Pseudo-rigid body networks: learning interpretable deformable object dynamics from partial observations

TL;DR

This work draws inspiration from the pseudo-rigid body method (PRB) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network.

Abstract

Accurately predicting deformable linear object (DLO) dynamics is challenging, especially when the task requires a model that is both human-interpretable and computationally efficient. In this work, we draw inspiration from the pseudo-rigid body method (PRB) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network. This dynamics network is trained jointly with a physics-informed encoder that maps observed motion variables to the DLO's hidden state. To encourage the state to acquire a physically meaningful representation, we leverage the forward kinematics of the PRB model as a decoder. We demonstrate in robot experiments that the proposed DLO dynamics model provides physically interpretable predictions from partial observations while being on par with black-box models regarding prediction accuracy. The project code is available at: http://tinyurl.com/prb-networks

Figures (10)

• Figure 1: A DLO -- an aluminium rod -- is actuated by a robot arm. Given an initial observation of $\{\mathrm{e}\}$'s translational state $y_k$ and $\{\mathrm{b}\}$'s position, velocity and acceleration vector $x_{k}$, a PRB-Net predicts $y_{k+1}$ while also estimating the DLO's hidden state $h_k$.
• Figure 2: Generalized coordinate representations of a body chain with $n_{\text{el}}=2$. The chain's joint states are described through rotation parameters $\Psi_i$ that provide two rotational DOF to each element.
• Figure 3: Architecture of PRB-Net with rollout length $N=2$. By resorting to the forward kinematics (FK) of a chain of PRBs and taking inspiration from hybrid dynamics to determine the inputs, the model learns a physically-plausible hidden state from partial observations.
• Figure 4: Errors arising in a rigid body chain approximation of a DLO with $n_{\text{el}}=2$ and fixed element length. Left: If the chain's first body is fixed to $\{b\}$ then errors $\epsilon_{\mathrm{el}}$ arise in the prediction of the DLO's end position $p_{\text{e}}$. Right: Upper bound on $\epsilon_{\mathrm{el}}$ for $L=1920\,\mathrm{mm}$ caused by fixing the first body to $\{b\}$ and setting its length to $L_{\mathrm{el}}/2$ plotted over different element counts $n_{\text{el}}$ and deflection angles $\zeta$.
• Figure 5: Aluminium rod DLO shape predicted by a PRB-Net with $n_{\text{el}}=7$. Top: $\alpha_q=0$. Bottom: $\alpha_q=1$.