the distances to those nearest neighbors. This process is repeated in both directions to ensure symmetry and a robust comparison. Lower Chamfer Distance values indicate a higher degree of geometric similarity between the simulated and real-world contact behaviors, providing a quantifiable measure of simulation accuracy. The metric is sensitive to both position and density differences between the point clouds.

System Identification within the SORS framework utilizes real-world data to refine simulation parameters, resulting in millimeter-scale accuracy in replicating physical behavior. Specifically, applying these techniques to a cantilever beam yielded a System Identification Error of 4.98 mm, while a soft arm exhibited an error of 2.53 mm. These error values, measured as the discrepancy between simulated and experimentally obtained deformation, demonstrate the capacity of SORS to accurately model complex deformable bodies and validate simulation results against physical counterparts. The methodology allows for quantitative comparison and iterative refinement of material properties and boundary conditions.

System identification successfully matched the frequency, phase, and amplitude of a 210g load on a passive soft cantilever to real-world data.
System identification successfully matched the frequency, phase, and amplitude of a 210g load on a passive soft cantilever to real-world data.

Beyond Prediction: Towards Autonomous Design and Real-Time Control

Soft robotic systems rely heavily on effective actuation methods to achieve desired movements and interactions, and the simulation framework SORS is designed to accommodate a diverse range of these techniques. Currently, SORS fully supports both pneumatic actuation – utilizing compressed air to inflate chambers and create motion – and muscle actuation, which models the behavior of cable-driven systems mimicking biological muscles. This flexibility is critical, as different actuation methods excel in different applications; pneumatic systems offer speed and simplicity, while muscle actuation provides more nuanced control and force capabilities. By integrating these approaches, SORS allows researchers to explore and optimize soft robot designs for a wider array of tasks, from delicate manipulation to robust locomotion, paving the way for more versatile and adaptable robotic solutions.

The strength of the SORS framework lies in its adaptable design, which readily accommodates innovations in actuation and control methodologies. This modularity allows researchers to seamlessly incorporate novel physical models – representing everything from dielectric elastomers to cable-driven systems – without requiring substantial code restructuring. Beyond simply adding new actuators, the framework supports the implementation of advanced control strategies, such as model predictive control or reinforcement learning algorithms, enabling increasingly complex robotic behaviors. This flexible architecture not only accelerates the development of new soft robots but also fosters cross-pollination of ideas between different research groups, ultimately broadening the capabilities and applications of the field.

The Soft Robot Simulation (SORS) framework demonstrates a powerful capability for automated design refinement through Bayesian Optimization. This technique efficiently explores the vast parameter space of a robotic system – in one instance, a muscle-actuated leg – to identify configurations that maximize performance for a given task. By intelligently balancing exploration and exploitation, the optimization process converges on optimal settings without requiring exhaustive trial-and-error. Recent studies utilizing this approach have successfully tuned model parameters to achieve a jumping height of 0.463 m, showcasing the potential for SORS to autonomously design soft robots capable of complex locomotion and manipulation. This adaptive tuning not only improves performance but also reduces the need for manual calibration, accelerating the development cycle for increasingly sophisticated soft robotic systems.

Continued development of the simulation framework prioritizes a shift towards real-time capabilities, allowing for more responsive design iteration and potentially enabling direct control of physical robots. This involves algorithmic optimization and efficient code implementation to reduce computational demands without sacrificing accuracy. Simultaneously, researchers aim to broaden the scope of phenomena accurately modeled within the simulation, moving beyond basic actuation to incorporate more complex material behaviors, environmental interactions – such as fluid dynamics and contact mechanics – and sensor feedback. Expanding the simulated world in this manner promises to unlock new possibilities for soft robot design, allowing for the creation of machines capable of navigating and manipulating increasingly challenging and realistic environments, ultimately bridging the gap between virtual prototyping and physical realization.

System identification reveals the pneumatic soft arm's response to individual actuation of its six chambers at 60 kPa, demonstrating control over six quasistatic tip positions.
System identification reveals the pneumatic soft arm’s response to individual actuation of its six chambers at 60 kPa, demonstrating control over six quasistatic tip positions.

The pursuit of accurate simulation, as demonstrated by SORS, isn’t merely about replicating reality-it’s about dismantling its assumptions. This framework, with its millimeter-scale precision achieved through energy minimization and constrained optimization, is a testament to that. Ada Lovelace observed, “The Analytical Engine has no pretensions whatever to originate anything.” SORS doesn’t create soft robotic behaviors; it meticulously models the underlying physics, revealing the inherent possibilities within a system. The engine-or, in this case, the simulator-exposes the potential, allowing designers to then exploit and refine it. It’s a beautiful act of controlled deconstruction, a reverse-engineering of the physical world.

Pushing the Limits

The presentation of SORS isn’t merely a simulator; it’s a controlled demolition of the sim-to-real gap. Millimeter-scale accuracy is, of course, a moving target. The exploit of comprehension here lies not in achieving that precision, but in establishing a modular system capable of measuring the failures, identifying where the energy minimization breaks down, and then rebuilding the model with targeted corrections. The current framework, while robust, still relies on predefined materials and geometries. The next iteration must actively seek out the boundaries of those definitions-can SORS model material fatigue, or the subtle creep of polymers under sustained stress?

A true test will involve moving beyond static optimization. Soft robots are rarely asked to perform a single task perfectly. They must adapt, learn, and recover from unexpected contact. SORS, as it stands, is a powerful tool for designing resilience, but not for simulating improvisation. Extending the framework to incorporate real-time feedback, or even stochastic modeling of environmental interactions, represents a considerable challenge, but also the path towards genuinely intelligent soft systems.

Ultimately, the value of SORS isn’t in creating perfect simulations, but in systematically revealing the imperfections of the physical world. Each discrepancy between simulation and reality is a data point, a constraint on the universe, and a potential avenue for a more complete understanding of mechanics itself. The simulator, in effect, becomes a reverse-engineering tool, and the robot, merely a beautifully complex test case.

Original article: https://arxiv.org/pdf/2512.15994.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2025-12-19 11:04