Sim-to-Real of Soft Robots with Learned Residual Physics

TL;DR

This work presents a residual physics method for modeling soft robots with large degrees of freedom and shows that residual physics need not be limited to low degrees of freedom but can effectively bridge the sim-to-real gap for high dimensional systems.

Abstract

Accurately modeling soft robots in simulation is computationally expensive and commonly falls short of representing the real world. This well-known discrepancy, known as the sim-to-real gap, can have several causes, such as coarsely approximated geometry and material models, manufacturing defects, viscoelasticity and plasticity, and hysteresis effects. Residual physics networks learn from real-world data to augment a discrepant model and bring it closer to reality. Here, we present a residual physics method for modeling soft robots with large degrees of freedom. We train neural networks to learn a residual term -- the modeling error between simulated and physical systems. Concretely, the residual term is a force applied on the whole simulated mesh, while real position data is collected with only sparse motion markers. The physical prior of the analytical simulation provides a starting point for the residual network, and the combined model is more informed than if physics were learned tabula rasa. We demonstrate our method on 1) a silicone elastomeric beam and 2) a soft pneumatic arm with hard-to-model, anisotropic fiber reinforcements. Our method outperforms traditional system identification up to 60%. We show that residual physics need not be limited to low degrees of freedom but can effectively bridge the sim-to-real gap for high dimensional systems.

Figures (8)

• Figure 1: Overview of the residual physics pipeline for high dimensional systems, demonstrated with a soft robotic arm. The learned residual force compensates for state-to-state prediction errors, such that sparse motion markers in simulation match those in reality.
• Figure 2: Pipeline of how the residual physics forces $\mathbf{f}_t^{\mathrm{res}}$ compensate the erroneous simulated next state $\mathbf{s}_{t+1}$ to match the real observed marker state $\overline{\mathbf{x}}_{t+1}$. Our state $\mathbf{s}_{t}$ is defined by position $\mathbf{q}_{t}$ and velocity $\mathbf{v}_{t}$, from which we extract the motion markers $\mathbf{x}_{t}$ on the simulated mesh. The residual forces are predicted by a neural network given state and external force $\mathbf{f}_t^{\mathrm{ext}}$ information (such as pressure actuation) as input. This network is trained on a labeled augmented dataset of residual forces $\mathbf{f}_t^{\mathrm{res}^*}$, collected through gradient-based optimization in our differentiable simulation.
• Figure 3: Sim-to-sim experiments include oscillating and twisting beams, where we either apply a weight at the tip or twist the beam and release this constraint to observe a desired motion trajectory. The sim-to-real experiments show the same passive oscillating beam and a pneumatic soft arm as an actuated robot.
• Figure 4: Box plot of displacement error in \ref{['eq:sim2sim error']}, varying the number of markers that are available for the residual forces in \ref{['eq:sim2real_op']}. The orange line is the median of 10 samples, and the box extends from the lower to the upper quartile of the samples.
• Figure 5: System identification performed with grid search.