Improving Out-of-Distribution Generalization of Learned Dynamics by Learning Pseudometrics and Constraint Manifolds

TL;DR

This work targets the robust generalization of learned robot dynamics to out-of-distribution states by discovering two structural priors: input-space sparsity and nonholonomic constraint manifolds. It jointly learns a sparsity-promoting distance metric $d_f$ via contrastive learning to reduce the dynamics input to a reduced set $x_{red}$, and a constraint manifold by approximating the normal space $N_x\mathcal{M}$ and training per-row GP models of the constraint in a reduced-input space, yielding a learned manifold $\hat{\mathcal{M}}$. During inference, predictions from a nominal GP dynamics model are projected onto $\hat{\mathcal{M}}$ by solving a quadratic program that enforces $\hat{G}(x)\dot{x} + \hat{g}(x) = 0$, thereby enforcing learned physical structure. Experiments on a differential-drive robot and a quadrotor show superior accuracy on OOD data compared with baselines, highlighting the practical impact of data-driven structure discovery for robust dynamics learning in robotics.

Abstract

We propose a method for improving the prediction accuracy of learned robot dynamics models on out-of-distribution (OOD) states. We achieve this by leveraging two key sources of structure often present in robot dynamics: 1) sparsity, i.e., some components of the state may not affect the dynamics, and 2) physical limits on the set of possible motions, in the form of nonholonomic constraints. Crucially, we do not assume this structure is known a priori, and instead learn it from data. We use contrastive learning to obtain a distance pseudometric that uncovers the sparsity pattern in the dynamics, and use it to reduce the input space when learning the dynamics. We then learn the unknown constraint manifold by approximating the normal space of possible motions from the data, which we use to train a Gaussian process (GP) representation of the constraint manifold. We evaluate our approach on a physical differential-drive robot and a simulated quadrotor, showing improved prediction accuracy on OOD data relative to baselines.

Figures (3)

• Figure 1: Left: Visualization of the constraint manifold $\mathcal{M} = \{x, \dot x \mid -\dot p_x \sin(\theta) + \dot p_y \cos(\theta) = 0\}$ satisfied by the unicycle \ref{['eqn:car']}. Right: The unicycle dynamics are sparse, i.e., the set of possible velocities (red dotted line) is the same for all $x$ with the same orientation. We learn the sparsity pattern and constraints (on a physical differential-drive robot), and project the predictions of our learned dynamics $\hat{f}(x,u)$ to be consistent with them.
• Figure 2: Example datasets (offline $\mathcal{D}_\textrm{off}$, one instance of noiseless online $\mathcal{D}_\textrm{on}$, and the associated test $\mathcal{D}_\textrm{test}$) used for training and evaluation for the unicycle \ref{['eqn:car']} (left) and quadrotor \ref{['eqn:quadrotor']} (right). The test data $\mathcal{D}_\textrm{test}$ is far from the training data $\mathcal{D}$, and can be considered OOD w.r.t. that data (this is confirmed by decreased prediction accuracy on these inputs; see Sec. \ref{['sec:results']}).
• Figure 3: Method. Dynamics learning: Given offline data $\mathcal{D}_\textrm{off}$, we learn a dynamics pseudometric $d_f$, which we use to reduce the input space dimension of the dynamics model $\hat{f}(x,u)$. We train $\hat{f}(x,u)$ on the input-reduced offline data. Constraint learning: We use approximate normal space data to learn a constraint distance pseudometric $d_\mathcal{M}$, which we use to reduce the constraint input space. We train the constraint $\mathcal{\hat{M}}$ using input-reduced offline and online data, paired with the normal space data. Evaluation: For prediction, we evaluate $\hat{f}(x,u)$ and project it onto $\mathcal{\hat{M}}$.