Physics-Grounded Differentiable Simulation for Soft Growing Robots

TL;DR

The paper tackles the challenge of predicting and controlling soft-growing vine robots by introducing a physics-grounded differentiable simulator that runs batched rollouts. It integrates a nonlinear bending moment derived from a wrinkling criterion, linking wrinkling angle and bending angle through $M = \pi P R^3 \frac{\sin 2\gamma_0 + 2\pi - 2\gamma_0}{4[\sin\gamma_0 + (\pi - \gamma_0)\cos\gamma_0]}$ and $\gamma_0 = \cos^{-1}\left(2\frac{\epsilon_{crit}}{\sin(\theta/2)} - 1\right)$, within a maximal-coordinate, rippled-link model solved as a differentiable quadratic program. The system uses differentiable optimization (SCS via CVXPyLayers) to enforce feasibility under contact and supports gradient-based parameter fitting for local buckling and stiffness, enabling effective sim-to-real transfer on real robot data with an open-source implementation. The results show scalable CPU-based performance, accurate trajectory reproduction, and improved parameter fitting for the nonlinear stiffness model, making the simulator a practical tool for planning, control, and shape optimization of vine robots. Overall, the work provides a practical, end-to-end differentiable framework for high-fidelity vine-robot simulation, with direct implications for differentiable model-predictive control and robot design in constrained environments.

Abstract

Soft-growing robots (i.e., vine robots) are a promising class of soft robots that allow for navigation and growth in tightly confined environments. However, these robots remain challenging to model and control due to the complex interplay of the inflated structure and inextensible materials, which leads to obstacles for autonomous operation and design optimization. Although there exist simulators for these systems that have achieved qualitative and quantitative success in matching high-level behavior, they still often fail to capture realistic vine robot shapes using simplified parameter models and have difficulties in high-throughput simulation necessary for planning and parameter optimization. We propose a differentiable simulator for these systems, enabling the use of the simulator "in-the-loop" of gradient-based optimization approaches to address the issues listed above. With the more complex parameter fitting made possible by this approach, we experimentally validate and integrate a closed-form nonlinear stiffness model for thin-walled inflated tubes based on a first-principles approach to local material wrinkling. Our simulator also takes advantage of data-parallel operations by leveraging existing differentiable computation frameworks, allowing multiple simultaneous rollouts. We demonstrate the feasibility of using a physics-grounded nonlinear stiffness model within our simulator, and how it can be an effective tool in sim-to-real transfer. We provide our implementation open source.

Figures (7)

• Figure 1: Snapshots from a simultaneous rollout of 64 independent vine robots with randomly sampled launch angles in a cluttered environment. Each independent trial is uniquely colored. Although the rollouts are overlayed, they do not interact with each other in simulation. Our simulator is able to efficiently batch operations to compute the dynamics of multiple robots in parallel, as well as retrieve gradients through the simulation.
• Figure 2: (a):The geometry at the joint of an inflated beam with variables in the joint model. Section A-A further shows the division of the wrinkled and tensioned regions. (b): Variation of the moment at various values of $\epsilon_{crit}$, as compared with the fully wrinkled moment, $\pi PR^3$.
• Figure 3: (a): Experimentally measured bending moment of an inflated beam segment and the proposed model prediction. (a).1 shows the full range of bending angles (with the measured data down-sampled for legibility), and (a).2 shows a magnified view of the initial increase of the restoring moment in log scale. (b): Wrinkling criterion $\epsilon$ obtained for various pressures and fitted third-degree polynomial. (c): Experimental setup.
• Figure 4: Illustration of the virtual rigid body model of the vine robot. A series of frames parameterized by $(x, y, \theta)$, each with a collision sphere, are connected by pin joints a fixed distance $d_\text{segment}$ apart. The final link is the only exception: it grows with respect to the $g_\text{distal}$ function. Contact complementarity conditions enforce collisions with the environment.
• Figure 5: Performance of our simulator averaged over 5 rollouts with batches of randomly sampled launch angles. The environment used is shown in \ref{['fig:batchsim']}, which shows an example rollout with a batch size of 64 and 40 maximum virtual links. On the left, time per iteration of the simulator is given for different numbers of maximum virtual links and batch sizes. On the right, time per iteration divided by the batch size (i.e., how efficient is the parallelism) is given.