Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots

TL;DR

KNODE-Cosserat is proposed, a framework that combines first-principle physics models and neural ordinary differential equations that significantly improves over the baseline models under different metrics and is validated in both simulation and real-world experiments.

Abstract

Soft robots have many advantages over rigid robots thanks to their compliant and passive nature. However, it is generally challenging to model the dynamics of soft robots due to their high spatial dimensionality, making it difficult to use model-based methods to accurately control soft robots. It often requires direct numerical simulation of partial differential equations to simulate soft robots. This not only requires an accurate numerical model, but also makes soft robot modeling slow and expensive. Deep learning algorithms have shown promises in data-driven modeling of soft robots. However, these algorithms usually require a large amount of data, which are difficult to obtain in either simulation or real-world experiments of soft robots. In this work, we propose KNODE-Cosserat, a framework that combines first-principle physics models and neural ordinary differential equations. We leverage the best from both worlds -- the generalization ability of physics-based models and the fast speed of deep learning methods. We validate our framework in both simulation and real-world experiments. In both cases, we show that the robot model significantly improves over the baseline models under different metrics.

Figures (10)

• Figure 1: Custom built open-source tendon-driven continuum robot. (a) CAD model of the robot. (b) Front view of the robot. (c) Isometric view with components annotations. (d) Close-up of the reel mechanism.
• Figure 2: Control inputs for simulation. (a) Sine Controls. The sine waves have period $1.5s$. Tensions 1–4 are positioned counterclockwise about the rod. (b) Step Controls. Tensions 1–4 are positioned counterclockwise about the rod.
• Figure 3: Baseline and KNODE trajectories in simulation using imperfect stiffness. (a) Trajectories from the imperfect model and the true model show different curvature under sine controls. (b) Trajectory generated using the KNODE model matches the true trajectory well.
• Figure 4: Example tip trajectories evaluated on sine controls in simulation. (a) The imperfect model has shorter length. (b) The imperfect model has stiffer centerbone.
• Figure 5: Example tip trajectories evaluated on step controls in simulation. (a) The imperfect model has shorter length. (b) The imperfect model has stiffer centerbone.